xref: /petsc/src/ts/utils/dmplexlandau/plexland.c (revision 1d27aa22b2f6148b2c4e3f06a75e0638d6493e09)

#include <../src/mat/impls/aij/seq/aij.h>
#include <petsc/private/dmpleximpl.h> /*I "petscdmplex.h" I*/
#include <petsclandau.h>              /*I "petsclandau.h"   I*/
#include <petscts.h>
#include <petscdmforest.h>
#include <petscdmcomposite.h>

/* Landau collision operator */

/* relativistic terms */
#if defined(PETSC_USE_REAL_SINGLE)
  #define SPEED_OF_LIGHT 2.99792458e8F
  #define C_0(v0)        (SPEED_OF_LIGHT / v0) /* needed for relativistic tensor on all architectures */
#else
  #define SPEED_OF_LIGHT 2.99792458e8
  #define C_0(v0)        (SPEED_OF_LIGHT / v0) /* needed for relativistic tensor on all architectures */
#endif

#include "land_tensors.h"

#if defined(PETSC_HAVE_OPENMP)
  #include <omp.h>
#endif

static PetscErrorCode LandauGPUMapsDestroy(void *ptr)
{
  P4estVertexMaps *maps = (P4estVertexMaps *)ptr;
  PetscFunctionBegin;
  // free device data
  if (maps[0].deviceType != LANDAU_CPU) {
#if defined(PETSC_HAVE_KOKKOS)
    if (maps[0].deviceType == LANDAU_KOKKOS) {
      PetscCall(LandauKokkosDestroyMatMaps(maps, maps[0].numgrids)); // implies Kokkos does
    }
#endif
  }
  // free host data
  for (PetscInt grid = 0; grid < maps[0].numgrids; grid++) {
    PetscCall(PetscFree(maps[grid].c_maps));
    PetscCall(PetscFree(maps[grid].gIdx));
  }
  PetscCall(PetscFree(maps));

  PetscFunctionReturn(PETSC_SUCCESS);
}
static PetscErrorCode energy_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
{
  PetscReal v2 = 0;
  PetscFunctionBegin;
  /* compute v^2 / 2 */
  for (int i = 0; i < dim; ++i) v2 += x[i] * x[i];
  /* evaluate the Maxwellian */
  u[0] = v2 / 2;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* needs double */
static PetscErrorCode gamma_m1_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
{
  PetscReal *c2_0_arr = ((PetscReal *)actx);
  double     u2 = 0, c02 = (double)*c2_0_arr, xx;

  PetscFunctionBegin;
  /* compute u^2 / 2 */
  for (int i = 0; i < dim; ++i) u2 += x[i] * x[i];
  /* gamma - 1 = g_eps, for conditioning and we only take derivatives */
  xx = u2 / c02;
#if defined(PETSC_USE_DEBUG)
  u[0] = PetscSqrtReal(1. + xx);
#else
  u[0] = xx / (PetscSqrtReal(1. + xx) + 1.) - 1.; // better conditioned. -1 might help condition and only used for derivative
#endif
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
 LandauFormJacobian_Internal - Evaluates Jacobian matrix.

 Input Parameters:
 .  globX - input vector
 .  actx - optional user-defined context
 .  dim - dimension

 Output Parameter:
 .  J0acP - Jacobian matrix filled, not created
 */
static PetscErrorCode LandauFormJacobian_Internal(Vec a_X, Mat JacP, const PetscInt dim, PetscReal shift, void *a_ctx)
{
  LandauCtx         *ctx = (LandauCtx *)a_ctx;
  PetscInt           numCells[LANDAU_MAX_GRIDS], Nq, Nb;
  PetscQuadrature    quad;
  PetscReal          Eq_m[LANDAU_MAX_SPECIES]; // could be static data w/o quench (ex2)
  PetscScalar       *cellClosure = NULL;
  const PetscScalar *xdata       = NULL;
  PetscDS            prob;
  PetscContainer     container;
  P4estVertexMaps   *maps;
  Mat                subJ[LANDAU_MAX_GRIDS * LANDAU_MAX_BATCH_SZ];

  PetscFunctionBegin;
  PetscValidHeaderSpecific(a_X, VEC_CLASSID, 1);
  PetscValidHeaderSpecific(JacP, MAT_CLASSID, 2);
  PetscAssertPointer(ctx, 5);
  /* check for matrix container for GPU assembly. Support CPU assembly for debugging */
  PetscCheck(ctx->plex[0] != NULL, ctx->comm, PETSC_ERR_ARG_WRONG, "Plex not created");
  PetscCall(PetscLogEventBegin(ctx->events[10], 0, 0, 0, 0));
  PetscCall(DMGetDS(ctx->plex[0], &prob)); // same DS for all grids
  PetscCall(PetscObjectQuery((PetscObject)JacP, "assembly_maps", (PetscObject *)&container));
  if (container) {
    PetscCheck(ctx->gpu_assembly, ctx->comm, PETSC_ERR_ARG_WRONG, "maps but no GPU assembly");
    PetscCall(PetscContainerGetPointer(container, (void **)&maps));
    PetscCheck(maps, ctx->comm, PETSC_ERR_ARG_WRONG, "empty GPU matrix container");
    for (PetscInt i = 0; i < ctx->num_grids * ctx->batch_sz; i++) subJ[i] = NULL;
  } else {
    PetscCheck(!ctx->gpu_assembly, ctx->comm, PETSC_ERR_ARG_WRONG, "No maps but GPU assembly");
    for (PetscInt tid = 0; tid < ctx->batch_sz; tid++) {
      for (PetscInt grid = 0; grid < ctx->num_grids; grid++) PetscCall(DMCreateMatrix(ctx->plex[grid], &subJ[LAND_PACK_IDX(tid, grid)]));
    }
    maps = NULL;
  }
  // get dynamic data (Eq is odd, for quench and Spitzer test) for CPU assembly and raw data for Jacobian GPU assembly. Get host numCells[], Nq (yuck)
  PetscCall(PetscFEGetQuadrature(ctx->fe[0], &quad));
  PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL));
  PetscCall(PetscFEGetDimension(ctx->fe[0], &Nb));
  PetscCheck(Nq <= LANDAU_MAX_NQND, ctx->comm, PETSC_ERR_ARG_WRONG, "Order too high. Nq = %" PetscInt_FMT " > LANDAU_MAX_NQND (%d)", Nq, LANDAU_MAX_NQND);
  PetscCheck(Nb <= LANDAU_MAX_NQND, ctx->comm, PETSC_ERR_ARG_WRONG, "Order too high. Nb = %" PetscInt_FMT " > LANDAU_MAX_NQND (%d)", Nb, LANDAU_MAX_NQND);
  // get metadata for collecting dynamic data
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
    PetscInt cStart, cEnd;
    PetscCheck(ctx->plex[grid] != NULL, ctx->comm, PETSC_ERR_ARG_WRONG, "Plex not created");
    PetscCall(DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd));
    numCells[grid] = cEnd - cStart; // grids can have different topology
  }
  PetscCall(PetscLogEventEnd(ctx->events[10], 0, 0, 0, 0));
  if (shift == 0) { /* create dynamic point data: f_alpha for closure of each cell (cellClosure[nbatch,ngrids,ncells[g],f[Nb,ns[g]]]) or xdata */
    DM pack;
    PetscCall(VecGetDM(a_X, &pack));
    PetscCheck(pack, PETSC_COMM_SELF, PETSC_ERR_PLIB, "pack has no DM");
    PetscCall(PetscLogEventBegin(ctx->events[1], 0, 0, 0, 0));
    for (PetscInt fieldA = 0; fieldA < ctx->num_species; fieldA++) {
      Eq_m[fieldA] = ctx->Ez * ctx->t_0 * ctx->charges[fieldA] / (ctx->v_0 * ctx->masses[fieldA]); /* normalize dimensionless */
      if (dim == 2) Eq_m[fieldA] *= 2 * PETSC_PI;                                                  /* add the 2pi term that is not in Landau */
    }
    if (!ctx->gpu_assembly) {
      Vec         *locXArray, *globXArray;
      PetscScalar *cellClosure_it;
      PetscInt     cellClosure_sz = 0, nDMs, Nf[LANDAU_MAX_GRIDS];
      PetscSection section[LANDAU_MAX_GRIDS], globsection[LANDAU_MAX_GRIDS];
      for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
        PetscCall(DMGetLocalSection(ctx->plex[grid], &section[grid]));
        PetscCall(DMGetGlobalSection(ctx->plex[grid], &globsection[grid]));
        PetscCall(PetscSectionGetNumFields(section[grid], &Nf[grid]));
      }
      /* count cellClosure size */
      PetscCall(DMCompositeGetNumberDM(pack, &nDMs));
      for (PetscInt grid = 0; grid < ctx->num_grids; grid++) cellClosure_sz += Nb * Nf[grid] * numCells[grid];
      PetscCall(PetscMalloc1(cellClosure_sz * ctx->batch_sz, &cellClosure));
      cellClosure_it = cellClosure;
      PetscCall(PetscMalloc(sizeof(*locXArray) * nDMs, &locXArray));
      PetscCall(PetscMalloc(sizeof(*globXArray) * nDMs, &globXArray));
      PetscCall(DMCompositeGetLocalAccessArray(pack, a_X, nDMs, NULL, locXArray));
      PetscCall(DMCompositeGetAccessArray(pack, a_X, nDMs, NULL, globXArray));
      for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) { // OpenMP (once)
        for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
          Vec      locX = locXArray[LAND_PACK_IDX(b_id, grid)], globX = globXArray[LAND_PACK_IDX(b_id, grid)], locX2;
          PetscInt cStart, cEnd, ei;
          PetscCall(VecDuplicate(locX, &locX2));
          PetscCall(DMGlobalToLocalBegin(ctx->plex[grid], globX, INSERT_VALUES, locX2));
          PetscCall(DMGlobalToLocalEnd(ctx->plex[grid], globX, INSERT_VALUES, locX2));
          PetscCall(DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd));
          for (ei = cStart; ei < cEnd; ++ei) {
            PetscScalar *coef = NULL;
            PetscCall(DMPlexVecGetClosure(ctx->plex[grid], section[grid], locX2, ei, NULL, &coef));
            PetscCall(PetscMemcpy(cellClosure_it, coef, Nb * Nf[grid] * sizeof(*cellClosure_it))); /* change if LandauIPReal != PetscScalar */
            PetscCall(DMPlexVecRestoreClosure(ctx->plex[grid], section[grid], locX2, ei, NULL, &coef));
            cellClosure_it += Nb * Nf[grid];
          }
          PetscCall(VecDestroy(&locX2));
        }
      }
      PetscCheck(cellClosure_it - cellClosure == cellClosure_sz * ctx->batch_sz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "iteration wrong %" PetscCount_FMT " != cellClosure_sz = %" PetscInt_FMT, (PetscCount)(cellClosure_it - cellClosure),
                 cellClosure_sz * ctx->batch_sz);
      PetscCall(DMCompositeRestoreLocalAccessArray(pack, a_X, nDMs, NULL, locXArray));
      PetscCall(DMCompositeRestoreAccessArray(pack, a_X, nDMs, NULL, globXArray));
      PetscCall(PetscFree(locXArray));
      PetscCall(PetscFree(globXArray));
      xdata = NULL;
    } else {
      PetscMemType mtype;
      if (ctx->jacobian_field_major_order) { // get data in batch ordering
        PetscCall(VecScatterBegin(ctx->plex_batch, a_X, ctx->work_vec, INSERT_VALUES, SCATTER_FORWARD));
        PetscCall(VecScatterEnd(ctx->plex_batch, a_X, ctx->work_vec, INSERT_VALUES, SCATTER_FORWARD));
        PetscCall(VecGetArrayReadAndMemType(ctx->work_vec, &xdata, &mtype));
      } else {
        PetscCall(VecGetArrayReadAndMemType(a_X, &xdata, &mtype));
      }
      PetscCheck(mtype == PETSC_MEMTYPE_HOST || ctx->deviceType != LANDAU_CPU, ctx->comm, PETSC_ERR_ARG_WRONG, "CPU run with device data: use -mat_type aij");
      cellClosure = NULL;
    }
    PetscCall(PetscLogEventEnd(ctx->events[1], 0, 0, 0, 0));
  } else xdata = cellClosure = NULL;

  /* do it */
  if (ctx->deviceType == LANDAU_KOKKOS) {
#if defined(PETSC_HAVE_KOKKOS)
    PetscCall(LandauKokkosJacobian(ctx->plex, Nq, Nb, ctx->batch_sz, ctx->num_grids, numCells, Eq_m, cellClosure, xdata, &ctx->SData_d, shift, ctx->events, ctx->mat_offset, ctx->species_offset, subJ, JacP));
#else
    SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONG, "-landau_device_type %s not built", "kokkos");
#endif
  } else {               /* CPU version */
    PetscTabulation *Tf; // used for CPU and print info. Same on all grids and all species
    PetscInt         ip_offset[LANDAU_MAX_GRIDS + 1], ipf_offset[LANDAU_MAX_GRIDS + 1], elem_offset[LANDAU_MAX_GRIDS + 1], IPf_sz_glb, IPf_sz_tot, num_grids = ctx->num_grids, Nf[LANDAU_MAX_GRIDS];
    PetscReal       *ff, *dudx, *dudy, *dudz, *invJ_a = (PetscReal *)ctx->SData_d.invJ, *xx = (PetscReal *)ctx->SData_d.x, *yy = (PetscReal *)ctx->SData_d.y, *zz = (PetscReal *)ctx->SData_d.z, *ww = (PetscReal *)ctx->SData_d.w;
    PetscReal       *nu_alpha = (PetscReal *)ctx->SData_d.alpha, *nu_beta = (PetscReal *)ctx->SData_d.beta, *invMass = (PetscReal *)ctx->SData_d.invMass;
    PetscReal(*lambdas)[LANDAU_MAX_GRIDS][LANDAU_MAX_GRIDS] = (PetscReal(*)[LANDAU_MAX_GRIDS][LANDAU_MAX_GRIDS])ctx->SData_d.lambdas;
    PetscSection section[LANDAU_MAX_GRIDS], globsection[LANDAU_MAX_GRIDS];
    PetscScalar *coo_vals = NULL;
    for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
      PetscCall(DMGetLocalSection(ctx->plex[grid], &section[grid]));
      PetscCall(DMGetGlobalSection(ctx->plex[grid], &globsection[grid]));
      PetscCall(PetscSectionGetNumFields(section[grid], &Nf[grid]));
    }
    /* count IPf size, etc */
    PetscCall(PetscDSGetTabulation(prob, &Tf)); // Bf, &Df same for all grids
    const PetscReal *const BB = Tf[0]->T[0], *const DD = Tf[0]->T[1];
    ip_offset[0] = ipf_offset[0] = elem_offset[0] = 0;
    for (PetscInt grid = 0; grid < num_grids; grid++) {
      PetscInt nfloc        = ctx->species_offset[grid + 1] - ctx->species_offset[grid];
      elem_offset[grid + 1] = elem_offset[grid] + numCells[grid];
      ip_offset[grid + 1]   = ip_offset[grid] + numCells[grid] * Nq;
      ipf_offset[grid + 1]  = ipf_offset[grid] + Nq * nfloc * numCells[grid];
    }
    IPf_sz_glb = ipf_offset[num_grids];
    IPf_sz_tot = IPf_sz_glb * ctx->batch_sz;
    // prep COO
    {
      PetscCall(PetscMalloc1(ctx->SData_d.coo_size, &coo_vals)); // allocate every time?
      PetscCall(PetscInfo(ctx->plex[0], "COO Allocate %" PetscInt_FMT " values\n", (PetscInt)ctx->SData_d.coo_size));
    }
    if (shift == 0.0) { /* compute dynamic data f and df and init data for Jacobian */
#if defined(PETSC_HAVE_THREADSAFETY)
      double starttime, endtime;
      starttime = MPI_Wtime();
#endif
      PetscCall(PetscLogEventBegin(ctx->events[8], 0, 0, 0, 0));
      PetscCall(PetscMalloc4(IPf_sz_tot, &ff, IPf_sz_tot, &dudx, IPf_sz_tot, &dudy, dim == 3 ? IPf_sz_tot : 0, &dudz));
      // F df/dx
      for (PetscInt tid = 0; tid < ctx->batch_sz * elem_offset[num_grids]; tid++) {                        // for each element
        const PetscInt b_Nelem = elem_offset[num_grids], b_elem_idx = tid % b_Nelem, b_id = tid / b_Nelem; // b_id == OMP thd_id in batch
        // find my grid:
        PetscInt grid = 0;
        while (b_elem_idx >= elem_offset[grid + 1]) grid++; // yuck search for grid
        {
          const PetscInt loc_nip = numCells[grid] * Nq, loc_Nf = ctx->species_offset[grid + 1] - ctx->species_offset[grid], loc_elem = b_elem_idx - elem_offset[grid];
          const PetscInt moffset = LAND_MOFFSET(b_id, grid, ctx->batch_sz, ctx->num_grids, ctx->mat_offset); //b_id*b_N + ctx->mat_offset[grid];
          PetscScalar   *coef, coef_buff[LANDAU_MAX_SPECIES * LANDAU_MAX_NQND];
          PetscReal     *invJe = &invJ_a[(ip_offset[grid] + loc_elem * Nq) * dim * dim]; // ingJ is static data on batch 0
          PetscInt       b, f, q;
          if (cellClosure) {
            coef = &cellClosure[b_id * IPf_sz_glb + ipf_offset[grid] + loc_elem * Nb * loc_Nf]; // this is const
          } else {
            coef = coef_buff;
            for (f = 0; f < loc_Nf; ++f) {
              LandauIdx *const Idxs = &maps[grid].gIdx[loc_elem][f][0];
              for (b = 0; b < Nb; ++b) {
                PetscInt idx = Idxs[b];
                if (idx >= 0) {
                  coef[f * Nb + b] = xdata[idx + moffset];
                } else {
                  idx              = -idx - 1;
                  coef[f * Nb + b] = 0;
                  for (q = 0; q < maps[grid].num_face; q++) {
                    PetscInt    id    = maps[grid].c_maps[idx][q].gid;
                    PetscScalar scale = maps[grid].c_maps[idx][q].scale;
                    coef[f * Nb + b] += scale * xdata[id + moffset];
                  }
                }
              }
            }
          }
          /* get f and df */
          for (PetscInt qi = 0; qi < Nq; qi++) {
            const PetscReal *invJ = &invJe[qi * dim * dim];
            const PetscReal *Bq   = &BB[qi * Nb];
            const PetscReal *Dq   = &DD[qi * Nb * dim];
            PetscReal        u_x[LANDAU_DIM];
            /* get f & df */
            for (f = 0; f < loc_Nf; ++f) {
              const PetscInt idx = b_id * IPf_sz_glb + ipf_offset[grid] + f * loc_nip + loc_elem * Nq + qi;
              PetscInt       b, e;
              PetscReal      refSpaceDer[LANDAU_DIM];
              ff[idx] = 0.0;
              for (int d = 0; d < LANDAU_DIM; ++d) refSpaceDer[d] = 0.0;
              for (b = 0; b < Nb; ++b) {
                const PetscInt cidx = b;
                ff[idx] += Bq[cidx] * PetscRealPart(coef[f * Nb + cidx]);
                for (int d = 0; d < dim; ++d) refSpaceDer[d] += Dq[cidx * dim + d] * PetscRealPart(coef[f * Nb + cidx]);
              }
              for (int d = 0; d < LANDAU_DIM; ++d) {
                for (e = 0, u_x[d] = 0.0; e < LANDAU_DIM; ++e) u_x[d] += invJ[e * dim + d] * refSpaceDer[e];
              }
              dudx[idx] = u_x[0];
              dudy[idx] = u_x[1];
#if LANDAU_DIM == 3
              dudz[idx] = u_x[2];
#endif
            }
          } // q
        }   // grid
      }     // grid*batch
      PetscCall(PetscLogEventEnd(ctx->events[8], 0, 0, 0, 0));
#if defined(PETSC_HAVE_THREADSAFETY)
      endtime = MPI_Wtime();
      if (ctx->stage) ctx->times[LANDAU_F_DF] += (endtime - starttime);
#endif
    } // Jacobian setup
    // assemble Jacobian (or mass)
    for (PetscInt tid = 0; tid < ctx->batch_sz * elem_offset[num_grids]; tid++) { // for each element
      const PetscInt b_Nelem      = elem_offset[num_grids];
      const PetscInt glb_elem_idx = tid % b_Nelem, b_id = tid / b_Nelem;
      PetscInt       grid = 0;
#if defined(PETSC_HAVE_THREADSAFETY)
      double starttime, endtime;
      starttime = MPI_Wtime();
#endif
      while (glb_elem_idx >= elem_offset[grid + 1]) grid++;
      {
        const PetscInt   loc_Nf = ctx->species_offset[grid + 1] - ctx->species_offset[grid], loc_elem = glb_elem_idx - elem_offset[grid];
        const PetscInt   moffset = LAND_MOFFSET(b_id, grid, ctx->batch_sz, ctx->num_grids, ctx->mat_offset), totDim = loc_Nf * Nq, elemMatSize = totDim * totDim;
        PetscScalar     *elemMat;
        const PetscReal *invJe = &invJ_a[(ip_offset[grid] + loc_elem * Nq) * dim * dim];
        PetscCall(PetscMalloc1(elemMatSize, &elemMat));
        PetscCall(PetscMemzero(elemMat, elemMatSize * sizeof(*elemMat)));
        if (shift == 0.0) { // Jacobian
          PetscCall(PetscLogEventBegin(ctx->events[4], 0, 0, 0, 0));
        } else { // mass
          PetscCall(PetscLogEventBegin(ctx->events[16], 0, 0, 0, 0));
        }
        for (PetscInt qj = 0; qj < Nq; ++qj) {
          const PetscInt jpidx_glb = ip_offset[grid] + qj + loc_elem * Nq;
          PetscReal      g0[LANDAU_MAX_SPECIES], g2[LANDAU_MAX_SPECIES][LANDAU_DIM], g3[LANDAU_MAX_SPECIES][LANDAU_DIM][LANDAU_DIM]; // could make a LANDAU_MAX_SPECIES_GRID ~ number of ions - 1
          PetscInt       d, d2, dp, d3, IPf_idx;
          if (shift == 0.0) { // Jacobian
            const PetscReal *const invJj = &invJe[qj * dim * dim];
            PetscReal              gg2[LANDAU_MAX_SPECIES][LANDAU_DIM], gg3[LANDAU_MAX_SPECIES][LANDAU_DIM][LANDAU_DIM], gg2_temp[LANDAU_DIM], gg3_temp[LANDAU_DIM][LANDAU_DIM];
            const PetscReal        vj[3] = {xx[jpidx_glb], yy[jpidx_glb], zz ? zz[jpidx_glb] : 0}, wj = ww[jpidx_glb];
            // create g2 & g3
            for (d = 0; d < LANDAU_DIM; d++) { // clear accumulation data D & K
              gg2_temp[d] = 0;
              for (d2 = 0; d2 < LANDAU_DIM; d2++) gg3_temp[d][d2] = 0;
            }
            /* inner beta reduction */
            IPf_idx = 0;
            for (PetscInt grid_r = 0, f_off = 0, ipidx = 0; grid_r < ctx->num_grids; grid_r++, f_off = ctx->species_offset[grid_r]) { // IPf_idx += nip_loc_r*Nfloc_r
              PetscInt nip_loc_r = numCells[grid_r] * Nq, Nfloc_r = Nf[grid_r];
              for (PetscInt ei_r = 0, loc_fdf_idx = 0; ei_r < numCells[grid_r]; ++ei_r) {
                for (PetscInt qi = 0; qi < Nq; qi++, ipidx++, loc_fdf_idx++) {
                  const PetscReal wi = ww[ipidx], x = xx[ipidx], y = yy[ipidx];
                  PetscReal       temp1[3] = {0, 0, 0}, temp2 = 0;
#if LANDAU_DIM == 2
                  PetscReal Ud[2][2], Uk[2][2], mask = (PetscAbs(vj[0] - x) < 100 * PETSC_SQRT_MACHINE_EPSILON && PetscAbs(vj[1] - y) < 100 * PETSC_SQRT_MACHINE_EPSILON) ? 0. : 1.;
                  LandauTensor2D(vj, x, y, Ud, Uk, mask);
#else
                  PetscReal U[3][3], z = zz[ipidx], mask = (PetscAbs(vj[0] - x) < 100 * PETSC_SQRT_MACHINE_EPSILON && PetscAbs(vj[1] - y) < 100 * PETSC_SQRT_MACHINE_EPSILON && PetscAbs(vj[2] - z) < 100 * PETSC_SQRT_MACHINE_EPSILON) ? 0. : 1.;
                  if (ctx->use_relativistic_corrections) {
                    LandauTensor3DRelativistic(vj, x, y, z, U, mask, C_0(ctx->v_0));
                  } else {
                    LandauTensor3D(vj, x, y, z, U, mask);
                  }
#endif
                  for (int f = 0; f < Nfloc_r; ++f) {
                    const PetscInt idx = b_id * IPf_sz_glb + ipf_offset[grid_r] + f * nip_loc_r + ei_r * Nq + qi; // IPf_idx + f*nip_loc_r + loc_fdf_idx;
                    temp1[0] += dudx[idx] * nu_beta[f + f_off] * invMass[f + f_off] * (*lambdas)[grid][grid_r];
                    temp1[1] += dudy[idx] * nu_beta[f + f_off] * invMass[f + f_off] * (*lambdas)[grid][grid_r];
#if LANDAU_DIM == 3
                    temp1[2] += dudz[idx] * nu_beta[f + f_off] * invMass[f + f_off] * (*lambdas)[grid][grid_r];
#endif
                    temp2 += ff[idx] * nu_beta[f + f_off] * (*lambdas)[grid][grid_r];
                  }
                  temp1[0] *= wi;
                  temp1[1] *= wi;
#if LANDAU_DIM == 3
                  temp1[2] *= wi;
#endif
                  temp2 *= wi;
#if LANDAU_DIM == 2
                  for (d2 = 0; d2 < 2; d2++) {
                    for (d3 = 0; d3 < 2; ++d3) {
                      /* K = U * grad(f): g2=e: i,A */
                      gg2_temp[d2] += Uk[d2][d3] * temp1[d3];
                      /* D = -U * (I \kron (fx)): g3=f: i,j,A */
                      gg3_temp[d2][d3] += Ud[d2][d3] * temp2;
                    }
                  }
#else
                  for (d2 = 0; d2 < 3; ++d2) {
                    for (d3 = 0; d3 < 3; ++d3) {
                      /* K = U * grad(f): g2 = e: i,A */
                      gg2_temp[d2] += U[d2][d3] * temp1[d3];
                      /* D = -U * (I \kron (fx)): g3 = f: i,j,A */
                      gg3_temp[d2][d3] += U[d2][d3] * temp2;
                    }
                  }
#endif
                } // qi
              }   // ei_r
              IPf_idx += nip_loc_r * Nfloc_r;
            } /* grid_r - IPs */
            PetscCheck(IPf_idx == IPf_sz_glb, PETSC_COMM_SELF, PETSC_ERR_PLIB, "IPf_idx != IPf_sz %" PetscInt_FMT " %" PetscInt_FMT, IPf_idx, IPf_sz_glb);
            // add alpha and put in gg2/3
            for (PetscInt fieldA = 0, f_off = ctx->species_offset[grid]; fieldA < loc_Nf; ++fieldA) {
              for (d2 = 0; d2 < LANDAU_DIM; d2++) {
                gg2[fieldA][d2] = gg2_temp[d2] * nu_alpha[fieldA + f_off];
                for (d3 = 0; d3 < LANDAU_DIM; d3++) gg3[fieldA][d2][d3] = -gg3_temp[d2][d3] * nu_alpha[fieldA + f_off] * invMass[fieldA + f_off];
              }
            }
            /* add electric field term once per IP */
            for (PetscInt fieldA = 0, f_off = ctx->species_offset[grid]; fieldA < loc_Nf; ++fieldA) gg2[fieldA][LANDAU_DIM - 1] += Eq_m[fieldA + f_off];
            /* Jacobian transform - g2, g3 */
            for (PetscInt fieldA = 0; fieldA < loc_Nf; ++fieldA) {
              for (d = 0; d < dim; ++d) {
                g2[fieldA][d] = 0.0;
                for (d2 = 0; d2 < dim; ++d2) {
                  g2[fieldA][d] += invJj[d * dim + d2] * gg2[fieldA][d2];
                  g3[fieldA][d][d2] = 0.0;
                  for (d3 = 0; d3 < dim; ++d3) {
                    for (dp = 0; dp < dim; ++dp) g3[fieldA][d][d2] += invJj[d * dim + d3] * gg3[fieldA][d3][dp] * invJj[d2 * dim + dp];
                  }
                  g3[fieldA][d][d2] *= wj;
                }
                g2[fieldA][d] *= wj;
              }
            }
          } else { // mass
            PetscReal wj = ww[jpidx_glb];
            /* Jacobian transform - g0 */
            for (PetscInt fieldA = 0; fieldA < loc_Nf; ++fieldA) {
              if (dim == 2) {
                g0[fieldA] = wj * shift * 2. * PETSC_PI; // move this to below and remove g0
              } else {
                g0[fieldA] = wj * shift; // move this to below and remove g0
              }
            }
          }
          /* FE matrix construction */
          {
            PetscInt         fieldA, d, f, d2, g;
            const PetscReal *BJq = &BB[qj * Nb], *DIq = &DD[qj * Nb * dim];
            /* assemble - on the diagonal (I,I) */
            for (fieldA = 0; fieldA < loc_Nf; fieldA++) {
              for (f = 0; f < Nb; f++) {
                const PetscInt i = fieldA * Nb + f; /* Element matrix row */
                for (g = 0; g < Nb; ++g) {
                  const PetscInt j    = fieldA * Nb + g; /* Element matrix column */
                  const PetscInt fOff = i * totDim + j;
                  if (shift == 0.0) {
                    for (d = 0; d < dim; ++d) {
                      elemMat[fOff] += DIq[f * dim + d] * g2[fieldA][d] * BJq[g];
                      for (d2 = 0; d2 < dim; ++d2) elemMat[fOff] += DIq[f * dim + d] * g3[fieldA][d][d2] * DIq[g * dim + d2];
                    }
                  } else { // mass
                    elemMat[fOff] += BJq[f] * g0[fieldA] * BJq[g];
                  }
                }
              }
            }
          }
        }                   /* qj loop */
        if (shift == 0.0) { // Jacobian
          PetscCall(PetscLogEventEnd(ctx->events[4], 0, 0, 0, 0));
        } else {
          PetscCall(PetscLogEventEnd(ctx->events[16], 0, 0, 0, 0));
        }
#if defined(PETSC_HAVE_THREADSAFETY)
        endtime = MPI_Wtime();
        if (ctx->stage) ctx->times[LANDAU_KERNEL] += (endtime - starttime);
#endif
        /* assemble matrix */
        if (!container) {
          PetscInt cStart;
          PetscCall(PetscLogEventBegin(ctx->events[6], 0, 0, 0, 0));
          PetscCall(DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, NULL));
          PetscCall(DMPlexMatSetClosure(ctx->plex[grid], section[grid], globsection[grid], subJ[LAND_PACK_IDX(b_id, grid)], loc_elem + cStart, elemMat, ADD_VALUES));
          PetscCall(PetscLogEventEnd(ctx->events[6], 0, 0, 0, 0));
        } else { // GPU like assembly for debugging
          PetscInt    fieldA, q, f, g, d, nr, nc, rows0[LANDAU_MAX_Q_FACE] = {0}, cols0[LANDAU_MAX_Q_FACE] = {0}, rows[LANDAU_MAX_Q_FACE], cols[LANDAU_MAX_Q_FACE];
          PetscScalar vals[LANDAU_MAX_Q_FACE * LANDAU_MAX_Q_FACE] = {0}, row_scale[LANDAU_MAX_Q_FACE] = {0}, col_scale[LANDAU_MAX_Q_FACE] = {0};
          LandauIdx *coo_elem_offsets = (LandauIdx *)ctx->SData_d.coo_elem_offsets, *coo_elem_fullNb = (LandauIdx *)ctx->SData_d.coo_elem_fullNb, (*coo_elem_point_offsets)[LANDAU_MAX_NQND + 1] = (LandauIdx(*)[LANDAU_MAX_NQND + 1]) ctx->SData_d.coo_elem_point_offsets;
          /* assemble - from the diagonal (I,I) in this format for DMPlexMatSetClosure */
          for (fieldA = 0; fieldA < loc_Nf; fieldA++) {
            LandauIdx *const Idxs = &maps[grid].gIdx[loc_elem][fieldA][0];
            for (f = 0; f < Nb; f++) {
              PetscInt idx = Idxs[f];
              if (idx >= 0) {
                nr           = 1;
                rows0[0]     = idx;
                row_scale[0] = 1.;
              } else {
                idx = -idx - 1;
                for (q = 0, nr = 0; q < maps[grid].num_face; q++, nr++) {
                  if (maps[grid].c_maps[idx][q].gid < 0) break;
                  rows0[q]     = maps[grid].c_maps[idx][q].gid;
                  row_scale[q] = maps[grid].c_maps[idx][q].scale;
                }
              }
              for (g = 0; g < Nb; ++g) {
                idx = Idxs[g];
                if (idx >= 0) {
                  nc           = 1;
                  cols0[0]     = idx;
                  col_scale[0] = 1.;
                } else {
                  idx = -idx - 1;
                  nc  = maps[grid].num_face;
                  for (q = 0, nc = 0; q < maps[grid].num_face; q++, nc++) {
                    if (maps[grid].c_maps[idx][q].gid < 0) break;
                    cols0[q]     = maps[grid].c_maps[idx][q].gid;
                    col_scale[q] = maps[grid].c_maps[idx][q].scale;
                  }
                }
                const PetscInt    i   = fieldA * Nb + f; /* Element matrix row */
                const PetscInt    j   = fieldA * Nb + g; /* Element matrix column */
                const PetscScalar Aij = elemMat[i * totDim + j];
                if (coo_vals) { // mirror (i,j) in CreateStaticGPUData
                  const int fullNb = coo_elem_fullNb[glb_elem_idx], fullNb2 = fullNb * fullNb;
                  const int idx0 = b_id * coo_elem_offsets[elem_offset[num_grids]] + coo_elem_offsets[glb_elem_idx] + fieldA * fullNb2 + fullNb * coo_elem_point_offsets[glb_elem_idx][f] + nr * coo_elem_point_offsets[glb_elem_idx][g];
                  for (int q = 0, idx2 = idx0; q < nr; q++) {
                    for (int d = 0; d < nc; d++, idx2++) coo_vals[idx2] = row_scale[q] * col_scale[d] * Aij;
                  }
                } else {
                  for (q = 0; q < nr; q++) rows[q] = rows0[q] + moffset;
                  for (d = 0; d < nc; d++) cols[d] = cols0[d] + moffset;
                  for (q = 0; q < nr; q++) {
                    for (d = 0; d < nc; d++) vals[q * nc + d] = row_scale[q] * col_scale[d] * Aij;
                  }
                  PetscCall(MatSetValues(JacP, nr, rows, nc, cols, vals, ADD_VALUES));
                }
              }
            }
          }
        }
        if (loc_elem == -1) {
          PetscCall(PetscPrintf(ctx->comm, "CPU Element matrix\n"));
          for (int d = 0; d < totDim; ++d) {
            for (int f = 0; f < totDim; ++f) PetscCall(PetscPrintf(ctx->comm, " %12.5e", (double)PetscRealPart(elemMat[d * totDim + f])));
            PetscCall(PetscPrintf(ctx->comm, "\n"));
          }
          exit(12);
        }
        PetscCall(PetscFree(elemMat));
      }                 /* grid */
    }                   /* outer element & batch loop */
    if (shift == 0.0) { // mass
      PetscCall(PetscFree4(ff, dudx, dudy, dudz));
    }
    if (!container) {                                         // 'CPU' assembly move nest matrix to global JacP
      for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) { // OpenMP
        for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
          const PetscInt     moffset = LAND_MOFFSET(b_id, grid, ctx->batch_sz, ctx->num_grids, ctx->mat_offset); // b_id*b_N + ctx->mat_offset[grid];
          PetscInt           nloc, nzl, colbuf[1024], row;
          const PetscInt    *cols;
          const PetscScalar *vals;
          Mat                B = subJ[LAND_PACK_IDX(b_id, grid)];
          PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
          PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
          PetscCall(MatGetSize(B, &nloc, NULL));
          for (int i = 0; i < nloc; i++) {
            PetscCall(MatGetRow(B, i, &nzl, &cols, &vals));
            PetscCheck(nzl <= 1024, PetscObjectComm((PetscObject)B), PETSC_ERR_PLIB, "Row too big: %" PetscInt_FMT, nzl);
            for (int j = 0; j < nzl; j++) colbuf[j] = moffset + cols[j];
            row = moffset + i;
            PetscCall(MatSetValues(JacP, 1, &row, nzl, colbuf, vals, ADD_VALUES));
            PetscCall(MatRestoreRow(B, i, &nzl, &cols, &vals));
          }
          PetscCall(MatDestroy(&B));
        }
      }
    }
    if (coo_vals) {
      PetscCall(MatSetValuesCOO(JacP, coo_vals, ADD_VALUES));
      PetscCall(PetscFree(coo_vals));
    }
  } /* CPU version */
  PetscCall(MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY));
  /* clean up */
  if (cellClosure) PetscCall(PetscFree(cellClosure));
  if (xdata) PetscCall(VecRestoreArrayReadAndMemType(a_X, &xdata));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GeometryDMLandau(DM base, PetscInt point, PetscInt dim, const PetscReal abc[], PetscReal xyz[], void *a_ctx)
{
  PetscReal r = abc[0], z = abc[1];

  PetscFunctionBegin;
  xyz[0] = r;
  xyz[1] = z;
  if (dim == 3) xyz[2] = abc[2];

  PetscFunctionReturn(PETSC_SUCCESS);
}

/* create DMComposite of meshes for each species group */
static PetscErrorCode LandauDMCreateVMeshes(MPI_Comm comm_self, const PetscInt dim, const char prefix[], LandauCtx *ctx, DM pack)
{
  PetscFunctionBegin;
  { /* p4est, quads */
    /* Create plex mesh of Landau domain */
    for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
      PetscReal par_radius = ctx->radius_par[grid], perp_radius = ctx->radius_perp[grid];
      if (!ctx->sphere && !ctx->simplex) { // 2 or 3D (only 3D option)
        PetscReal      lo[] = {-perp_radius, -par_radius, -par_radius}, hi[] = {perp_radius, par_radius, par_radius};
        DMBoundaryType periodicity[3] = {DM_BOUNDARY_NONE, dim == 2 ? DM_BOUNDARY_NONE : DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
        if (dim == 2) lo[0] = 0;
        else {
          lo[1] = -perp_radius;
          hi[1] = perp_radius; // 3D y is a perp
        }
        PetscCall(DMPlexCreateBoxMesh(comm_self, dim, PETSC_FALSE, ctx->cells0, lo, hi, periodicity, PETSC_TRUE, &ctx->plex[grid])); // todo: make composite and create dm[grid] here
        PetscCall(DMLocalizeCoordinates(ctx->plex[grid]));                                                                           /* needed for periodic */
        if (dim == 3) PetscCall(PetscObjectSetName((PetscObject)ctx->plex[grid], "cube"));
        else PetscCall(PetscObjectSetName((PetscObject)ctx->plex[grid], "half-plane"));
      } else if (dim == 2) {
        size_t len;
        PetscCall(PetscStrlen(ctx->filename, &len));
        if (len) {
          Vec          coords;
          PetscScalar *x;
          PetscInt     N;
          char         str[] = "-dm_landau_view_file_0";
          str[21] += grid;
          PetscCall(DMPlexCreateFromFile(comm_self, ctx->filename, "plexland.c", PETSC_TRUE, &ctx->plex[grid]));
          PetscCall(DMPlexOrient(ctx->plex[grid]));
          PetscCall(DMGetCoordinatesLocal(ctx->plex[grid], &coords));
          PetscCall(VecGetSize(coords, &N));
          PetscCall(VecGetArray(coords, &x));
          /* scale by domain size */
          for (PetscInt i = 0; i < N; i += 2) {
            x[i + 0] *= ctx->radius_perp[grid];
            x[i + 1] *= ctx->radius_par[grid];
          }
          PetscCall(VecRestoreArray(coords, &x));
          PetscCall(PetscObjectSetName((PetscObject)ctx->plex[grid], ctx->filename));
          PetscCall(PetscInfo(ctx->plex[grid], "%d) Read %s mesh file (%s)\n", (int)grid, ctx->filename, str));
          PetscCall(DMViewFromOptions(ctx->plex[grid], NULL, str));
        } else {
          PetscInt       numCells = ctx->simplex ? 12 : 6, cell_size = ctx->simplex ? 3 : 4, j;
          const PetscInt numVerts    = 11;
          PetscInt       cellsT[][4] = {
            {0,  1, 6, 5 },
            {1,  2, 7, 6 },
            {2,  3, 8, 7 },
            {3,  4, 9, 8 },
            {5,  6, 7, 10},
            {10, 7, 8, 9 }
          };
          PetscInt cellsS[][3] = {
            {0,  1, 6 },
            {1,  2, 6 },
            {6,  2, 7 },
            {7,  2, 8 },
            {8,  2, 3 },
            {8,  3, 4 },
            {0,  6, 5 },
            {5,  6, 7 },
            {5,  7, 10},
            {10, 7, 9 },
            {9,  7, 8 },
            {9,  8, 4 }
          };
          const PetscInt *pcell = (const PetscInt *)(ctx->simplex ? &cellsS[0][0] : &cellsT[0][0]);
          PetscReal       coords[11][2], *flatCoords = (PetscReal *)&coords[0][0];
          PetscReal       rad = ctx->radius[grid];
          for (j = 0; j < 5; j++) { // outside edge
            PetscReal z, r, theta = -PETSC_PI / 2 + (j % 5) * PETSC_PI / 4;
            r            = rad * PetscCosReal(theta);
            coords[j][0] = r;
            z            = rad * PetscSinReal(theta);
            coords[j][1] = z;
          }
          coords[j][0]   = 0;
          coords[j++][1] = -rad * ctx->sphere_inner_radius_90degree;
          coords[j][0]   = rad * ctx->sphere_inner_radius_45degree;
          coords[j++][1] = -rad * ctx->sphere_inner_radius_45degree;
          coords[j][0]   = rad * ctx->sphere_inner_radius_90degree;
          coords[j++][1] = 0;
          coords[j][0]   = rad * ctx->sphere_inner_radius_45degree;
          coords[j++][1] = rad * ctx->sphere_inner_radius_45degree;
          coords[j][0]   = 0;
          coords[j++][1] = rad * ctx->sphere_inner_radius_90degree;
          coords[j][0]   = 0;
          coords[j++][1] = 0;
          PetscCall(DMPlexCreateFromCellListPetsc(comm_self, 2, numCells, numVerts, cell_size, ctx->interpolate, pcell, 2, flatCoords, &ctx->plex[grid]));
          PetscCall(PetscObjectSetName((PetscObject)ctx->plex[grid], "semi-circle"));
          PetscCall(PetscInfo(ctx->plex[grid], "\t%" PetscInt_FMT ") Make circle %s mesh\n", grid, ctx->simplex ? "simplex" : "tensor"));
        }
      } else SETERRQ(ctx->comm, PETSC_ERR_PLIB, "Velocity space meshes does not support 3V cubed sphere or simplex");
      PetscCall(DMSetFromOptions(ctx->plex[grid]));
    } // grid loop
    PetscCall(PetscObjectSetOptionsPrefix((PetscObject)pack, prefix));
    { /* convert to p4est (or whatever), wait for discretization to create pack */
      char      convType[256];
      PetscBool flg;

      PetscOptionsBegin(ctx->comm, prefix, "Mesh conversion options", "DMPLEX");
      PetscCall(PetscOptionsFList("-dm_landau_type", "Convert DMPlex to another format (p4est)", "plexland.c", DMList, DMPLEX, convType, 256, &flg));
      PetscOptionsEnd();
      if (flg) {
        ctx->use_p4est = PETSC_TRUE; /* flag for Forest */
        for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
          DM dmforest;
          PetscCall(DMConvert(ctx->plex[grid], convType, &dmforest));
          if (dmforest) {
            PetscBool isForest;
            PetscCall(PetscObjectSetOptionsPrefix((PetscObject)dmforest, prefix));
            PetscCall(DMIsForest(dmforest, &isForest));
            if (isForest) {
              if (ctx->sphere) PetscCall(DMForestSetBaseCoordinateMapping(dmforest, GeometryDMLandau, ctx));
              PetscCall(DMDestroy(&ctx->plex[grid]));
              ctx->plex[grid] = dmforest; // Forest for adaptivity
            } else SETERRQ(ctx->comm, PETSC_ERR_PLIB, "Converted to non Forest?");
          } else SETERRQ(ctx->comm, PETSC_ERR_PLIB, "Convert failed?");
        }
      } else ctx->use_p4est = PETSC_FALSE; /* flag for Forest */
    }
  } /* non-file */
  PetscCall(DMSetDimension(pack, dim));
  PetscCall(PetscObjectSetName((PetscObject)pack, "Mesh"));
  PetscCall(DMSetApplicationContext(pack, ctx));

  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode SetupDS(DM pack, PetscInt dim, PetscInt grid, LandauCtx *ctx)
{
  PetscInt     ii, i0;
  char         buf[256];
  PetscSection section;

  PetscFunctionBegin;
  for (ii = ctx->species_offset[grid], i0 = 0; ii < ctx->species_offset[grid + 1]; ii++, i0++) {
    if (ii == 0) PetscCall(PetscSNPrintf(buf, sizeof(buf), "e"));
    else PetscCall(PetscSNPrintf(buf, sizeof(buf), "i%" PetscInt_FMT, ii));
    /* Setup Discretization - FEM */
    PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, ctx->simplex, NULL, PETSC_DECIDE, &ctx->fe[ii]));
    PetscCall(PetscObjectSetName((PetscObject)ctx->fe[ii], buf));
    PetscCall(DMSetField(ctx->plex[grid], i0, NULL, (PetscObject)ctx->fe[ii]));
  }
  PetscCall(DMCreateDS(ctx->plex[grid]));
  PetscCall(DMGetSection(ctx->plex[grid], &section));
  for (PetscInt ii = ctx->species_offset[grid], i0 = 0; ii < ctx->species_offset[grid + 1]; ii++, i0++) {
    if (ii == 0) PetscCall(PetscSNPrintf(buf, sizeof(buf), "se"));
    else PetscCall(PetscSNPrintf(buf, sizeof(buf), "si%" PetscInt_FMT, ii));
    PetscCall(PetscSectionSetComponentName(section, i0, 0, buf));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Define a Maxwellian function for testing out the operator. */

/* Using cartesian velocity space coordinates, the particle */
/* density, [1/m^3], is defined according to */

/* $$ n=\int_{R^3} dv^3 \left(\frac{m}{2\pi T}\right)^{3/2}\exp [- mv^2/(2T)] $$ */

/* Using some constant, c, we normalize the velocity vector into a */
/* dimensionless variable according to v=c*x. Thus the density, $n$, becomes */

/* $$ n=\int_{R^3} dx^3 \left(\frac{mc^2}{2\pi T}\right)^{3/2}\exp [- mc^2/(2T)*x^2] $$ */

/* Defining $\theta=2T/mc^2$, we thus find that the probability density */
/* for finding the particle within the interval in a box dx^3 around x is */

/* f(x;\theta)=\left(\frac{1}{\pi\theta}\right)^{3/2} \exp [ -x^2/\theta ] */

typedef struct {
  PetscReal v_0;
  PetscReal kT_m;
  PetscReal n;
  PetscReal shift;
} MaxwellianCtx;

static PetscErrorCode maxwellian(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf_dummy, PetscScalar *u, void *actx)
{
  MaxwellianCtx *mctx = (MaxwellianCtx *)actx;
  PetscInt       i;
  PetscReal      v2 = 0, theta = 2 * mctx->kT_m / (mctx->v_0 * mctx->v_0), shift; /* theta = 2kT/mc^2 */
  PetscFunctionBegin;
  /* compute the exponents, v^2 */
  for (i = 0; i < dim; ++i) v2 += x[i] * x[i];
  /* evaluate the Maxwellian */
  if (mctx->shift < 0) shift = -mctx->shift;
  else {
    u[0]  = mctx->n * PetscPowReal(PETSC_PI * theta, -1.5) * (PetscExpReal(-v2 / theta));
    shift = mctx->shift;
  }
  if (shift != 0.) {
    v2 = 0;
    for (i = 0; i < dim - 1; ++i) v2 += x[i] * x[i];
    v2 += (x[dim - 1] - shift) * (x[dim - 1] - shift);
    /* evaluate the shifted Maxwellian */
    u[0] += mctx->n * PetscPowReal(PETSC_PI * theta, -1.5) * (PetscExpReal(-v2 / theta));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexLandauAddMaxwellians - Add a Maxwellian distribution to a state

  Collective

  Input Parameters:
+ dm      - The mesh (local)
. time    - Current time
. temps   - Temperatures of each species (global)
. ns      - Number density of each species (global)
. grid    - index into current grid - just used for offset into `temp` and `ns`
. b_id    - batch index
. n_batch - number of batches
- actx    - Landau context

  Output Parameter:
. X - The state (local to this grid)

  Level: beginner

.seealso: `DMPlexLandauCreateVelocitySpace()`
 @*/
PetscErrorCode DMPlexLandauAddMaxwellians(DM dm, Vec X, PetscReal time, PetscReal temps[], PetscReal ns[], PetscInt grid, PetscInt b_id, PetscInt n_batch, void *actx)
{
  LandauCtx *ctx = (LandauCtx *)actx;
  PetscErrorCode (*initu[LANDAU_MAX_SPECIES])(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar[], void *);
  PetscInt       dim;
  MaxwellianCtx *mctxs[LANDAU_MAX_SPECIES], data[LANDAU_MAX_SPECIES];

  PetscFunctionBegin;
  PetscCall(DMGetDimension(dm, &dim));
  if (!ctx) PetscCall(DMGetApplicationContext(dm, &ctx));
  for (PetscInt ii = ctx->species_offset[grid], i0 = 0; ii < ctx->species_offset[grid + 1]; ii++, i0++) {
    mctxs[i0]      = &data[i0];
    data[i0].v_0   = ctx->v_0;                             // v_0 same for all grids
    data[i0].kT_m  = ctx->k * temps[ii] / ctx->masses[ii]; /* kT/m */
    data[i0].n     = ns[ii];
    initu[i0]      = maxwellian;
    data[i0].shift = 0;
  }
  data[0].shift = ctx->electronShift;
  /* need to make ADD_ALL_VALUES work - TODO */
  PetscCall(DMProjectFunction(dm, time, initu, (void **)mctxs, INSERT_ALL_VALUES, X));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
 LandauSetInitialCondition - Adds Maxwellians with context

 Collective

 Input Parameters:
 .   dm - The mesh
 -   grid - index into current grid - just used for offset into temp and ns
 .   b_id - batch index
 -   n_batch - number of batches
 +   actx - Landau context with T and n

 Output Parameter:
 .   X  - The state

 Level: beginner

.seealso: `DMPlexLandauCreateVelocitySpace()`, `DMPlexLandauAddMaxwellians()`
 */
static PetscErrorCode LandauSetInitialCondition(DM dm, Vec X, PetscInt grid, PetscInt b_id, PetscInt n_batch, void *actx)
{
  LandauCtx *ctx = (LandauCtx *)actx;
  PetscFunctionBegin;
  if (!ctx) PetscCall(DMGetApplicationContext(dm, &ctx));
  PetscCall(VecZeroEntries(X));
  PetscCall(DMPlexLandauAddMaxwellians(dm, X, 0.0, ctx->thermal_temps, ctx->n, grid, b_id, n_batch, ctx));
  PetscFunctionReturn(PETSC_SUCCESS);
}

// adapt a level once. Forest in/out
#if defined(PETSC_USE_INFO)
static const char *s_refine_names[] = {"RE", "Z1", "Origin", "Z2", "Uniform"};
#endif
static PetscErrorCode adaptToleranceFEM(PetscFE fem, Vec sol, PetscInt type, PetscInt grid, LandauCtx *ctx, DM *newForest)
{
  DM              forest, plex, adaptedDM = NULL;
  PetscDS         prob;
  PetscBool       isForest;
  PetscQuadrature quad;
  PetscInt        Nq, Nb, *Nb2, cStart, cEnd, c, dim, qj, k;
  DMLabel         adaptLabel = NULL;

  PetscFunctionBegin;
  forest = ctx->plex[grid];
  PetscCall(DMCreateDS(forest));
  PetscCall(DMGetDS(forest, &prob));
  PetscCall(DMGetDimension(forest, &dim));
  PetscCall(DMIsForest(forest, &isForest));
  PetscCheck(isForest, ctx->comm, PETSC_ERR_ARG_WRONG, "! Forest");
  PetscCall(DMConvert(forest, DMPLEX, &plex));
  PetscCall(DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd));
  PetscCall(DMLabelCreate(PETSC_COMM_SELF, "adapt", &adaptLabel));
  PetscCall(PetscFEGetQuadrature(fem, &quad));
  PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL));
  PetscCheck(Nq <= LANDAU_MAX_NQND, ctx->comm, PETSC_ERR_ARG_WRONG, "Order too high. Nq = %" PetscInt_FMT " > LANDAU_MAX_NQND (%d)", Nq, LANDAU_MAX_NQND);
  PetscCall(PetscFEGetDimension(ctx->fe[0], &Nb));
  PetscCall(PetscDSGetDimensions(prob, &Nb2));
  PetscCheck(Nb2[0] == Nb, ctx->comm, PETSC_ERR_ARG_WRONG, " Nb = %" PetscInt_FMT " != Nb (%d)", Nb, (int)Nb2[0]);
  PetscCheck(Nb <= LANDAU_MAX_NQND, ctx->comm, PETSC_ERR_ARG_WRONG, "Order too high. Nb = %" PetscInt_FMT " > LANDAU_MAX_NQND (%d)", Nb, LANDAU_MAX_NQND);
  PetscCall(PetscInfo(sol, "%" PetscInt_FMT ") Refine phase: %s\n", grid, s_refine_names[type]));
  if (type == 4) {
    for (c = cStart; c < cEnd; c++) PetscCall(DMLabelSetValue(adaptLabel, c, DM_ADAPT_REFINE));
  } else if (type == 2) {
    PetscInt  rCellIdx[8], nr = 0, nrmax = (dim == 3) ? 8 : 2;
    PetscReal minRad = PETSC_INFINITY, r;
    for (c = cStart; c < cEnd; c++) {
      PetscReal tt, v0[LANDAU_MAX_NQND * 3], detJ[LANDAU_MAX_NQND];
      PetscCall(DMPlexComputeCellGeometryFEM(plex, c, quad, v0, NULL, NULL, detJ));
      for (qj = 0; qj < Nq; ++qj) {
        tt = PetscSqr(v0[dim * qj + 0]) + PetscSqr(v0[dim * qj + 1]) + PetscSqr(((dim == 3) ? v0[dim * qj + 2] : 0));
        r  = PetscSqrtReal(tt);
        if (r < minRad - PETSC_SQRT_MACHINE_EPSILON * 10.) {
          minRad         = r;
          nr             = 0;
          rCellIdx[nr++] = c;
          PetscCall(PetscInfo(sol, "\t\t%" PetscInt_FMT ") Found first inner r=%e, cell %" PetscInt_FMT ", qp %" PetscInt_FMT "/%" PetscInt_FMT "\n", grid, (double)r, c, qj + 1, Nq));
        } else if ((r - minRad) < PETSC_SQRT_MACHINE_EPSILON * 100. && nr < nrmax) {
          for (k = 0; k < nr; k++)
            if (c == rCellIdx[k]) break;
          if (k == nr) {
            rCellIdx[nr++] = c;
            PetscCall(PetscInfo(sol, "\t\t\t%" PetscInt_FMT ") Found another inner r=%e, cell %" PetscInt_FMT ", qp %" PetscInt_FMT "/%" PetscInt_FMT ", d=%e\n", grid, (double)r, c, qj + 1, Nq, (double)(r - minRad)));
          }
        }
      }
    }
    for (k = 0; k < nr; k++) PetscCall(DMLabelSetValue(adaptLabel, rCellIdx[k], DM_ADAPT_REFINE));
    PetscCall(PetscInfo(sol, "\t\t\t%" PetscInt_FMT ") Refined %" PetscInt_FMT " origin cells %" PetscInt_FMT ",%" PetscInt_FMT " r=%g\n", grid, nr, rCellIdx[0], rCellIdx[1], (double)minRad));
  } else if (type == 0 || type == 1 || type == 3) { /* refine along r=0 axis */
    PetscScalar *coef = NULL;
    Vec          coords;
    PetscInt     csize, Nv, d, nz, nrefined = 0;
    DM           cdm;
    PetscSection cs;
    PetscCall(DMGetCoordinatesLocal(forest, &coords));
    PetscCall(DMGetCoordinateDM(forest, &cdm));
    PetscCall(DMGetLocalSection(cdm, &cs));
    for (c = cStart; c < cEnd; c++) {
      PetscInt doit = 0, outside = 0;
      PetscCall(DMPlexVecGetClosure(cdm, cs, coords, c, &csize, &coef));
      Nv = csize / dim;
      for (nz = d = 0; d < Nv; d++) {
        PetscReal z = PetscRealPart(coef[d * dim + (dim - 1)]), x = PetscSqr(PetscRealPart(coef[d * dim + 0])) + ((dim == 3) ? PetscSqr(PetscRealPart(coef[d * dim + 1])) : 0);
        x = PetscSqrtReal(x);
        if (type == 0) {
          if (ctx->re_radius > PETSC_SQRT_MACHINE_EPSILON && (z < -PETSC_MACHINE_EPSILON * 10. || z > ctx->re_radius + PETSC_MACHINE_EPSILON * 10.)) outside++; /* first pass don't refine bottom */
        } else if (type == 1 && (z > ctx->vperp0_radius1 || z < -ctx->vperp0_radius1)) {
          outside++; /* don't refine outside electron refine radius */
          PetscCall(PetscInfo(sol, "\t%" PetscInt_FMT ") (debug) found %s cells\n", grid, s_refine_names[type]));
        } else if (type == 3 && (z > ctx->vperp0_radius2 || z < -ctx->vperp0_radius2)) {
          outside++; /* refine r=0 cells on refinement front */
          PetscCall(PetscInfo(sol, "\t%" PetscInt_FMT ") (debug) found %s cells\n", grid, s_refine_names[type]));
        }
        if (x < PETSC_MACHINE_EPSILON * 10. && (type != 0 || ctx->re_radius > PETSC_SQRT_MACHINE_EPSILON)) nz++;
      }
      PetscCall(DMPlexVecRestoreClosure(cdm, cs, coords, c, &csize, &coef));
      if (doit || (outside < Nv && nz)) {
        PetscCall(DMLabelSetValue(adaptLabel, c, DM_ADAPT_REFINE));
        nrefined++;
      }
    }
    PetscCall(PetscInfo(sol, "\t%" PetscInt_FMT ") Refined %" PetscInt_FMT " cells\n", grid, nrefined));
  }
  PetscCall(DMDestroy(&plex));
  PetscCall(DMAdaptLabel(forest, adaptLabel, &adaptedDM));
  PetscCall(DMLabelDestroy(&adaptLabel));
  *newForest = adaptedDM;
  if (adaptedDM) {
    if (isForest) {
      PetscCall(DMForestSetAdaptivityForest(adaptedDM, NULL)); // ????
    }
    PetscCall(DMConvert(adaptedDM, DMPLEX, &plex));
    PetscCall(DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd));
    PetscCall(PetscInfo(sol, "\t\t\t\t%" PetscInt_FMT ") %" PetscInt_FMT " cells, %" PetscInt_FMT " total quadrature points\n", grid, cEnd - cStart, Nq * (cEnd - cStart)));
    PetscCall(DMDestroy(&plex));
  } else *newForest = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

// forest goes in (ctx->plex[grid]), plex comes out
static PetscErrorCode adapt(PetscInt grid, LandauCtx *ctx, Vec *uu)
{
  PetscInt adaptIter;

  PetscFunctionBegin;
  PetscInt type, limits[5] = {(grid == 0) ? ctx->numRERefine : 0, (grid == 0) ? ctx->nZRefine1 : 0, ctx->numAMRRefine[grid], (grid == 0) ? ctx->nZRefine2 : 0, ctx->postAMRRefine[grid]};
  for (type = 0; type < 5; type++) {
    for (adaptIter = 0; adaptIter < limits[type]; adaptIter++) {
      DM newForest = NULL;
      PetscCall(adaptToleranceFEM(ctx->fe[0], *uu, type, grid, ctx, &newForest));
      if (newForest) {
        PetscCall(DMDestroy(&ctx->plex[grid]));
        PetscCall(VecDestroy(uu));
        PetscCall(DMCreateGlobalVector(newForest, uu));
        PetscCall(PetscObjectSetName((PetscObject)*uu, "uAMR"));
        PetscCall(LandauSetInitialCondition(newForest, *uu, grid, 0, 1, ctx));
        ctx->plex[grid] = newForest;
      } else {
        PetscCall(PetscInfo(*uu, "No refinement\n"));
      }
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

// make log(Lambdas) from NRL Plasma formulary
static PetscErrorCode makeLambdas(LandauCtx *ctx)
{
  PetscFunctionBegin;
  for (PetscInt gridi = 0; gridi < ctx->num_grids; gridi++) {
    int       iii   = ctx->species_offset[gridi];
    PetscReal Ti_ev = (ctx->thermal_temps[iii] / 1.1604525e7) * 1000; // convert (back) to eV
    PetscReal ni    = ctx->n[iii] * ctx->n_0;
    for (PetscInt gridj = gridi; gridj < ctx->num_grids; gridj++) {
      PetscInt  jjj = ctx->species_offset[gridj];
      PetscReal Zj  = ctx->charges[jjj] / 1.6022e-19;
      if (gridi == 0) {
        if (gridj == 0) { // lam_ee
          ctx->lambdas[gridi][gridj] = 23.5 - PetscLogReal(PetscSqrtReal(ni) * PetscPowReal(Ti_ev, -1.25)) - PetscSqrtReal(1e-5 + PetscSqr(PetscLogReal(Ti_ev) - 2) / 16);
        } else { // lam_ei == lam_ie
          if (10 * Zj * Zj > Ti_ev) {
            ctx->lambdas[gridi][gridj] = ctx->lambdas[gridj][gridi] = 23 - PetscLogReal(PetscSqrtReal(ni) * Zj * PetscPowReal(Ti_ev, -1.5));
          } else {
            ctx->lambdas[gridi][gridj] = ctx->lambdas[gridj][gridi] = 24 - PetscLogReal(PetscSqrtReal(ni) / Ti_ev);
          }
        }
      } else { // lam_ii'
        PetscReal mui = ctx->masses[iii] / 1.6720e-27, Zi = ctx->charges[iii] / 1.6022e-19;
        PetscReal Tj_ev            = (ctx->thermal_temps[jjj] / 1.1604525e7) * 1000; // convert (back) to eV
        PetscReal muj              = ctx->masses[jjj] / 1.6720e-27;
        PetscReal nj               = ctx->n[jjj] * ctx->n_0;
        ctx->lambdas[gridi][gridj] = ctx->lambdas[gridj][gridi] = 23 - PetscLogReal(Zi * Zj * (mui + muj) / (mui * Tj_ev + muj * Ti_ev) * PetscSqrtReal(ni * Zi * Zi / Ti_ev + nj * Zj * Zj / Tj_ev));
      }
    }
  }
  //PetscReal v0 = PetscSqrtReal(ctx->k * ctx->thermal_temps[iii] / ctx->masses[iii]); /* arbitrary units for non-dimensionalization: plasma formulary def */
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode ProcessOptions(LandauCtx *ctx, const char prefix[])
{
  PetscBool flg, fileflg;
  PetscInt  ii, nt, nm, nc, num_species_grid[LANDAU_MAX_GRIDS], non_dim_grid;
  PetscReal lnLam = 10;
  DM        dummy;

  PetscFunctionBegin;
  PetscCall(DMCreate(ctx->comm, &dummy));
  /* get options - initialize context */
  ctx->verbose        = 1; // should be 0 for silent compliance
  ctx->batch_sz       = 1;
  ctx->batch_view_idx = 0;
  ctx->interpolate    = PETSC_TRUE;
  ctx->gpu_assembly   = PETSC_TRUE;
  ctx->norm_state     = 0;
  ctx->electronShift  = 0;
  ctx->M              = NULL;
  ctx->J              = NULL;
  /* geometry and grids */
  ctx->sphere    = PETSC_FALSE;
  ctx->use_p4est = PETSC_FALSE;
  ctx->simplex   = PETSC_FALSE;
  for (PetscInt grid = 0; grid < LANDAU_MAX_GRIDS; grid++) {
    ctx->radius[grid]             = 5.; /* thermal radius (velocity) */
    ctx->radius_perp[grid]        = 5.; /* thermal radius (velocity) */
    ctx->radius_par[grid]         = 5.; /* thermal radius (velocity) */
    ctx->numAMRRefine[grid]       = 0;
    ctx->postAMRRefine[grid]      = 0;
    ctx->species_offset[grid + 1] = 1; // one species default
    num_species_grid[grid]        = 0;
    ctx->plex[grid]               = NULL; /* cache as expensive to Convert */
  }
  ctx->species_offset[0] = 0;
  ctx->re_radius         = 0.;
  ctx->vperp0_radius1    = 0;
  ctx->vperp0_radius2    = 0;
  ctx->nZRefine1         = 0;
  ctx->nZRefine2         = 0;
  ctx->numRERefine       = 0;
  num_species_grid[0]    = 1; // one species default
  /* species - [0] electrons, [1] one ion species eg, duetarium, [2] heavy impurity ion, ... */
  ctx->charges[0]       = -1;                       /* electron charge (MKS) */
  ctx->masses[0]        = 1 / 1835.469965278441013; /* temporary value in proton mass */
  ctx->n[0]             = 1;
  ctx->v_0              = 1; /* thermal velocity, we could start with a scale != 1 */
  ctx->thermal_temps[0] = 1;
  /* constants, etc. */
  ctx->epsilon0 = 8.8542e-12;     /* permittivity of free space (MKS) F/m */
  ctx->k        = 1.38064852e-23; /* Boltzmann constant (MKS) J/K */
  ctx->n_0      = 1.e20;          /* typical plasma n, but could set it to 1 */
  ctx->Ez       = 0;
  for (PetscInt grid = 0; grid < LANDAU_NUM_TIMERS; grid++) ctx->times[grid] = 0;
  for (PetscInt ii = 0; ii < LANDAU_DIM; ii++) ctx->cells0[ii] = 2;
  if (LANDAU_DIM == 2) ctx->cells0[0] = 1;
  ctx->use_matrix_mass                = PETSC_FALSE;
  ctx->use_relativistic_corrections   = PETSC_FALSE;
  ctx->use_energy_tensor_trick        = PETSC_FALSE; /* Use Eero's trick for energy conservation v --> grad(v^2/2) */
  ctx->SData_d.w                      = NULL;
  ctx->SData_d.x                      = NULL;
  ctx->SData_d.y                      = NULL;
  ctx->SData_d.z                      = NULL;
  ctx->SData_d.invJ                   = NULL;
  ctx->jacobian_field_major_order     = PETSC_FALSE;
  ctx->SData_d.coo_elem_offsets       = NULL;
  ctx->SData_d.coo_elem_point_offsets = NULL;
  ctx->SData_d.coo_elem_fullNb        = NULL;
  ctx->SData_d.coo_size               = 0;
  PetscOptionsBegin(ctx->comm, prefix, "Options for Fokker-Plank-Landau collision operator", "none");
#if defined(PETSC_HAVE_KOKKOS)
  ctx->deviceType = LANDAU_KOKKOS;
  PetscCall(PetscStrncpy(ctx->filename, "kokkos", sizeof(ctx->filename)));
#else
  ctx->deviceType = LANDAU_CPU;
  PetscCall(PetscStrncpy(ctx->filename, "cpu", sizeof(ctx->filename)));
#endif
  PetscCall(PetscOptionsString("-dm_landau_device_type", "Use kernels on 'cpu' 'kokkos'", "plexland.c", ctx->filename, ctx->filename, sizeof(ctx->filename), NULL));
  PetscCall(PetscStrcmp("cpu", ctx->filename, &flg));
  if (flg) {
    ctx->deviceType = LANDAU_CPU;
  } else {
    PetscCall(PetscStrcmp("kokkos", ctx->filename, &flg));
    if (flg) ctx->deviceType = LANDAU_KOKKOS;
    else SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_device_type %s", ctx->filename);
  }
  ctx->filename[0] = '\0';
  PetscCall(PetscOptionsString("-dm_landau_filename", "file to read mesh from", "plexland.c", ctx->filename, ctx->filename, sizeof(ctx->filename), &fileflg));
  PetscCall(PetscOptionsReal("-dm_landau_electron_shift", "Shift in thermal velocity of electrons", "none", ctx->electronShift, &ctx->electronShift, NULL));
  PetscCall(PetscOptionsInt("-dm_landau_verbose", "Level of verbosity output", "plexland.c", ctx->verbose, &ctx->verbose, NULL));
  PetscCall(PetscOptionsInt("-dm_landau_batch_size", "Number of 'vertices' to batch", "ex2.c", ctx->batch_sz, &ctx->batch_sz, NULL));
  PetscCheck(LANDAU_MAX_BATCH_SZ >= ctx->batch_sz, ctx->comm, PETSC_ERR_ARG_WRONG, "LANDAU_MAX_BATCH_SZ %" PetscInt_FMT " < ctx->batch_sz %" PetscInt_FMT, (PetscInt)LANDAU_MAX_BATCH_SZ, ctx->batch_sz);
  PetscCall(PetscOptionsInt("-dm_landau_batch_view_idx", "Index of batch for diagnostics like plotting", "ex2.c", ctx->batch_view_idx, &ctx->batch_view_idx, NULL));
  PetscCheck(ctx->batch_view_idx < ctx->batch_sz, ctx->comm, PETSC_ERR_ARG_WRONG, "-ctx->batch_view_idx %" PetscInt_FMT " > ctx->batch_sz %" PetscInt_FMT, ctx->batch_view_idx, ctx->batch_sz);
  PetscCall(PetscOptionsReal("-dm_landau_Ez", "Initial parallel electric field in unites of Conner-Hastie critical field", "plexland.c", ctx->Ez, &ctx->Ez, NULL));
  PetscCall(PetscOptionsReal("-dm_landau_n_0", "Normalization constant for number density", "plexland.c", ctx->n_0, &ctx->n_0, NULL));
  PetscCall(PetscOptionsBool("-dm_landau_use_mataxpy_mass", "Use fast but slightly fragile MATAXPY to add mass term", "plexland.c", ctx->use_matrix_mass, &ctx->use_matrix_mass, NULL));
  PetscCall(PetscOptionsBool("-dm_landau_use_relativistic_corrections", "Use relativistic corrections", "plexland.c", ctx->use_relativistic_corrections, &ctx->use_relativistic_corrections, NULL));
  PetscCall(PetscOptionsBool("-dm_landau_simplex", "Use simplex elements", "plexland.c", ctx->simplex, &ctx->simplex, NULL));
  if (LANDAU_DIM == 2 && ctx->use_relativistic_corrections) ctx->use_relativistic_corrections = PETSC_FALSE; // should warn
  PetscCall(PetscOptionsBool("-dm_landau_use_energy_tensor_trick", "Use Eero's trick of using grad(v^2/2) instead of v as args to Landau tensor to conserve energy with relativistic corrections and Q1 elements", "plexland.c", ctx->use_energy_tensor_trick,
                             &ctx->use_energy_tensor_trick, NULL));

  /* get num species with temperature, set defaults */
  for (ii = 1; ii < LANDAU_MAX_SPECIES; ii++) {
    ctx->thermal_temps[ii] = 1;
    ctx->charges[ii]       = 1;
    ctx->masses[ii]        = 1;
    ctx->n[ii]             = 1;
  }
  nt = LANDAU_MAX_SPECIES;
  PetscCall(PetscOptionsRealArray("-dm_landau_thermal_temps", "Temperature of each species [e,i_0,i_1,...] in keV (must be set to set number of species)", "plexland.c", ctx->thermal_temps, &nt, &flg));
  if (flg) {
    PetscCall(PetscInfo(dummy, "num_species set to number of thermal temps provided (%" PetscInt_FMT ")\n", nt));
    ctx->num_species = nt;
  } else SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_thermal_temps ,t1,t2,.. must be provided to set the number of species");
  for (ii = 0; ii < ctx->num_species; ii++) ctx->thermal_temps[ii] *= 1.1604525e7; /* convert to Kelvin */
  nm = LANDAU_MAX_SPECIES - 1;
  PetscCall(PetscOptionsRealArray("-dm_landau_ion_masses", "Mass of each species in units of proton mass [i_0=2,i_1=40...]", "plexland.c", &ctx->masses[1], &nm, &flg));
  PetscCheck(!flg || nm == ctx->num_species - 1, ctx->comm, PETSC_ERR_ARG_WRONG, "num ion masses %" PetscInt_FMT " != num species %" PetscInt_FMT, nm, ctx->num_species - 1);
  nm = LANDAU_MAX_SPECIES;
  PetscCall(PetscOptionsRealArray("-dm_landau_n", "Number density of each species = n_s * n_0", "plexland.c", ctx->n, &nm, &flg));
  PetscCheck(!flg || nm == ctx->num_species, ctx->comm, PETSC_ERR_ARG_WRONG, "wrong num n: %" PetscInt_FMT " != num species %" PetscInt_FMT, nm, ctx->num_species);
  for (ii = 0; ii < LANDAU_MAX_SPECIES; ii++) ctx->masses[ii] *= 1.6720e-27; /* scale by proton mass kg */
  ctx->masses[0] = 9.10938356e-31;                                           /* electron mass kg (should be about right already) */
  nc             = LANDAU_MAX_SPECIES - 1;
  PetscCall(PetscOptionsRealArray("-dm_landau_ion_charges", "Charge of each species in units of proton charge [i_0=2,i_1=18,...]", "plexland.c", &ctx->charges[1], &nc, &flg));
  if (flg) PetscCheck(nc == ctx->num_species - 1, ctx->comm, PETSC_ERR_ARG_WRONG, "num charges %" PetscInt_FMT " != num species %" PetscInt_FMT, nc, ctx->num_species - 1);
  for (ii = 0; ii < LANDAU_MAX_SPECIES; ii++) ctx->charges[ii] *= 1.6022e-19; /* electron/proton charge (MKS) */
  /* geometry and grids */
  nt = LANDAU_MAX_GRIDS;
  PetscCall(PetscOptionsIntArray("-dm_landau_num_species_grid", "Number of species on each grid: [ 1, ....] or [S, 0 ....] for single grid", "plexland.c", num_species_grid, &nt, &flg));
  if (flg) {
    ctx->num_grids = nt;
    for (ii = nt = 0; ii < ctx->num_grids; ii++) nt += num_species_grid[ii];
    PetscCheck(ctx->num_species == nt, ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_num_species_grid: sum %" PetscInt_FMT " != num_species = %" PetscInt_FMT ". %" PetscInt_FMT " grids (check that number of grids <= LANDAU_MAX_GRIDS = %d)", nt, ctx->num_species,
               ctx->num_grids, LANDAU_MAX_GRIDS);
  } else {
    if (ctx->num_species > LANDAU_MAX_GRIDS) {
      num_species_grid[0] = 1;
      num_species_grid[1] = ctx->num_species - 1;
      ctx->num_grids      = 2;
    } else {
      ctx->num_grids = ctx->num_species;
      for (ii = 0; ii < ctx->num_grids; ii++) num_species_grid[ii] = 1;
    }
  }
  for (ctx->species_offset[0] = ii = 0; ii < ctx->num_grids; ii++) ctx->species_offset[ii + 1] = ctx->species_offset[ii] + num_species_grid[ii];
  PetscCheck(ctx->species_offset[ctx->num_grids] == ctx->num_species, ctx->comm, PETSC_ERR_ARG_WRONG, "ctx->species_offset[ctx->num_grids] %" PetscInt_FMT " != ctx->num_species = %" PetscInt_FMT " ???????????", ctx->species_offset[ctx->num_grids],
             ctx->num_species);
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
    int iii                  = ctx->species_offset[grid];                                          // normalize with first (arbitrary) species on grid
    ctx->thermal_speed[grid] = PetscSqrtReal(ctx->k * ctx->thermal_temps[iii] / ctx->masses[iii]); /* arbitrary units for non-dimensionalization: plasma formulary def */
  }
  // get lambdas here because we need them for t_0 etc
  PetscCall(PetscOptionsReal("-dm_landau_ln_lambda", "Universal cross section parameter. Default uses NRL formulas", "plexland.c", lnLam, &lnLam, &flg));
  if (flg) {
    for (PetscInt grid = 0; grid < LANDAU_MAX_GRIDS; grid++) {
      for (PetscInt gridj = 0; gridj < LANDAU_MAX_GRIDS; gridj++) ctx->lambdas[gridj][grid] = lnLam; /* cross section ratio large - small angle collisions */
    }
  } else {
    PetscCall(makeLambdas(ctx));
  }
  non_dim_grid = 0;
  PetscCall(PetscOptionsInt("-dm_landau_normalization_grid", "Index of grid to use for setting v_0, m_0, t_0. (Not recommended)", "plexland.c", non_dim_grid, &non_dim_grid, &flg));
  if (non_dim_grid != 0) PetscCall(PetscInfo(dummy, "Normalization grid set to %" PetscInt_FMT ", but non-default not well verified\n", non_dim_grid));
  PetscCheck(non_dim_grid >= 0 && non_dim_grid < ctx->num_species, ctx->comm, PETSC_ERR_ARG_WRONG, "Normalization grid wrong: %" PetscInt_FMT, non_dim_grid);
  ctx->v_0 = ctx->thermal_speed[non_dim_grid]; /* arbitrary units for non dimensionalization: global mean velocity in 1D of electrons */
  ctx->m_0 = ctx->masses[non_dim_grid];        /* arbitrary reference mass, electrons */
  ctx->t_0 = 8 * PETSC_PI * PetscSqr(ctx->epsilon0 * ctx->m_0 / PetscSqr(ctx->charges[non_dim_grid])) / ctx->lambdas[non_dim_grid][non_dim_grid] / ctx->n_0 * PetscPowReal(ctx->v_0, 3); /* note, this t_0 makes nu[non_dim_grid,non_dim_grid]=1 */
  /* domain */
  nt = LANDAU_MAX_GRIDS;
  PetscCall(PetscOptionsRealArray("-dm_landau_domain_radius", "Phase space size in units of thermal velocity of grid", "plexland.c", ctx->radius, &nt, &flg));
  if (flg) {
    PetscCheck(nt >= ctx->num_grids, ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_domain_radius: given %" PetscInt_FMT " radius != number grids %" PetscInt_FMT, nt, ctx->num_grids);
    while (nt--) ctx->radius_par[nt] = ctx->radius_perp[nt] = ctx->radius[nt];
  } else {
    nt = LANDAU_MAX_GRIDS;
    PetscCall(PetscOptionsRealArray("-dm_landau_domain_max_par", "Parallel velocity domain size in units of thermal velocity of grid", "plexland.c", ctx->radius_par, &nt, &flg));
    if (flg) PetscCheck(nt >= ctx->num_grids, ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_domain_max_par: given %" PetscInt_FMT " radius != number grids %" PetscInt_FMT, nt, ctx->num_grids);
    PetscCall(PetscOptionsRealArray("-dm_landau_domain_max_perp", "Perpendicular velocity domain size in units of thermal velocity of grid", "plexland.c", ctx->radius_perp, &nt, &flg));
    if (flg) PetscCheck(nt >= ctx->num_grids, ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_domain_max_perp: given %" PetscInt_FMT " radius != number grids %" PetscInt_FMT, nt, ctx->num_grids);
  }
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
    if (flg && ctx->radius[grid] <= 0) { /* negative is ratio of c - need to set par and perp with this -- todo */
      if (ctx->radius[grid] == 0) ctx->radius[grid] = 0.75;
      else ctx->radius[grid] = -ctx->radius[grid];
      ctx->radius[grid] = ctx->radius[grid] * SPEED_OF_LIGHT / ctx->v_0; // use any species on grid to normalize (v_0 same for all on grid)
      PetscCall(PetscInfo(dummy, "Change domain radius to %g for grid %" PetscInt_FMT "\n", (double)ctx->radius[grid], grid));
    }
    ctx->radius[grid] *= ctx->thermal_speed[grid] / ctx->v_0;      // scale domain by thermal radius relative to v_0
    ctx->radius_perp[grid] *= ctx->thermal_speed[grid] / ctx->v_0; // scale domain by thermal radius relative to v_0
    ctx->radius_par[grid] *= ctx->thermal_speed[grid] / ctx->v_0;  // scale domain by thermal radius relative to v_0
  }
  /* amr parameters */
  if (!fileflg) {
    nt = LANDAU_MAX_GRIDS;
    PetscCall(PetscOptionsIntArray("-dm_landau_amr_levels_max", "Number of AMR levels of refinement around origin, after (RE) refinements along z", "plexland.c", ctx->numAMRRefine, &nt, &flg));
    PetscCheck(!flg || nt >= ctx->num_grids, ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_amr_levels_max: given %" PetscInt_FMT " != number grids %" PetscInt_FMT, nt, ctx->num_grids);
    nt = LANDAU_MAX_GRIDS;
    PetscCall(PetscOptionsIntArray("-dm_landau_amr_post_refine", "Number of levels to uniformly refine after AMR", "plexland.c", ctx->postAMRRefine, &nt, &flg));
    for (ii = 1; ii < ctx->num_grids; ii++) ctx->postAMRRefine[ii] = ctx->postAMRRefine[0]; // all grids the same now
    PetscCall(PetscOptionsInt("-dm_landau_amr_re_levels", "Number of levels to refine along v_perp=0, z>0", "plexland.c", ctx->numRERefine, &ctx->numRERefine, &flg));
    PetscCall(PetscOptionsInt("-dm_landau_amr_z_refine_pre", "Number of levels to refine along v_perp=0 before origin refine", "plexland.c", ctx->nZRefine1, &ctx->nZRefine1, &flg));
    PetscCall(PetscOptionsInt("-dm_landau_amr_z_refine_post", "Number of levels to refine along v_perp=0 after origin refine", "plexland.c", ctx->nZRefine2, &ctx->nZRefine2, &flg));
    PetscCall(PetscOptionsReal("-dm_landau_re_radius", "velocity range to refine on positive (z>0) r=0 axis for runaways", "plexland.c", ctx->re_radius, &ctx->re_radius, &flg));
    PetscCall(PetscOptionsReal("-dm_landau_z_radius_pre", "velocity range to refine r=0 axis (for electrons)", "plexland.c", ctx->vperp0_radius1, &ctx->vperp0_radius1, &flg));
    PetscCall(PetscOptionsReal("-dm_landau_z_radius_post", "velocity range to refine r=0 axis (for electrons) after origin AMR", "plexland.c", ctx->vperp0_radius2, &ctx->vperp0_radius2, &flg));
    /* spherical domain (not used) */
    PetscCall(PetscOptionsBool("-dm_landau_sphere", "use sphere/semi-circle domain instead of rectangle", "plexland.c", ctx->sphere, &ctx->sphere, NULL));
    if (ctx->sphere || ctx->simplex) {
      ctx->sphere_inner_radius_90degree = 0.40;
      ctx->sphere_inner_radius_45degree = 0.35;
      PetscCall(PetscOptionsReal("-dm_landau_sphere_inner_radius_90degree_scale", "Scaling of radius for inner circle on 90 degree grid", "plexland.c", ctx->sphere_inner_radius_90degree, &ctx->sphere_inner_radius_90degree, NULL));
      PetscCall(PetscOptionsReal("-dm_landau_sphere_inner_radius_45degree_scale", "Scaling of radius for inner circle on 45 degree grid", "plexland.c", ctx->sphere_inner_radius_45degree, &ctx->sphere_inner_radius_45degree, NULL));
    } else {
      nt = LANDAU_DIM;
      PetscCall(PetscOptionsIntArray("-dm_landau_num_cells", "Number of cells in each dimension of base grid", "plexland.c", ctx->cells0, &nt, &flg));
    }
  }
  /* processing options */
  PetscCall(PetscOptionsBool("-dm_landau_gpu_assembly", "Assemble Jacobian on GPU", "plexland.c", ctx->gpu_assembly, &ctx->gpu_assembly, NULL));
  PetscCall(PetscOptionsBool("-dm_landau_jacobian_field_major_order", "Reorder Jacobian for GPU assembly with field major, or block diagonal, ordering (DEPRECATED)", "plexland.c", ctx->jacobian_field_major_order, &ctx->jacobian_field_major_order, NULL));
  if (ctx->jacobian_field_major_order) PetscCheck(ctx->gpu_assembly, ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_jacobian_field_major_order requires -dm_landau_gpu_assembly");
  PetscCheck(!ctx->jacobian_field_major_order, ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_jacobian_field_major_order DEPRECATED");
  PetscOptionsEnd();

  for (ii = ctx->num_species; ii < LANDAU_MAX_SPECIES; ii++) ctx->masses[ii] = ctx->thermal_temps[ii] = ctx->charges[ii] = 0;
  if (ctx->verbose != 0) {
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "masses:        e=%10.3e; ions in proton mass units:   %10.3e %10.3e ...\n", (double)ctx->masses[0], (double)(ctx->masses[1] / 1.6720e-27), (double)(ctx->num_species > 2 ? ctx->masses[2] / 1.6720e-27 : 0)));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "charges:       e=%10.3e; charges in elementary units: %10.3e %10.3e\n", (double)ctx->charges[0], (double)(-ctx->charges[1] / ctx->charges[0]), (double)(ctx->num_species > 2 ? -ctx->charges[2] / ctx->charges[0] : 0)));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "n:             e: %10.3e                           i: %10.3e %10.3e\n", (double)ctx->n[0], (double)ctx->n[1], (double)(ctx->num_species > 2 ? ctx->n[2] : 0)));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "thermal T (K): e=%10.3e i=%10.3e %10.3e. Normalization grid %d: v_0=%10.3e (%10.3ec) n_0=%10.3e t_0=%10.3e %" PetscInt_FMT " batched, view batch %" PetscInt_FMT "\n", (double)ctx->thermal_temps[0],
                          (double)ctx->thermal_temps[1], (double)((ctx->num_species > 2) ? ctx->thermal_temps[2] : 0), (int)non_dim_grid, (double)ctx->v_0, (double)(ctx->v_0 / SPEED_OF_LIGHT), (double)ctx->n_0, (double)ctx->t_0, ctx->batch_sz, ctx->batch_view_idx));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Domain radius (AMR levels) grid %d: par=%10.3e perp=%10.3e (%" PetscInt_FMT ") ", 0, (double)ctx->radius_par[0], (double)ctx->radius_perp[0], ctx->numAMRRefine[0]));
    for (ii = 1; ii < ctx->num_grids; ii++) PetscCall(PetscPrintf(PETSC_COMM_WORLD, ", %" PetscInt_FMT ": par=%10.3e perp=%10.3e (%" PetscInt_FMT ") ", ii, (double)ctx->radius_par[ii], (double)ctx->radius_perp[ii], ctx->numAMRRefine[ii]));
    if (ctx->use_relativistic_corrections) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\nUse relativistic corrections\n"));
    else PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n"));
  }
  PetscCall(DMDestroy(&dummy));
  {
    PetscMPIInt rank;
    PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
    ctx->stage = 0;
    PetscCall(PetscLogEventRegister("Landau Create", DM_CLASSID, &ctx->events[13]));   /* 13 */
    PetscCall(PetscLogEventRegister(" GPU ass. setup", DM_CLASSID, &ctx->events[2]));  /* 2 */
    PetscCall(PetscLogEventRegister(" Build matrix", DM_CLASSID, &ctx->events[12]));   /* 12 */
    PetscCall(PetscLogEventRegister(" Assembly maps", DM_CLASSID, &ctx->events[15]));  /* 15 */
    PetscCall(PetscLogEventRegister("Landau Mass mat", DM_CLASSID, &ctx->events[14])); /* 14 */
    PetscCall(PetscLogEventRegister("Landau Operator", DM_CLASSID, &ctx->events[11])); /* 11 */
    PetscCall(PetscLogEventRegister("Landau Jacobian", DM_CLASSID, &ctx->events[0]));  /* 0 */
    PetscCall(PetscLogEventRegister("Landau Mass", DM_CLASSID, &ctx->events[9]));      /* 9 */
    PetscCall(PetscLogEventRegister(" Preamble", DM_CLASSID, &ctx->events[10]));       /* 10 */
    PetscCall(PetscLogEventRegister(" static IP Data", DM_CLASSID, &ctx->events[7]));  /* 7 */
    PetscCall(PetscLogEventRegister(" dynamic IP-Jac", DM_CLASSID, &ctx->events[1]));  /* 1 */
    PetscCall(PetscLogEventRegister(" Kernel-init", DM_CLASSID, &ctx->events[3]));     /* 3 */
    PetscCall(PetscLogEventRegister(" Jac-f-df (GPU)", DM_CLASSID, &ctx->events[8]));  /* 8 */
    PetscCall(PetscLogEventRegister(" J Kernel (GPU)", DM_CLASSID, &ctx->events[4]));  /* 4 */
    PetscCall(PetscLogEventRegister(" M Kernel (GPU)", DM_CLASSID, &ctx->events[16])); /* 16 */
    PetscCall(PetscLogEventRegister(" Copy to CPU", DM_CLASSID, &ctx->events[5]));     /* 5 */
    PetscCall(PetscLogEventRegister(" CPU assemble", DM_CLASSID, &ctx->events[6]));    /* 6 */

    if (rank) { /* turn off output stuff for duplicate runs - do we need to add the prefix to all this? */
      PetscCall(PetscOptionsClearValue(NULL, "-snes_converged_reason"));
      PetscCall(PetscOptionsClearValue(NULL, "-ksp_converged_reason"));
      PetscCall(PetscOptionsClearValue(NULL, "-snes_monitor"));
      PetscCall(PetscOptionsClearValue(NULL, "-ksp_monitor"));
      PetscCall(PetscOptionsClearValue(NULL, "-ts_monitor"));
      PetscCall(PetscOptionsClearValue(NULL, "-ts_view"));
      PetscCall(PetscOptionsClearValue(NULL, "-ts_adapt_monitor"));
      PetscCall(PetscOptionsClearValue(NULL, "-dm_landau_amr_dm_view"));
      PetscCall(PetscOptionsClearValue(NULL, "-dm_landau_amr_vec_view"));
      PetscCall(PetscOptionsClearValue(NULL, "-dm_landau_mass_dm_view"));
      PetscCall(PetscOptionsClearValue(NULL, "-dm_landau_mass_view"));
      PetscCall(PetscOptionsClearValue(NULL, "-dm_landau_jacobian_view"));
      PetscCall(PetscOptionsClearValue(NULL, "-dm_landau_mat_view"));
      PetscCall(PetscOptionsClearValue(NULL, "-pc_bjkokkos_ksp_converged_reason"));
      PetscCall(PetscOptionsClearValue(NULL, "-pc_bjkokkos_ksp_monitor"));
      PetscCall(PetscOptionsClearValue(NULL, "-"));
      PetscCall(PetscOptionsClearValue(NULL, "-info"));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode CreateStaticData(PetscInt dim, IS grid_batch_is_inv[], LandauCtx *ctx)
{
  PetscSection     section[LANDAU_MAX_GRIDS], globsection[LANDAU_MAX_GRIDS];
  PetscQuadrature  quad;
  const PetscReal *quadWeights;
  PetscReal        invMass[LANDAU_MAX_SPECIES], nu_alpha[LANDAU_MAX_SPECIES], nu_beta[LANDAU_MAX_SPECIES];
  PetscInt         numCells[LANDAU_MAX_GRIDS], Nq, Nb, Nf[LANDAU_MAX_GRIDS], ncellsTot = 0, MAP_BF_SIZE = 64 * LANDAU_DIM * LANDAU_DIM * LANDAU_MAX_Q_FACE * LANDAU_MAX_SPECIES;
  PetscTabulation *Tf;
  PetscDS          prob;

  PetscFunctionBegin;
  PetscCall(PetscFEGetDimension(ctx->fe[0], &Nb));
  PetscCheck(Nb <= LANDAU_MAX_NQND, ctx->comm, PETSC_ERR_ARG_WRONG, "Order too high. Nb = %" PetscInt_FMT " > LANDAU_MAX_NQND (%d)", Nb, LANDAU_MAX_NQND);
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
    for (PetscInt ii = ctx->species_offset[grid]; ii < ctx->species_offset[grid + 1]; ii++) {
      invMass[ii]  = ctx->m_0 / ctx->masses[ii];
      nu_alpha[ii] = PetscSqr(ctx->charges[ii] / ctx->m_0) * ctx->m_0 / ctx->masses[ii];
      nu_beta[ii]  = PetscSqr(ctx->charges[ii] / ctx->epsilon0) / (8 * PETSC_PI) * ctx->t_0 * ctx->n_0 / PetscPowReal(ctx->v_0, 3);
    }
  }
  if (ctx->verbose == 4) {
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "nu_alpha: "));
    for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
      int iii = ctx->species_offset[grid];
      for (PetscInt ii = iii; ii < ctx->species_offset[grid + 1]; ii++) PetscCall(PetscPrintf(PETSC_COMM_WORLD, " %e", (double)nu_alpha[ii]));
    }
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\nnu_beta: "));
    for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
      int iii = ctx->species_offset[grid];
      for (PetscInt ii = iii; ii < ctx->species_offset[grid + 1]; ii++) PetscCall(PetscPrintf(PETSC_COMM_WORLD, " %e", (double)nu_beta[ii]));
    }
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\nnu_alpha[i]*nu_beta[j]*lambda[i][j]:\n"));
    for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
      int iii = ctx->species_offset[grid];
      for (PetscInt ii = iii; ii < ctx->species_offset[grid + 1]; ii++) {
        for (PetscInt gridj = 0; gridj < ctx->num_grids; gridj++) {
          int jjj = ctx->species_offset[gridj];
          for (PetscInt jj = jjj; jj < ctx->species_offset[gridj + 1]; jj++) PetscCall(PetscPrintf(PETSC_COMM_WORLD, " %14.9e", (double)(nu_alpha[ii] * nu_beta[jj] * ctx->lambdas[grid][gridj])));
        }
        PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n"));
      }
    }
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "lambda[i][j]:\n"));
    for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
      int iii = ctx->species_offset[grid];
      for (PetscInt ii = iii; ii < ctx->species_offset[grid + 1]; ii++) {
        for (PetscInt gridj = 0; gridj < ctx->num_grids; gridj++) {
          int jjj = ctx->species_offset[gridj];
          for (PetscInt jj = jjj; jj < ctx->species_offset[gridj + 1]; jj++) PetscCall(PetscPrintf(PETSC_COMM_WORLD, " %14.9e", (double)ctx->lambdas[grid][gridj]));
        }
        PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n"));
      }
    }
  }
  PetscCall(DMGetDS(ctx->plex[0], &prob));    // same DS for all grids
  PetscCall(PetscDSGetTabulation(prob, &Tf)); // Bf, &Df same for all grids
  /* DS, Tab and quad is same on all grids */
  PetscCheck(ctx->plex[0], ctx->comm, PETSC_ERR_ARG_WRONG, "Plex not created");
  PetscCall(PetscFEGetQuadrature(ctx->fe[0], &quad));
  PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, &quadWeights));
  PetscCheck(Nq <= LANDAU_MAX_NQND, ctx->comm, PETSC_ERR_ARG_WRONG, "Order too high. Nq = %" PetscInt_FMT " > LANDAU_MAX_NQND (%d)", Nq, LANDAU_MAX_NQND);
  /* setup each grid */
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
    PetscInt cStart, cEnd;
    PetscCheck(ctx->plex[grid] != NULL, ctx->comm, PETSC_ERR_ARG_WRONG, "Plex not created");
    PetscCall(DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd));
    numCells[grid] = cEnd - cStart; // grids can have different topology
    PetscCall(DMGetLocalSection(ctx->plex[grid], &section[grid]));
    PetscCall(DMGetGlobalSection(ctx->plex[grid], &globsection[grid]));
    PetscCall(PetscSectionGetNumFields(section[grid], &Nf[grid]));
    ncellsTot += numCells[grid];
  }
  /* create GPU assembly data */
  if (ctx->gpu_assembly) { /* we need GPU object with GPU assembly */
    PetscContainer container;
    PetscScalar   *elemMatrix, *elMat;
    pointInterpolationP4est(*pointMaps)[LANDAU_MAX_Q_FACE];
    P4estVertexMaps *maps;
    const PetscInt  *plex_batch = NULL, elMatSz = Nb * Nb * ctx->num_species * ctx->num_species;
    LandauIdx       *coo_elem_offsets = NULL, *coo_elem_fullNb = NULL, (*coo_elem_point_offsets)[LANDAU_MAX_NQND + 1] = NULL;
    /* create GPU assembly data */
    PetscCall(PetscInfo(ctx->plex[0], "Make GPU maps %d\n", 1));
    PetscCall(PetscLogEventBegin(ctx->events[2], 0, 0, 0, 0));
    PetscCall(PetscMalloc(sizeof(*maps) * ctx->num_grids, &maps));
    PetscCall(PetscMalloc(sizeof(*pointMaps) * MAP_BF_SIZE, &pointMaps));
    PetscCall(PetscMalloc(sizeof(*elemMatrix) * elMatSz, &elemMatrix));

    {                                                                                                                             // setup COO assembly -- put COO metadata directly in ctx->SData_d
      PetscCall(PetscMalloc3(ncellsTot + 1, &coo_elem_offsets, ncellsTot, &coo_elem_fullNb, ncellsTot, &coo_elem_point_offsets)); // array of integer pointers
      coo_elem_offsets[0] = 0;                                                                                                    // finish later
      PetscCall(PetscInfo(ctx->plex[0], "COO initialization, %" PetscInt_FMT " cells\n", ncellsTot));
      ctx->SData_d.coo_n_cellsTot         = ncellsTot;
      ctx->SData_d.coo_elem_offsets       = (void *)coo_elem_offsets;
      ctx->SData_d.coo_elem_fullNb        = (void *)coo_elem_fullNb;
      ctx->SData_d.coo_elem_point_offsets = (void *)coo_elem_point_offsets;
    }

    ctx->SData_d.coo_max_fullnb = 0;
    for (PetscInt grid = 0, glb_elem_idx = 0; grid < ctx->num_grids; grid++) {
      PetscInt cStart, cEnd, Nfloc = Nf[grid], totDim = Nfloc * Nb;
      if (grid_batch_is_inv[grid]) PetscCall(ISGetIndices(grid_batch_is_inv[grid], &plex_batch));
      PetscCheck(!plex_batch, ctx->comm, PETSC_ERR_ARG_WRONG, "-dm_landau_jacobian_field_major_order DEPRECATED");
      PetscCall(DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd));
      // make maps
      maps[grid].d_self       = NULL;
      maps[grid].num_elements = numCells[grid];
      maps[grid].num_face     = (PetscInt)(pow(Nq, 1. / ((double)dim)) + .001);                 // Q
      maps[grid].num_face     = (PetscInt)(pow(maps[grid].num_face, (double)(dim - 1)) + .001); // Q^2
      maps[grid].num_reduced  = 0;
      maps[grid].deviceType   = ctx->deviceType;
      maps[grid].numgrids     = ctx->num_grids;
      // count reduced and get
      PetscCall(PetscMalloc(maps[grid].num_elements * sizeof(*maps[grid].gIdx), &maps[grid].gIdx));
      for (int ej = cStart, eidx = 0; ej < cEnd; ++ej, ++eidx, glb_elem_idx++) {
        if (coo_elem_offsets) coo_elem_offsets[glb_elem_idx + 1] = coo_elem_offsets[glb_elem_idx]; // start with last one, then add
        for (int fieldA = 0; fieldA < Nf[grid]; fieldA++) {
          int fullNb = 0;
          for (int q = 0; q < Nb; ++q) {
            PetscInt     numindices, *indices;
            PetscScalar *valuesOrig = elMat = elemMatrix;
            PetscCall(PetscArrayzero(elMat, totDim * totDim));
            elMat[(fieldA * Nb + q) * totDim + fieldA * Nb + q] = 1;
            PetscCall(DMPlexGetClosureIndices(ctx->plex[grid], section[grid], globsection[grid], ej, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **)&elMat));
            if (ctx->simplex) {
              PetscCheck(numindices == Nb, ctx->comm, PETSC_ERR_ARG_WRONG, "numindices != Nb numindices=%d Nb=%d", (int)numindices, (int)Nb);
              for (int q = 0; q < numindices; ++q) { maps[grid].gIdx[eidx][fieldA][q] = (LandauIdx)indices[q]; }
              fullNb++;
            } else {
              for (PetscInt f = 0; f < numindices; ++f) { // look for a non-zero on the diagonal (is this too complicated for simplices?)
                if (PetscAbs(PetscRealPart(elMat[f * numindices + f])) > PETSC_MACHINE_EPSILON) {
                  // found it
                  if (PetscAbs(PetscRealPart(elMat[f * numindices + f] - 1.)) < PETSC_MACHINE_EPSILON) { // normal vertex 1.0
                    if (plex_batch) {
                      maps[grid].gIdx[eidx][fieldA][q] = (LandauIdx)plex_batch[indices[f]];
                    } else {
                      maps[grid].gIdx[eidx][fieldA][q] = (LandauIdx)indices[f];
                    }
                    fullNb++;
                  } else { //found a constraint
                    int            jj                = 0;
                    PetscReal      sum               = 0;
                    const PetscInt ff                = f;
                    maps[grid].gIdx[eidx][fieldA][q] = -maps[grid].num_reduced - 1; // store (-)index: id = -(idx+1): idx = -id - 1
                    PetscCheck(!ctx->simplex, ctx->comm, PETSC_ERR_ARG_WRONG, "No constraints with simplex");
                    do {                                                                                              // constraints are continuous in Plex - exploit that here
                      int ii;                                                                                         // get 'scale'
                      for (ii = 0, pointMaps[maps[grid].num_reduced][jj].scale = 0; ii < maps[grid].num_face; ii++) { // sum row of outer product to recover vector value
                        if (ff + ii < numindices) {                                                                   // 3D has Q and Q^2 interps so might run off end. We could test that elMat[f*numindices + ff + ii] > 0, and break if not
                          pointMaps[maps[grid].num_reduced][jj].scale += PetscRealPart(elMat[f * numindices + ff + ii]);
                        }
                      }
                      sum += pointMaps[maps[grid].num_reduced][jj].scale; // diagnostic
                      // get 'gid'
                      if (pointMaps[maps[grid].num_reduced][jj].scale == 0) pointMaps[maps[grid].num_reduced][jj].gid = -1; // 3D has Q and Q^2 interps
                      else {
                        if (plex_batch) {
                          pointMaps[maps[grid].num_reduced][jj].gid = plex_batch[indices[f]];
                        } else {
                          pointMaps[maps[grid].num_reduced][jj].gid = indices[f];
                        }
                        fullNb++;
                      }
                    } while (++jj < maps[grid].num_face && ++f < numindices); // jj is incremented if we hit the end
                    while (jj < maps[grid].num_face) {
                      pointMaps[maps[grid].num_reduced][jj].scale = 0;
                      pointMaps[maps[grid].num_reduced][jj].gid   = -1;
                      jj++;
                    }
                    if (PetscAbs(sum - 1.0) > 10 * PETSC_MACHINE_EPSILON) { // debug
                      int       d, f;
                      PetscReal tmp = 0;
                      PetscCall(PetscPrintf(PETSC_COMM_SELF, "\t\t%d.%d.%d) ERROR total I = %22.16e (LANDAU_MAX_Q_FACE=%d, #face=%d)\n", eidx, q, fieldA, (double)sum, LANDAU_MAX_Q_FACE, maps[grid].num_face));
                      for (d = 0, tmp = 0; d < numindices; ++d) {
                        if (tmp != 0 && PetscAbs(tmp - 1.0) > 10 * PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%3d) %3" PetscInt_FMT ": ", d, indices[d]));
                        for (f = 0; f < numindices; ++f) tmp += PetscRealPart(elMat[d * numindices + f]);
                        if (tmp != 0) PetscCall(PetscPrintf(ctx->comm, " | %22.16e\n", (double)tmp));
                      }
                    }
                    maps[grid].num_reduced++;
                    PetscCheck(maps[grid].num_reduced < MAP_BF_SIZE, PETSC_COMM_SELF, PETSC_ERR_PLIB, "maps[grid].num_reduced %d > %" PetscInt_FMT, maps[grid].num_reduced, MAP_BF_SIZE);
                  }
                  break;
                }
              }
            } // !simplex
            // cleanup
            PetscCall(DMPlexRestoreClosureIndices(ctx->plex[grid], section[grid], globsection[grid], ej, PETSC_TRUE, &numindices, &indices, NULL, (PetscScalar **)&elMat));
            if (elMat != valuesOrig) PetscCall(DMRestoreWorkArray(ctx->plex[grid], numindices * numindices, MPIU_SCALAR, &elMat));
          }
          {                                                        // setup COO assembly
            coo_elem_offsets[glb_elem_idx + 1] += fullNb * fullNb; // one species block, adds a block for each species, on this element in this grid
            if (fieldA == 0) {                                     // cache full Nb for this element, on this grid per species
              coo_elem_fullNb[glb_elem_idx] = fullNb;
              if (fullNb > ctx->SData_d.coo_max_fullnb) ctx->SData_d.coo_max_fullnb = fullNb;
            } else PetscCheck(coo_elem_fullNb[glb_elem_idx] == fullNb, PETSC_COMM_SELF, PETSC_ERR_PLIB, "full element size change with species %d %d", coo_elem_fullNb[glb_elem_idx], fullNb);
          }
        } // field
      }   // cell
      // allocate and copy point data maps[grid].gIdx[eidx][field][q]
      PetscCall(PetscMalloc(maps[grid].num_reduced * sizeof(*maps[grid].c_maps), &maps[grid].c_maps));
      for (int ej = 0; ej < maps[grid].num_reduced; ++ej) {
        for (int q = 0; q < maps[grid].num_face; ++q) {
          maps[grid].c_maps[ej][q].scale = pointMaps[ej][q].scale;
          maps[grid].c_maps[ej][q].gid   = pointMaps[ej][q].gid;
        }
      }
#if defined(PETSC_HAVE_KOKKOS)
      if (ctx->deviceType == LANDAU_KOKKOS) {
        PetscCall(LandauKokkosCreateMatMaps(maps, pointMaps, Nf, grid)); // implies Kokkos does
      }
#endif
      if (plex_batch) {
        PetscCall(ISRestoreIndices(grid_batch_is_inv[grid], &plex_batch));
        PetscCall(ISDestroy(&grid_batch_is_inv[grid])); // we are done with this
      }
    } /* grids */
    // finish COO
    { // setup COO assembly
      PetscInt *oor, *ooc;
      ctx->SData_d.coo_size = coo_elem_offsets[ncellsTot] * ctx->batch_sz;
      PetscCall(PetscMalloc2(ctx->SData_d.coo_size, &oor, ctx->SData_d.coo_size, &ooc));
      for (int i = 0; i < ctx->SData_d.coo_size; i++) oor[i] = ooc[i] = -1;
      // get
      for (int grid = 0, glb_elem_idx = 0; grid < ctx->num_grids; grid++) {
        for (int ej = 0; ej < numCells[grid]; ++ej, glb_elem_idx++) {
          const int              fullNb           = coo_elem_fullNb[glb_elem_idx];
          const LandauIdx *const Idxs             = &maps[grid].gIdx[ej][0][0]; // just use field-0 maps, They should be the same but this is just for COO storage
          coo_elem_point_offsets[glb_elem_idx][0] = 0;
          for (int f = 0, cnt2 = 0; f < Nb; f++) {
            int idx                                     = Idxs[f];
            coo_elem_point_offsets[glb_elem_idx][f + 1] = coo_elem_point_offsets[glb_elem_idx][f]; // start at last
            if (idx >= 0) {
              cnt2++;
              coo_elem_point_offsets[glb_elem_idx][f + 1]++; // inc
            } else {
              idx = -idx - 1;
              for (int q = 0; q < maps[grid].num_face; q++) {
                if (maps[grid].c_maps[idx][q].gid < 0) break;
                cnt2++;
                coo_elem_point_offsets[glb_elem_idx][f + 1]++; // inc
              }
            }
            PetscCheck(cnt2 <= fullNb, PETSC_COMM_SELF, PETSC_ERR_PLIB, "wrong count %d < %d", fullNb, cnt2);
          }
          PetscCheck(coo_elem_point_offsets[glb_elem_idx][Nb] == fullNb, PETSC_COMM_SELF, PETSC_ERR_PLIB, "coo_elem_point_offsets size %d != fullNb=%d", coo_elem_point_offsets[glb_elem_idx][Nb], fullNb);
        }
      }
      // set
      for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) {
        for (int grid = 0, glb_elem_idx = 0; grid < ctx->num_grids; grid++) {
          const PetscInt moffset = LAND_MOFFSET(b_id, grid, ctx->batch_sz, ctx->num_grids, ctx->mat_offset);
          for (int ej = 0; ej < numCells[grid]; ++ej, glb_elem_idx++) {
            const int fullNb = coo_elem_fullNb[glb_elem_idx], fullNb2 = fullNb * fullNb;
            // set (i,j)
            for (int fieldA = 0; fieldA < Nf[grid]; fieldA++) {
              const LandauIdx *const Idxs = &maps[grid].gIdx[ej][fieldA][0];
              int                    rows[LANDAU_MAX_Q_FACE], cols[LANDAU_MAX_Q_FACE];
              for (int f = 0; f < Nb; ++f) {
                const int nr = coo_elem_point_offsets[glb_elem_idx][f + 1] - coo_elem_point_offsets[glb_elem_idx][f];
                if (nr == 1) rows[0] = Idxs[f];
                else {
                  const int idx = -Idxs[f] - 1;
                  for (int q = 0; q < nr; q++) rows[q] = maps[grid].c_maps[idx][q].gid;
                }
                for (int g = 0; g < Nb; ++g) {
                  const int nc = coo_elem_point_offsets[glb_elem_idx][g + 1] - coo_elem_point_offsets[glb_elem_idx][g];
                  if (nc == 1) cols[0] = Idxs[g];
                  else {
                    const int idx = -Idxs[g] - 1;
                    for (int q = 0; q < nc; q++) cols[q] = maps[grid].c_maps[idx][q].gid;
                  }
                  const int idx0 = b_id * coo_elem_offsets[ncellsTot] + coo_elem_offsets[glb_elem_idx] + fieldA * fullNb2 + fullNb * coo_elem_point_offsets[glb_elem_idx][f] + nr * coo_elem_point_offsets[glb_elem_idx][g];
                  for (int q = 0, idx = idx0; q < nr; q++) {
                    for (int d = 0; d < nc; d++, idx++) {
                      oor[idx] = rows[q] + moffset;
                      ooc[idx] = cols[d] + moffset;
                    }
                  }
                }
              }
            }
          } // cell
        }   // grid
      }     // batch
      PetscCall(MatSetPreallocationCOO(ctx->J, ctx->SData_d.coo_size, oor, ooc));
      PetscCall(PetscFree2(oor, ooc));
    }
    PetscCall(PetscFree(pointMaps));
    PetscCall(PetscFree(elemMatrix));
    PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
    PetscCall(PetscContainerSetPointer(container, (void *)maps));
    PetscCall(PetscContainerSetUserDestroy(container, LandauGPUMapsDestroy));
    PetscCall(PetscObjectCompose((PetscObject)ctx->J, "assembly_maps", (PetscObject)container));
    PetscCall(PetscContainerDestroy(&container));
    PetscCall(PetscLogEventEnd(ctx->events[2], 0, 0, 0, 0));
  } // end GPU assembly
  { /* create static point data, Jacobian called first, only one vertex copy */
    PetscReal *invJe, *ww, *xx, *yy, *zz = NULL, *invJ_a;
    PetscInt   outer_ipidx, outer_ej, grid, nip_glb = 0;
    PetscFE    fe;
    PetscCall(PetscLogEventBegin(ctx->events[7], 0, 0, 0, 0));
    PetscCall(PetscInfo(ctx->plex[0], "Initialize static data\n"));
    for (PetscInt grid = 0; grid < ctx->num_grids; grid++) nip_glb += Nq * numCells[grid];
    /* collect f data, first time is for Jacobian, but make mass now */
    if (ctx->verbose != 0) {
      PetscInt ncells = 0, N;
      PetscCall(MatGetSize(ctx->J, &N, NULL));
      for (PetscInt grid = 0; grid < ctx->num_grids; grid++) ncells += numCells[grid];
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d) %s %" PetscInt_FMT " IPs, %" PetscInt_FMT " cells total, Nb=%" PetscInt_FMT ", Nq=%" PetscInt_FMT ", dim=%" PetscInt_FMT ", Tab: Nb=%" PetscInt_FMT " Nf=%" PetscInt_FMT " Np=%" PetscInt_FMT " cdim=%" PetscInt_FMT " N=%" PetscInt_FMT "\n", 0, "FormLandau", nip_glb, ncells, Nb, Nq, dim, Nb,
                            ctx->num_species, Nb, dim, N));
    }
    PetscCall(PetscMalloc4(nip_glb, &ww, nip_glb, &xx, nip_glb, &yy, nip_glb * dim * dim, &invJ_a));
    if (dim == 3) PetscCall(PetscMalloc1(nip_glb, &zz));
    if (ctx->use_energy_tensor_trick) {
      PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, ctx->simplex, NULL, PETSC_DECIDE, &fe));
      PetscCall(PetscObjectSetName((PetscObject)fe, "energy"));
    }
    /* init each grids static data - no batch */
    for (grid = 0, outer_ipidx = 0, outer_ej = 0; grid < ctx->num_grids; grid++) { // OpenMP (once)
      Vec          v2_2 = NULL;                                                    // projected function: v^2/2 for non-relativistic, gamma... for relativistic
      PetscSection e_section;
      DM           dmEnergy;
      PetscInt     cStart, cEnd, ej;

      PetscCall(DMPlexGetHeightStratum(ctx->plex[grid], 0, &cStart, &cEnd));
      // prep energy trick, get v^2 / 2 vector
      if (ctx->use_energy_tensor_trick) {
        PetscErrorCode (*energyf[1])(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar[], void *) = {ctx->use_relativistic_corrections ? gamma_m1_f : energy_f};
        Vec        glob_v2;
        PetscReal *c2_0[1], data[1] = {PetscSqr(C_0(ctx->v_0))};

        PetscCall(DMClone(ctx->plex[grid], &dmEnergy));
        PetscCall(PetscObjectSetName((PetscObject)dmEnergy, "energy"));
        PetscCall(DMSetField(dmEnergy, 0, NULL, (PetscObject)fe));
        PetscCall(DMCreateDS(dmEnergy));
        PetscCall(DMGetSection(dmEnergy, &e_section));
        PetscCall(DMGetGlobalVector(dmEnergy, &glob_v2));
        PetscCall(PetscObjectSetName((PetscObject)glob_v2, "trick"));
        c2_0[0] = &data[0];
        PetscCall(DMProjectFunction(dmEnergy, 0., energyf, (void **)c2_0, INSERT_ALL_VALUES, glob_v2));
        PetscCall(DMGetLocalVector(dmEnergy, &v2_2));
        PetscCall(VecZeroEntries(v2_2)); /* zero BCs so don't set */
        PetscCall(DMGlobalToLocalBegin(dmEnergy, glob_v2, INSERT_VALUES, v2_2));
        PetscCall(DMGlobalToLocalEnd(dmEnergy, glob_v2, INSERT_VALUES, v2_2));
        PetscCall(DMViewFromOptions(dmEnergy, NULL, "-energy_dm_view"));
        PetscCall(VecViewFromOptions(glob_v2, NULL, "-energy_vec_view"));
        PetscCall(DMRestoreGlobalVector(dmEnergy, &glob_v2));
      }
      /* append part of the IP data for each grid */
      for (ej = 0; ej < numCells[grid]; ++ej, ++outer_ej) {
        PetscScalar *coefs = NULL;
        PetscReal    vj[LANDAU_MAX_NQND * LANDAU_DIM], detJj[LANDAU_MAX_NQND], Jdummy[LANDAU_MAX_NQND * LANDAU_DIM * LANDAU_DIM], c0 = C_0(ctx->v_0), c02 = PetscSqr(c0);
        invJe = invJ_a + outer_ej * Nq * dim * dim;
        PetscCall(DMPlexComputeCellGeometryFEM(ctx->plex[grid], ej + cStart, quad, vj, Jdummy, invJe, detJj));
        if (ctx->use_energy_tensor_trick) PetscCall(DMPlexVecGetClosure(dmEnergy, e_section, v2_2, ej + cStart, NULL, &coefs));
        /* create static point data */
        for (PetscInt qj = 0; qj < Nq; qj++, outer_ipidx++) {
          const PetscInt   gidx = outer_ipidx;
          const PetscReal *invJ = &invJe[qj * dim * dim];
          ww[gidx]              = detJj[qj] * quadWeights[qj];
          if (dim == 2) ww[gidx] *= vj[qj * dim + 0]; /* cylindrical coordinate, w/o 2pi */
          // get xx, yy, zz
          if (ctx->use_energy_tensor_trick) {
            double                 refSpaceDer[3], eGradPhi[3];
            const PetscReal *const DD = Tf[0]->T[1];
            const PetscReal       *Dq = &DD[qj * Nb * dim];
            for (int d = 0; d < 3; ++d) refSpaceDer[d] = eGradPhi[d] = 0.0;
            for (int b = 0; b < Nb; ++b) {
              for (int d = 0; d < dim; ++d) refSpaceDer[d] += Dq[b * dim + d] * PetscRealPart(coefs[b]);
            }
            xx[gidx] = 1e10;
            if (ctx->use_relativistic_corrections) {
              double dg2_c2 = 0;
              //for (int d = 0; d < dim; ++d) refSpaceDer[d] *= c02;
              for (int d = 0; d < dim; ++d) dg2_c2 += PetscSqr(refSpaceDer[d]);
              dg2_c2 *= (double)c02;
              if (dg2_c2 >= .999) {
                xx[gidx] = vj[qj * dim + 0]; /* coordinate */
                yy[gidx] = vj[qj * dim + 1];
                if (dim == 3) zz[gidx] = vj[qj * dim + 2];
                PetscCall(PetscPrintf(ctx->comm, "Error: %12.5e %" PetscInt_FMT ".%" PetscInt_FMT ") dg2/c02 = %12.5e x= %12.5e %12.5e %12.5e\n", (double)PetscSqrtReal(xx[gidx] * xx[gidx] + yy[gidx] * yy[gidx] + zz[gidx] * zz[gidx]), ej, qj, dg2_c2, (double)xx[gidx], (double)yy[gidx], (double)zz[gidx]));
              } else {
                PetscReal fact = c02 / PetscSqrtReal(1. - dg2_c2);
                for (int d = 0; d < dim; ++d) refSpaceDer[d] *= fact;
                // could test with other point u' that (grad - grad') * U (refSpaceDer, refSpaceDer') == 0
              }
            }
            if (xx[gidx] == 1e10) {
              for (int d = 0; d < dim; ++d) {
                for (int e = 0; e < dim; ++e) eGradPhi[d] += invJ[e * dim + d] * refSpaceDer[e];
              }
              xx[gidx] = eGradPhi[0];
              yy[gidx] = eGradPhi[1];
              if (dim == 3) zz[gidx] = eGradPhi[2];
            }
          } else {
            xx[gidx] = vj[qj * dim + 0]; /* coordinate */
            yy[gidx] = vj[qj * dim + 1];
            if (dim == 3) zz[gidx] = vj[qj * dim + 2];
          }
        } /* q */
        if (ctx->use_energy_tensor_trick) PetscCall(DMPlexVecRestoreClosure(dmEnergy, e_section, v2_2, ej + cStart, NULL, &coefs));
      } /* ej */
      if (ctx->use_energy_tensor_trick) {
        PetscCall(DMRestoreLocalVector(dmEnergy, &v2_2));
        PetscCall(DMDestroy(&dmEnergy));
      }
    } /* grid */
    if (ctx->use_energy_tensor_trick) PetscCall(PetscFEDestroy(&fe));
    /* cache static data */
    if (ctx->deviceType == LANDAU_KOKKOS) {
#if defined(PETSC_HAVE_KOKKOS)
      PetscCall(LandauKokkosStaticDataSet(ctx->plex[0], Nq, Nb, ctx->batch_sz, ctx->num_grids, numCells, ctx->species_offset, ctx->mat_offset, nu_alpha, nu_beta, invMass, (PetscReal *)ctx->lambdas, invJ_a, xx, yy, zz, ww, &ctx->SData_d));
#else
      SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONG, "-landau_device_type kokkos not built");
#endif
      /* free */
      PetscCall(PetscFree4(ww, xx, yy, invJ_a));
      if (dim == 3) PetscCall(PetscFree(zz));
    } else {                                                                                                                                                                   /* CPU version, just copy in, only use part */
      PetscReal *nu_alpha_p = (PetscReal *)ctx->SData_d.alpha, *nu_beta_p = (PetscReal *)ctx->SData_d.beta, *invMass_p = (PetscReal *)ctx->SData_d.invMass, *lambdas_p = NULL; // why set these ?
      ctx->SData_d.w    = (void *)ww;
      ctx->SData_d.x    = (void *)xx;
      ctx->SData_d.y    = (void *)yy;
      ctx->SData_d.z    = (void *)zz;
      ctx->SData_d.invJ = (void *)invJ_a;
      PetscCall(PetscMalloc4(ctx->num_species, &nu_alpha_p, ctx->num_species, &nu_beta_p, ctx->num_species, &invMass_p, LANDAU_MAX_GRIDS * LANDAU_MAX_GRIDS, &lambdas_p));
      for (PetscInt ii = 0; ii < ctx->num_species; ii++) {
        nu_alpha_p[ii] = nu_alpha[ii];
        nu_beta_p[ii]  = nu_beta[ii];
        invMass_p[ii]  = invMass[ii];
      }
      ctx->SData_d.alpha   = (void *)nu_alpha_p;
      ctx->SData_d.beta    = (void *)nu_beta_p;
      ctx->SData_d.invMass = (void *)invMass_p;
      ctx->SData_d.lambdas = (void *)lambdas_p;
      for (PetscInt grid = 0; grid < LANDAU_MAX_GRIDS; grid++) {
        PetscReal(*lambdas)[LANDAU_MAX_GRIDS][LANDAU_MAX_GRIDS] = (PetscReal(*)[LANDAU_MAX_GRIDS][LANDAU_MAX_GRIDS])ctx->SData_d.lambdas;
        for (PetscInt gridj = 0; gridj < LANDAU_MAX_GRIDS; gridj++) { (*lambdas)[grid][gridj] = ctx->lambdas[grid][gridj]; }
      }
    }
    PetscCall(PetscLogEventEnd(ctx->events[7], 0, 0, 0, 0));
  } // initialize
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* < v, u > */
static void g0_1(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
{
  g0[0] = 1.;
}

/* < v, u > */
static void g0_fake(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
{
  static double ttt = 1e-12;
  g0[0]             = ttt++;
}

/* < v, u > */
static void g0_r(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
{
  g0[0] = 2. * PETSC_PI * x[0];
}

static PetscErrorCode MatrixNfDestroy(void *ptr)
{
  PetscInt *nf = (PetscInt *)ptr;
  PetscFunctionBegin;
  PetscCall(PetscFree(nf));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
 LandauCreateJacobianMatrix - creates ctx->J with without real data. Hard to keep sparse.
  - Like DMPlexLandauCreateMassMatrix. Should remove one and combine
  - has old support for field major ordering
 */
static PetscErrorCode LandauCreateJacobianMatrix(MPI_Comm comm, Vec X, IS grid_batch_is_inv[LANDAU_MAX_GRIDS], LandauCtx *ctx)
{
  PetscInt *idxs = NULL;
  Mat       subM[LANDAU_MAX_GRIDS];

  PetscFunctionBegin;
  if (!ctx->gpu_assembly) { /* we need GPU object with GPU assembly */
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  // get the RCM for this grid to separate out species into blocks -- create 'idxs' & 'ctx->batch_is' -- not used
  if (ctx->gpu_assembly && ctx->jacobian_field_major_order) PetscCall(PetscMalloc1(ctx->mat_offset[ctx->num_grids] * ctx->batch_sz, &idxs));
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
    const PetscInt *values, n = ctx->mat_offset[grid + 1] - ctx->mat_offset[grid];
    Mat             gMat;
    DM              massDM;
    PetscDS         prob;
    Vec             tvec;
    // get "mass" matrix for reordering
    PetscCall(DMClone(ctx->plex[grid], &massDM));
    PetscCall(DMCopyFields(ctx->plex[grid], massDM));
    PetscCall(DMCreateDS(massDM));
    PetscCall(DMGetDS(massDM, &prob));
    for (int ix = 0, ii = ctx->species_offset[grid]; ii < ctx->species_offset[grid + 1]; ii++, ix++) PetscCall(PetscDSSetJacobian(prob, ix, ix, g0_fake, NULL, NULL, NULL));
    PetscCall(PetscOptionsInsertString(NULL, "-dm_preallocate_only")); // this trick is need to both sparsify the matrix and avoid runtime error
    PetscCall(DMCreateMatrix(massDM, &gMat));
    PetscCall(PetscOptionsInsertString(NULL, "-dm_preallocate_only false"));
    PetscCall(MatSetOption(gMat, MAT_STRUCTURALLY_SYMMETRIC, PETSC_TRUE));
    PetscCall(MatSetOption(gMat, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE));
    PetscCall(DMCreateLocalVector(ctx->plex[grid], &tvec));
    PetscCall(DMPlexSNESComputeJacobianFEM(massDM, tvec, gMat, gMat, ctx));
    PetscCall(MatViewFromOptions(gMat, NULL, "-dm_landau_reorder_mat_view"));
    PetscCall(DMDestroy(&massDM));
    PetscCall(VecDestroy(&tvec));
    subM[grid] = gMat;
    if (ctx->gpu_assembly && ctx->jacobian_field_major_order) {
      MatOrderingType rtype = MATORDERINGRCM;
      IS              isrow, isicol;
      PetscCall(MatGetOrdering(gMat, rtype, &isrow, &isicol));
      PetscCall(ISInvertPermutation(isrow, PETSC_DECIDE, &grid_batch_is_inv[grid]));
      PetscCall(ISGetIndices(isrow, &values));
      for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) { // add batch size DMs for this species grid
#if !defined(LANDAU_SPECIES_MAJOR)
        PetscInt N = ctx->mat_offset[ctx->num_grids], n0 = ctx->mat_offset[grid] + b_id * N;
        for (int ii = 0; ii < n; ++ii) idxs[n0 + ii] = values[ii] + n0;
#else
        PetscInt n0 = ctx->mat_offset[grid] * ctx->batch_sz + b_id * n;
        for (int ii = 0; ii < n; ++ii) idxs[n0 + ii] = values[ii] + n0;
#endif
      }
      PetscCall(ISRestoreIndices(isrow, &values));
      PetscCall(ISDestroy(&isrow));
      PetscCall(ISDestroy(&isicol));
    }
  }
  if (ctx->gpu_assembly && ctx->jacobian_field_major_order) PetscCall(ISCreateGeneral(comm, ctx->mat_offset[ctx->num_grids] * ctx->batch_sz, idxs, PETSC_OWN_POINTER, &ctx->batch_is));
  // get a block matrix
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
    Mat      B = subM[grid];
    PetscInt nloc, nzl, *colbuf, row, COL_BF_SIZE = 1024;
    PetscCall(PetscMalloc(sizeof(*colbuf) * COL_BF_SIZE, &colbuf));
    PetscCall(MatGetSize(B, &nloc, NULL));
    for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) {
      const PetscInt     moffset = LAND_MOFFSET(b_id, grid, ctx->batch_sz, ctx->num_grids, ctx->mat_offset);
      const PetscInt    *cols;
      const PetscScalar *vals;
      for (int i = 0; i < nloc; i++) {
        PetscCall(MatGetRow(B, i, &nzl, NULL, NULL));
        if (nzl > COL_BF_SIZE) {
          PetscCall(PetscFree(colbuf));
          PetscCall(PetscInfo(ctx->plex[grid], "Realloc buffer %" PetscInt_FMT " to %" PetscInt_FMT " (row size %" PetscInt_FMT ") \n", COL_BF_SIZE, 2 * COL_BF_SIZE, nzl));
          COL_BF_SIZE = nzl;
          PetscCall(PetscMalloc(sizeof(*colbuf) * COL_BF_SIZE, &colbuf));
        }
        PetscCall(MatGetRow(B, i, &nzl, &cols, &vals));
        for (int j = 0; j < nzl; j++) colbuf[j] = cols[j] + moffset;
        row = i + moffset;
        PetscCall(MatSetValues(ctx->J, 1, &row, nzl, colbuf, vals, INSERT_VALUES));
        PetscCall(MatRestoreRow(B, i, &nzl, &cols, &vals));
      }
    }
    PetscCall(PetscFree(colbuf));
  }
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) PetscCall(MatDestroy(&subM[grid]));
  PetscCall(MatAssemblyBegin(ctx->J, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(ctx->J, MAT_FINAL_ASSEMBLY));

  // debug
  PetscCall(MatViewFromOptions(ctx->J, NULL, "-dm_landau_mat_view"));
  if (ctx->gpu_assembly && ctx->jacobian_field_major_order) {
    Mat mat_block_order;
    PetscCall(MatCreateSubMatrix(ctx->J, ctx->batch_is, ctx->batch_is, MAT_INITIAL_MATRIX, &mat_block_order)); // use MatPermute
    PetscCall(MatViewFromOptions(mat_block_order, NULL, "-dm_landau_mat_view"));
    PetscCall(MatDestroy(&mat_block_order));
    PetscCall(VecScatterCreate(X, ctx->batch_is, X, NULL, &ctx->plex_batch));
    PetscCall(VecDuplicate(X, &ctx->work_vec));
  }

  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMPlexLandauCreateMassMatrix(DM pack, Mat *Amat);
/*@C
  DMPlexLandauCreateVelocitySpace - Create a `DMPLEX` velocity space mesh

  Collective

  Input Parameters:
+ comm   - The MPI communicator
. dim    - velocity space dimension (2 for axisymmetric, 3 for full 3X + 3V solver)
- prefix - prefix for options (not tested)

  Output Parameters:
+ pack - The `DM` object representing the mesh
. X    - A vector (user destroys)
- J    - Optional matrix (object destroys)

  Level: beginner

.seealso: `DMPlexCreate()`, `DMPlexLandauDestroyVelocitySpace()`
 @*/
PetscErrorCode DMPlexLandauCreateVelocitySpace(MPI_Comm comm, PetscInt dim, const char prefix[], Vec *X, Mat *J, DM *pack)
{
  LandauCtx *ctx;
  Vec        Xsub[LANDAU_MAX_GRIDS];
  IS         grid_batch_is_inv[LANDAU_MAX_GRIDS];

  PetscFunctionBegin;
  PetscCheck(dim == 2 || dim == 3, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Only 2D and 3D supported");
  PetscCheck(LANDAU_DIM == dim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "dim %" PetscInt_FMT " != LANDAU_DIM %d", dim, LANDAU_DIM);
  PetscCall(PetscNew(&ctx));
  ctx->comm = comm; /* used for diagnostics and global errors */
  /* process options */
  PetscCall(ProcessOptions(ctx, prefix));
  if (dim == 2) ctx->use_relativistic_corrections = PETSC_FALSE;
  /* Create Mesh */
  PetscCall(DMCompositeCreate(PETSC_COMM_SELF, pack));
  PetscCall(PetscLogEventBegin(ctx->events[13], 0, 0, 0, 0));
  PetscCall(PetscLogEventBegin(ctx->events[15], 0, 0, 0, 0));
  PetscCall(LandauDMCreateVMeshes(PETSC_COMM_SELF, dim, prefix, ctx, *pack)); // creates grids (Forest of AMR)
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
    /* create FEM */
    PetscCall(SetupDS(ctx->plex[grid], dim, grid, ctx));
    /* set initial state */
    PetscCall(DMCreateGlobalVector(ctx->plex[grid], &Xsub[grid]));
    PetscCall(PetscObjectSetName((PetscObject)Xsub[grid], "u_orig"));
    /* initial static refinement, no solve */
    PetscCall(LandauSetInitialCondition(ctx->plex[grid], Xsub[grid], grid, 0, 1, ctx));
    /* forest refinement - forest goes in (if forest), plex comes out */
    if (ctx->use_p4est) {
      DM plex;
      PetscCall(adapt(grid, ctx, &Xsub[grid]));                                      // forest goes in, plex comes out
      PetscCall(DMViewFromOptions(ctx->plex[grid], NULL, "-dm_landau_amr_dm_view")); // need to differentiate - todo
      PetscCall(VecViewFromOptions(Xsub[grid], NULL, "-dm_landau_amr_vec_view"));
      // convert to plex, all done with this level
      PetscCall(DMConvert(ctx->plex[grid], DMPLEX, &plex));
      PetscCall(DMDestroy(&ctx->plex[grid]));
      ctx->plex[grid] = plex;
    }
#if !defined(LANDAU_SPECIES_MAJOR)
    PetscCall(DMCompositeAddDM(*pack, ctx->plex[grid]));
#else
    for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) { // add batch size DMs for this species grid
      PetscCall(DMCompositeAddDM(*pack, ctx->plex[grid]));
    }
#endif
    PetscCall(DMSetApplicationContext(ctx->plex[grid], ctx));
  }
#if !defined(LANDAU_SPECIES_MAJOR)
  // stack the batched DMs, could do it all here!!! b_id=0
  for (PetscInt b_id = 1; b_id < ctx->batch_sz; b_id++) {
    for (PetscInt grid = 0; grid < ctx->num_grids; grid++) PetscCall(DMCompositeAddDM(*pack, ctx->plex[grid]));
  }
#endif
  // create ctx->mat_offset
  ctx->mat_offset[0] = 0;
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
    PetscInt n;
    PetscCall(VecGetLocalSize(Xsub[grid], &n));
    ctx->mat_offset[grid + 1] = ctx->mat_offset[grid] + n;
  }
  // creat DM & Jac
  PetscCall(DMSetApplicationContext(*pack, ctx));
  PetscCall(PetscOptionsInsertString(NULL, "-dm_preallocate_only"));
  PetscCall(DMCreateMatrix(*pack, &ctx->J));
  PetscCall(PetscOptionsInsertString(NULL, "-dm_preallocate_only false"));
  PetscCall(MatSetOption(ctx->J, MAT_STRUCTURALLY_SYMMETRIC, PETSC_TRUE));
  PetscCall(MatSetOption(ctx->J, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE));
  PetscCall(PetscObjectSetName((PetscObject)ctx->J, "Jac"));
  // construct initial conditions in X
  PetscCall(DMCreateGlobalVector(*pack, X));
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
    PetscInt n;
    PetscCall(VecGetLocalSize(Xsub[grid], &n));
    for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) {
      PetscScalar const *values;
      const PetscInt     moffset = LAND_MOFFSET(b_id, grid, ctx->batch_sz, ctx->num_grids, ctx->mat_offset);
      PetscCall(LandauSetInitialCondition(ctx->plex[grid], Xsub[grid], grid, b_id, ctx->batch_sz, ctx));
      PetscCall(VecGetArrayRead(Xsub[grid], &values)); // Drop whole grid in Plex ordering
      for (int i = 0, idx = moffset; i < n; i++, idx++) PetscCall(VecSetValue(*X, idx, values[i], INSERT_VALUES));
      PetscCall(VecRestoreArrayRead(Xsub[grid], &values));
    }
  }
  // cleanup
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) PetscCall(VecDestroy(&Xsub[grid]));
  /* check for correct matrix type */
  if (ctx->gpu_assembly) { /* we need GPU object with GPU assembly */
    PetscBool flg;
    if (ctx->deviceType == LANDAU_KOKKOS) {
      PetscCall(PetscObjectTypeCompareAny((PetscObject)ctx->J, &flg, MATSEQAIJKOKKOS, MATMPIAIJKOKKOS, MATAIJKOKKOS, ""));
#if defined(PETSC_HAVE_KOKKOS)
      PetscCheck(flg, ctx->comm, PETSC_ERR_ARG_WRONG, "must use '-dm_mat_type aijkokkos -dm_vec_type kokkos' for GPU assembly and Kokkos or use '-dm_landau_device_type cpu'");
#else
      PetscCheck(flg, ctx->comm, PETSC_ERR_ARG_WRONG, "must configure with '--download-kokkos-kernels' for GPU assembly and Kokkos or use '-dm_landau_device_type cpu'");
#endif
    }
  }
  PetscCall(PetscLogEventEnd(ctx->events[15], 0, 0, 0, 0));

  // create field major ordering
  ctx->work_vec   = NULL;
  ctx->plex_batch = NULL;
  ctx->batch_is   = NULL;
  for (int i = 0; i < LANDAU_MAX_GRIDS; i++) grid_batch_is_inv[i] = NULL;
  PetscCall(PetscLogEventBegin(ctx->events[12], 0, 0, 0, 0));
  PetscCall(LandauCreateJacobianMatrix(comm, *X, grid_batch_is_inv, ctx));
  PetscCall(PetscLogEventEnd(ctx->events[12], 0, 0, 0, 0));

  // create AMR GPU assembly maps and static GPU data
  PetscCall(CreateStaticData(dim, grid_batch_is_inv, ctx));

  PetscCall(PetscLogEventEnd(ctx->events[13], 0, 0, 0, 0));

  // create mass matrix
  PetscCall(DMPlexLandauCreateMassMatrix(*pack, NULL));

  if (J) *J = ctx->J;

  if (ctx->gpu_assembly && ctx->jacobian_field_major_order) {
    PetscContainer container;
    // cache ctx for KSP with batch/field major Jacobian ordering -ksp_type gmres/etc -dm_landau_jacobian_field_major_order
    PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
    PetscCall(PetscContainerSetPointer(container, (void *)ctx));
    PetscCall(PetscObjectCompose((PetscObject)ctx->J, "LandauCtx", (PetscObject)container));
    PetscCall(PetscContainerDestroy(&container));
    // batch solvers need to map -- can batch solvers work
    PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
    PetscCall(PetscContainerSetPointer(container, (void *)ctx->plex_batch));
    PetscCall(PetscObjectCompose((PetscObject)ctx->J, "plex_batch_is", (PetscObject)container));
    PetscCall(PetscContainerDestroy(&container));
  }
  // for batch solvers
  {
    PetscContainer container;
    PetscInt      *pNf;
    PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
    PetscCall(PetscMalloc1(sizeof(*pNf), &pNf));
    *pNf = ctx->batch_sz;
    PetscCall(PetscContainerSetPointer(container, (void *)pNf));
    PetscCall(PetscContainerSetUserDestroy(container, MatrixNfDestroy));
    PetscCall(PetscObjectCompose((PetscObject)ctx->J, "batch size", (PetscObject)container));
    PetscCall(PetscContainerDestroy(&container));
  }

  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexLandauAccess - Access to the distribution function with user callback

  Collective

  Input Parameters:
+ pack     - the `DMCOMPOSITE`
. func     - call back function
- user_ctx - user context

  Input/Output Parameter:
. X - Vector to data to

  Level: advanced

.seealso: `DMPlexLandauCreateVelocitySpace()`
 @*/
PetscErrorCode DMPlexLandauAccess(DM pack, Vec X, PetscErrorCode (*func)(DM, Vec, PetscInt, PetscInt, PetscInt, void *), void *user_ctx)
{
  LandauCtx *ctx;
  PetscFunctionBegin;
  PetscCall(DMGetApplicationContext(pack, &ctx)); // uses ctx->num_grids; ctx->plex[grid]; ctx->batch_sz; ctx->mat_offset
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
    PetscInt dim, n;
    PetscCall(DMGetDimension(pack, &dim));
    for (PetscInt sp = ctx->species_offset[grid], i0 = 0; sp < ctx->species_offset[grid + 1]; sp++, i0++) {
      Vec      vec;
      PetscInt vf[1] = {i0};
      IS       vis;
      DM       vdm;
      PetscCall(DMCreateSubDM(ctx->plex[grid], 1, vf, &vis, &vdm));
      PetscCall(DMSetApplicationContext(vdm, ctx)); // the user might want this
      PetscCall(DMCreateGlobalVector(vdm, &vec));
      PetscCall(VecGetSize(vec, &n));
      for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) {
        const PetscInt moffset = LAND_MOFFSET(b_id, grid, ctx->batch_sz, ctx->num_grids, ctx->mat_offset);
        PetscCall(VecZeroEntries(vec));
        /* Add your data with 'dm' for species 'sp' to 'vec' */
        PetscCall(func(vdm, vec, i0, grid, b_id, user_ctx));
        /* add to global */
        PetscScalar const *values;
        const PetscInt    *offsets;
        PetscCall(VecGetArrayRead(vec, &values));
        PetscCall(ISGetIndices(vis, &offsets));
        for (int i = 0; i < n; i++) PetscCall(VecSetValue(X, moffset + offsets[i], values[i], ADD_VALUES));
        PetscCall(VecRestoreArrayRead(vec, &values));
        PetscCall(ISRestoreIndices(vis, &offsets));
      } // batch
      PetscCall(VecDestroy(&vec));
      PetscCall(ISDestroy(&vis));
      PetscCall(DMDestroy(&vdm));
    }
  } // grid
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexLandauDestroyVelocitySpace - Destroy a `DMPLEX` velocity space mesh

  Collective

  Input/Output Parameters:
. dm - the `DM` to destroy

  Level: beginner

.seealso: `DMPlexLandauCreateVelocitySpace()`
 @*/
PetscErrorCode DMPlexLandauDestroyVelocitySpace(DM *dm)
{
  LandauCtx *ctx;
  PetscFunctionBegin;
  PetscCall(DMGetApplicationContext(*dm, &ctx));
  PetscCall(MatDestroy(&ctx->M));
  PetscCall(MatDestroy(&ctx->J));
  for (PetscInt ii = 0; ii < ctx->num_species; ii++) PetscCall(PetscFEDestroy(&ctx->fe[ii]));
  PetscCall(ISDestroy(&ctx->batch_is));
  PetscCall(VecDestroy(&ctx->work_vec));
  PetscCall(VecScatterDestroy(&ctx->plex_batch));
  if (ctx->deviceType == LANDAU_KOKKOS) {
#if defined(PETSC_HAVE_KOKKOS)
    PetscCall(LandauKokkosStaticDataClear(&ctx->SData_d));
#else
    SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONG, "-landau_device_type %s not built", "kokkos");
#endif
  } else {
    if (ctx->SData_d.x) { /* in a CPU run */
      PetscReal *invJ = (PetscReal *)ctx->SData_d.invJ, *xx = (PetscReal *)ctx->SData_d.x, *yy = (PetscReal *)ctx->SData_d.y, *zz = (PetscReal *)ctx->SData_d.z, *ww = (PetscReal *)ctx->SData_d.w;
      LandauIdx *coo_elem_offsets = (LandauIdx *)ctx->SData_d.coo_elem_offsets, *coo_elem_fullNb = (LandauIdx *)ctx->SData_d.coo_elem_fullNb, (*coo_elem_point_offsets)[LANDAU_MAX_NQND + 1] = (LandauIdx(*)[LANDAU_MAX_NQND + 1]) ctx->SData_d.coo_elem_point_offsets;
      PetscCall(PetscFree4(ww, xx, yy, invJ));
      if (zz) PetscCall(PetscFree(zz));
      if (coo_elem_offsets) {
        PetscCall(PetscFree3(coo_elem_offsets, coo_elem_fullNb, coo_elem_point_offsets)); // could be NULL
      }
      PetscCall(PetscFree4(ctx->SData_d.alpha, ctx->SData_d.beta, ctx->SData_d.invMass, ctx->SData_d.lambdas));
    }
  }

  if (ctx->times[LANDAU_MATRIX_TOTAL] > 0) { // OMP timings
    PetscCall(PetscPrintf(ctx->comm, "TSStep               N  1.0 %10.3e\n", ctx->times[LANDAU_EX2_TSSOLVE]));
    PetscCall(PetscPrintf(ctx->comm, "2:           Solve:  %10.3e with %" PetscInt_FMT " threads\n", ctx->times[LANDAU_EX2_TSSOLVE] - ctx->times[LANDAU_MATRIX_TOTAL], ctx->batch_sz));
    PetscCall(PetscPrintf(ctx->comm, "3:          Landau:  %10.3e\n", ctx->times[LANDAU_MATRIX_TOTAL]));
    PetscCall(PetscPrintf(ctx->comm, "Landau Jacobian       %" PetscInt_FMT " 1.0 %10.3e\n", (PetscInt)ctx->times[LANDAU_JACOBIAN_COUNT], ctx->times[LANDAU_JACOBIAN]));
    PetscCall(PetscPrintf(ctx->comm, "Landau Operator       N 1.0  %10.3e\n", ctx->times[LANDAU_OPERATOR]));
    PetscCall(PetscPrintf(ctx->comm, "Landau Mass           N 1.0  %10.3e\n", ctx->times[LANDAU_MASS]));
    PetscCall(PetscPrintf(ctx->comm, " Jac-f-df (GPU)       N 1.0  %10.3e\n", ctx->times[LANDAU_F_DF]));
    PetscCall(PetscPrintf(ctx->comm, " Kernel (GPU)         N 1.0  %10.3e\n", ctx->times[LANDAU_KERNEL]));
    PetscCall(PetscPrintf(ctx->comm, "MatLUFactorNum        X 1.0 %10.3e\n", ctx->times[KSP_FACTOR]));
    PetscCall(PetscPrintf(ctx->comm, "MatSolve              X 1.0 %10.3e\n", ctx->times[KSP_SOLVE]));
  }
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) PetscCall(DMDestroy(&ctx->plex[grid]));
  PetscCall(PetscFree(ctx));
  PetscCall(DMDestroy(dm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* < v, ru > */
static void f0_s_den(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
{
  PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
  f0[0]       = u[ii];
}

/* < v, ru > */
static void f0_s_mom(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
{
  PetscInt ii = (PetscInt)PetscRealPart(constants[0]), jj = (PetscInt)PetscRealPart(constants[1]);
  f0[0] = x[jj] * u[ii]; /* x momentum */
}

static void f0_s_v2(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
{
  PetscInt i, ii = (PetscInt)PetscRealPart(constants[0]);
  double   tmp1 = 0.;
  for (i = 0; i < dim; ++i) tmp1 += x[i] * x[i];
  f0[0] = tmp1 * u[ii];
}

static PetscErrorCode gamma_n_f(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *actx)
{
  const PetscReal *c2_0_arr = ((PetscReal *)actx);
  const PetscReal  c02      = c2_0_arr[0];

  PetscFunctionBegin;
  for (int s = 0; s < Nf; s++) {
    PetscReal tmp1 = 0.;
    for (int i = 0; i < dim; ++i) tmp1 += x[i] * x[i];
#if defined(PETSC_USE_DEBUG)
    u[s] = PetscSqrtReal(1. + tmp1 / c02); //  u[0] = PetscSqrtReal(1. + xx);
#else
    {
      PetscReal xx = tmp1 / c02;
      u[s]         = xx / (PetscSqrtReal(1. + xx) + 1.); // better conditioned = xx/(PetscSqrtReal(1. + xx) + 1.)
    }
#endif
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* < v, ru > */
static void f0_s_rden(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
{
  PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
  f0[0]       = 2. * PETSC_PI * x[0] * u[ii];
}

/* < v, ru > */
static void f0_s_rmom(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
{
  PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
  f0[0]       = 2. * PETSC_PI * x[0] * x[1] * u[ii];
}

static void f0_s_rv2(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
{
  PetscInt ii = (PetscInt)PetscRealPart(constants[0]);
  f0[0]       = 2. * PETSC_PI * x[0] * (x[0] * x[0] + x[1] * x[1]) * u[ii];
}

/*@
  DMPlexLandauPrintNorms - collects moments and prints them

  Collective

  Input Parameters:
+ X     - the state
- stepi - current step to print

  Level: beginner

.seealso: `DMPlexLandauCreateVelocitySpace()`
 @*/
PetscErrorCode DMPlexLandauPrintNorms(Vec X, PetscInt stepi)
{
  LandauCtx  *ctx;
  PetscDS     prob;
  DM          pack;
  PetscInt    cStart, cEnd, dim, ii, i0, nDMs;
  PetscScalar xmomentumtot = 0, ymomentumtot = 0, zmomentumtot = 0, energytot = 0, densitytot = 0, tt[LANDAU_MAX_SPECIES];
  PetscScalar xmomentum[LANDAU_MAX_SPECIES], ymomentum[LANDAU_MAX_SPECIES], zmomentum[LANDAU_MAX_SPECIES], energy[LANDAU_MAX_SPECIES], density[LANDAU_MAX_SPECIES];
  Vec        *globXArray;

  PetscFunctionBegin;
  PetscCall(VecGetDM(X, &pack));
  PetscCheck(pack, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Vector has no DM");
  PetscCall(DMGetDimension(pack, &dim));
  PetscCheck(dim == 2 || dim == 3, PETSC_COMM_SELF, PETSC_ERR_PLIB, "dim %" PetscInt_FMT " not in [2,3]", dim);
  PetscCall(DMGetApplicationContext(pack, &ctx));
  PetscCheck(ctx, PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
  /* print momentum and energy */
  PetscCall(DMCompositeGetNumberDM(pack, &nDMs));
  PetscCheck(nDMs == ctx->num_grids * ctx->batch_sz, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "#DM wrong %" PetscInt_FMT " %" PetscInt_FMT, nDMs, ctx->num_grids * ctx->batch_sz);
  PetscCall(PetscMalloc(sizeof(*globXArray) * nDMs, &globXArray));
  PetscCall(DMCompositeGetAccessArray(pack, X, nDMs, NULL, globXArray));
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
    Vec Xloc = globXArray[LAND_PACK_IDX(ctx->batch_view_idx, grid)];
    PetscCall(DMGetDS(ctx->plex[grid], &prob));
    for (ii = ctx->species_offset[grid], i0 = 0; ii < ctx->species_offset[grid + 1]; ii++, i0++) {
      PetscScalar user[2] = {(PetscScalar)i0, (PetscScalar)ctx->charges[ii]};
      PetscCall(PetscDSSetConstants(prob, 2, user));
      if (dim == 2) { /* 2/3X + 3V (cylindrical coordinates) */
        PetscCall(PetscDSSetObjective(prob, 0, &f0_s_rden));
        PetscCall(DMPlexComputeIntegralFEM(ctx->plex[grid], Xloc, tt, ctx));
        density[ii] = tt[0] * ctx->n_0 * ctx->charges[ii];
        PetscCall(PetscDSSetObjective(prob, 0, &f0_s_rmom));
        PetscCall(DMPlexComputeIntegralFEM(ctx->plex[grid], Xloc, tt, ctx));
        zmomentum[ii] = tt[0] * ctx->n_0 * ctx->v_0 * ctx->masses[ii];
        PetscCall(PetscDSSetObjective(prob, 0, &f0_s_rv2));
        PetscCall(DMPlexComputeIntegralFEM(ctx->plex[grid], Xloc, tt, ctx));
        energy[ii] = tt[0] * 0.5 * ctx->n_0 * ctx->v_0 * ctx->v_0 * ctx->masses[ii];
        zmomentumtot += zmomentum[ii];
        energytot += energy[ii];
        densitytot += density[ii];
        PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%3" PetscInt_FMT ") species-%" PetscInt_FMT ": charge density= %20.13e z-momentum= %20.13e energy= %20.13e", stepi, ii, (double)PetscRealPart(density[ii]), (double)PetscRealPart(zmomentum[ii]), (double)PetscRealPart(energy[ii])));
      } else { /* 2/3Xloc + 3V */
        PetscCall(PetscDSSetObjective(prob, 0, &f0_s_den));
        PetscCall(DMPlexComputeIntegralFEM(ctx->plex[grid], Xloc, tt, ctx));
        density[ii] = tt[0] * ctx->n_0 * ctx->charges[ii];
        PetscCall(PetscDSSetObjective(prob, 0, &f0_s_mom));
        user[1] = 0;
        PetscCall(PetscDSSetConstants(prob, 2, user));
        PetscCall(DMPlexComputeIntegralFEM(ctx->plex[grid], Xloc, tt, ctx));
        xmomentum[ii] = tt[0] * ctx->n_0 * ctx->v_0 * ctx->masses[ii];
        user[1]       = 1;
        PetscCall(PetscDSSetConstants(prob, 2, user));
        PetscCall(DMPlexComputeIntegralFEM(ctx->plex[grid], Xloc, tt, ctx));
        ymomentum[ii] = tt[0] * ctx->n_0 * ctx->v_0 * ctx->masses[ii];
        user[1]       = 2;
        PetscCall(PetscDSSetConstants(prob, 2, user));
        PetscCall(DMPlexComputeIntegralFEM(ctx->plex[grid], Xloc, tt, ctx));
        zmomentum[ii] = tt[0] * ctx->n_0 * ctx->v_0 * ctx->masses[ii];
        if (ctx->use_relativistic_corrections) {
          /* gamma * M * f */
          if (ii == 0 && grid == 0) { // do all at once
            Vec Mf, globGamma, *globMfArray, *globGammaArray;
            PetscErrorCode (*gammaf[1])(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar[], void *) = {gamma_n_f};
            PetscReal *c2_0[1], data[1];

            PetscCall(VecDuplicate(X, &globGamma));
            PetscCall(VecDuplicate(X, &Mf));
            PetscCall(PetscMalloc(sizeof(*globMfArray) * nDMs, &globMfArray));
            PetscCall(PetscMalloc(sizeof(*globMfArray) * nDMs, &globGammaArray));
            /* M * f */
            PetscCall(MatMult(ctx->M, X, Mf));
            /* gamma */
            PetscCall(DMCompositeGetAccessArray(pack, globGamma, nDMs, NULL, globGammaArray));
            for (PetscInt grid = 0; grid < ctx->num_grids; grid++) { // yes a grid loop in a grid loop to print nice, need to fix for batching
              Vec v1  = globGammaArray[LAND_PACK_IDX(ctx->batch_view_idx, grid)];
              data[0] = PetscSqr(C_0(ctx->v_0));
              c2_0[0] = &data[0];
              PetscCall(DMProjectFunction(ctx->plex[grid], 0., gammaf, (void **)c2_0, INSERT_ALL_VALUES, v1));
            }
            PetscCall(DMCompositeRestoreAccessArray(pack, globGamma, nDMs, NULL, globGammaArray));
            /* gamma * Mf */
            PetscCall(DMCompositeGetAccessArray(pack, globGamma, nDMs, NULL, globGammaArray));
            PetscCall(DMCompositeGetAccessArray(pack, Mf, nDMs, NULL, globMfArray));
            for (PetscInt grid = 0; grid < ctx->num_grids; grid++) { // yes a grid loop in a grid loop to print nice
              PetscInt Nf    = ctx->species_offset[grid + 1] - ctx->species_offset[grid], N, bs;
              Vec      Mfsub = globMfArray[LAND_PACK_IDX(ctx->batch_view_idx, grid)], Gsub = globGammaArray[LAND_PACK_IDX(ctx->batch_view_idx, grid)], v1, v2;
              // get each component
              PetscCall(VecGetSize(Mfsub, &N));
              PetscCall(VecCreate(ctx->comm, &v1));
              PetscCall(VecSetSizes(v1, PETSC_DECIDE, N / Nf));
              PetscCall(VecCreate(ctx->comm, &v2));
              PetscCall(VecSetSizes(v2, PETSC_DECIDE, N / Nf));
              PetscCall(VecSetFromOptions(v1)); // ???
              PetscCall(VecSetFromOptions(v2));
              // get each component
              PetscCall(VecGetBlockSize(Gsub, &bs));
              PetscCheck(bs == Nf, PETSC_COMM_SELF, PETSC_ERR_PLIB, "bs %" PetscInt_FMT " != num_species %" PetscInt_FMT " in Gsub", bs, Nf);
              PetscCall(VecGetBlockSize(Mfsub, &bs));
              PetscCheck(bs == Nf, PETSC_COMM_SELF, PETSC_ERR_PLIB, "bs %" PetscInt_FMT " != num_species %" PetscInt_FMT, bs, Nf);
              for (int i = 0, ix = ctx->species_offset[grid]; i < Nf; i++, ix++) {
                PetscScalar val;
                PetscCall(VecStrideGather(Gsub, i, v1, INSERT_VALUES)); // this is not right -- TODO
                PetscCall(VecStrideGather(Mfsub, i, v2, INSERT_VALUES));
                PetscCall(VecDot(v1, v2, &val));
                energy[ix] = PetscRealPart(val) * ctx->n_0 * ctx->v_0 * ctx->v_0 * ctx->masses[ix];
              }
              PetscCall(VecDestroy(&v1));
              PetscCall(VecDestroy(&v2));
            } /* grids */
            PetscCall(DMCompositeRestoreAccessArray(pack, globGamma, nDMs, NULL, globGammaArray));
            PetscCall(DMCompositeRestoreAccessArray(pack, Mf, nDMs, NULL, globMfArray));
            PetscCall(PetscFree(globGammaArray));
            PetscCall(PetscFree(globMfArray));
            PetscCall(VecDestroy(&globGamma));
            PetscCall(VecDestroy(&Mf));
          }
        } else {
          PetscCall(PetscDSSetObjective(prob, 0, &f0_s_v2));
          PetscCall(DMPlexComputeIntegralFEM(ctx->plex[grid], Xloc, tt, ctx));
          energy[ii] = 0.5 * tt[0] * ctx->n_0 * ctx->v_0 * ctx->v_0 * ctx->masses[ii];
        }
        PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%3" PetscInt_FMT ") species %" PetscInt_FMT ": density=%20.13e, x-momentum=%20.13e, y-momentum=%20.13e, z-momentum=%20.13e, energy=%21.13e", stepi, ii, (double)PetscRealPart(density[ii]), (double)PetscRealPart(xmomentum[ii]), (double)PetscRealPart(ymomentum[ii]), (double)PetscRealPart(zmomentum[ii]), (double)PetscRealPart(energy[ii])));
        xmomentumtot += xmomentum[ii];
        ymomentumtot += ymomentum[ii];
        zmomentumtot += zmomentum[ii];
        energytot += energy[ii];
        densitytot += density[ii];
      }
      if (ctx->num_species > 1) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n"));
    }
  }
  PetscCall(DMCompositeRestoreAccessArray(pack, X, nDMs, NULL, globXArray));
  PetscCall(PetscFree(globXArray));
  /* totals */
  PetscCall(DMPlexGetHeightStratum(ctx->plex[0], 0, &cStart, &cEnd));
  if (ctx->num_species > 1) {
    if (dim == 2) {
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\t%3" PetscInt_FMT ") Total: charge density=%21.13e, momentum=%21.13e, energy=%21.13e (m_i[0]/m_e = %g, %" PetscInt_FMT " cells on electron grid)", stepi, (double)PetscRealPart(densitytot), (double)PetscRealPart(zmomentumtot), (double)PetscRealPart(energytot),
                            (double)(ctx->masses[1] / ctx->masses[0]), cEnd - cStart));
    } else {
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\t%3" PetscInt_FMT ") Total: charge density=%21.13e, x-momentum=%21.13e, y-momentum=%21.13e, z-momentum=%21.13e, energy=%21.13e (m_i[0]/m_e = %g, %" PetscInt_FMT " cells)", stepi, (double)PetscRealPart(densitytot), (double)PetscRealPart(xmomentumtot), (double)PetscRealPart(ymomentumtot), (double)PetscRealPart(zmomentumtot), (double)PetscRealPart(energytot),
                            (double)(ctx->masses[1] / ctx->masses[0]), cEnd - cStart));
    }
  } else PetscCall(PetscPrintf(PETSC_COMM_WORLD, " -- %" PetscInt_FMT " cells", cEnd - cStart));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n"));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexLandauCreateMassMatrix - Create mass matrix for Landau in Plex space (not field major order of Jacobian)
  - puts mass matrix into ctx->M

  Collective

  Input Parameter:
. pack - the `DM` object. Puts matrix in Landau context M field

  Output Parameter:
. Amat - The mass matrix (optional), mass matrix is added to the `DM` context

  Level: beginner

.seealso: `DMPlexLandauCreateVelocitySpace()`
 @*/
PetscErrorCode DMPlexLandauCreateMassMatrix(DM pack, Mat *Amat)
{
  DM         mass_pack, massDM[LANDAU_MAX_GRIDS];
  PetscDS    prob;
  PetscInt   ii, dim, N1 = 1, N2;
  LandauCtx *ctx;
  Mat        packM, subM[LANDAU_MAX_GRIDS];

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pack, DM_CLASSID, 1);
  if (Amat) PetscAssertPointer(Amat, 2);
  PetscCall(DMGetApplicationContext(pack, &ctx));
  PetscCheck(ctx, PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
  PetscCall(PetscLogEventBegin(ctx->events[14], 0, 0, 0, 0));
  PetscCall(DMGetDimension(pack, &dim));
  PetscCall(DMCompositeCreate(PetscObjectComm((PetscObject)pack), &mass_pack));
  /* create pack mass matrix */
  for (PetscInt grid = 0, ix = 0; grid < ctx->num_grids; grid++) {
    PetscCall(DMClone(ctx->plex[grid], &massDM[grid]));
    PetscCall(DMCopyFields(ctx->plex[grid], massDM[grid]));
    PetscCall(DMCreateDS(massDM[grid]));
    PetscCall(DMGetDS(massDM[grid], &prob));
    for (ix = 0, ii = ctx->species_offset[grid]; ii < ctx->species_offset[grid + 1]; ii++, ix++) {
      if (dim == 3) PetscCall(PetscDSSetJacobian(prob, ix, ix, g0_1, NULL, NULL, NULL));
      else PetscCall(PetscDSSetJacobian(prob, ix, ix, g0_r, NULL, NULL, NULL));
    }
#if !defined(LANDAU_SPECIES_MAJOR)
    PetscCall(DMCompositeAddDM(mass_pack, massDM[grid]));
#else
    for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) { // add batch size DMs for this species grid
      PetscCall(DMCompositeAddDM(mass_pack, massDM[grid]));
    }
#endif
    PetscCall(DMCreateMatrix(massDM[grid], &subM[grid]));
  }
#if !defined(LANDAU_SPECIES_MAJOR)
  // stack the batched DMs
  for (PetscInt b_id = 1; b_id < ctx->batch_sz; b_id++) {
    for (PetscInt grid = 0; grid < ctx->num_grids; grid++) PetscCall(DMCompositeAddDM(mass_pack, massDM[grid]));
  }
#endif
  PetscCall(PetscOptionsInsertString(NULL, "-dm_preallocate_only"));
  PetscCall(DMCreateMatrix(mass_pack, &packM));
  PetscCall(PetscOptionsInsertString(NULL, "-dm_preallocate_only false"));
  PetscCall(MatSetOption(packM, MAT_STRUCTURALLY_SYMMETRIC, PETSC_TRUE));
  PetscCall(MatSetOption(packM, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE));
  PetscCall(DMDestroy(&mass_pack));
  /* make mass matrix for each block */
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
    Vec locX;
    DM  plex = massDM[grid];
    PetscCall(DMGetLocalVector(plex, &locX));
    /* Mass matrix is independent of the input, so no need to fill locX */
    PetscCall(DMPlexSNESComputeJacobianFEM(plex, locX, subM[grid], subM[grid], ctx));
    PetscCall(DMRestoreLocalVector(plex, &locX));
    PetscCall(DMDestroy(&massDM[grid]));
  }
  PetscCall(MatGetSize(ctx->J, &N1, NULL));
  PetscCall(MatGetSize(packM, &N2, NULL));
  PetscCheck(N1 == N2, PetscObjectComm((PetscObject)pack), PETSC_ERR_PLIB, "Incorrect matrix sizes: |Jacobian| = %" PetscInt_FMT ", |Mass|=%" PetscInt_FMT, N1, N2);
  /* assemble block diagonals */
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) {
    Mat      B = subM[grid];
    PetscInt nloc, nzl, *colbuf, COL_BF_SIZE = 1024, row;
    PetscCall(PetscMalloc(sizeof(*colbuf) * COL_BF_SIZE, &colbuf));
    PetscCall(MatGetSize(B, &nloc, NULL));
    for (PetscInt b_id = 0; b_id < ctx->batch_sz; b_id++) {
      const PetscInt     moffset = LAND_MOFFSET(b_id, grid, ctx->batch_sz, ctx->num_grids, ctx->mat_offset);
      const PetscInt    *cols;
      const PetscScalar *vals;
      for (int i = 0; i < nloc; i++) {
        PetscCall(MatGetRow(B, i, &nzl, NULL, NULL));
        if (nzl > COL_BF_SIZE) {
          PetscCall(PetscFree(colbuf));
          PetscCall(PetscInfo(pack, "Realloc buffer %" PetscInt_FMT " to %" PetscInt_FMT " (row size %" PetscInt_FMT ") \n", COL_BF_SIZE, 2 * COL_BF_SIZE, nzl));
          COL_BF_SIZE = nzl;
          PetscCall(PetscMalloc(sizeof(*colbuf) * COL_BF_SIZE, &colbuf));
        }
        PetscCall(MatGetRow(B, i, &nzl, &cols, &vals));
        for (int j = 0; j < nzl; j++) colbuf[j] = cols[j] + moffset;
        row = i + moffset;
        PetscCall(MatSetValues(packM, 1, &row, nzl, colbuf, vals, INSERT_VALUES));
        PetscCall(MatRestoreRow(B, i, &nzl, &cols, &vals));
      }
    }
    PetscCall(PetscFree(colbuf));
  }
  // cleanup
  for (PetscInt grid = 0; grid < ctx->num_grids; grid++) PetscCall(MatDestroy(&subM[grid]));
  PetscCall(MatAssemblyBegin(packM, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(packM, MAT_FINAL_ASSEMBLY));
  PetscCall(PetscObjectSetName((PetscObject)packM, "mass"));
  PetscCall(MatViewFromOptions(packM, NULL, "-dm_landau_mass_view"));
  ctx->M = packM;
  if (Amat) *Amat = packM;
  PetscCall(PetscLogEventEnd(ctx->events[14], 0, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexLandauIFunction - `TS` residual calculation, confusingly this computes the Jacobian w/o mass

  Collective

  Input Parameters:
+ ts         - The time stepping context
. time_dummy - current time (not used)
. X          - Current state
. X_t        - Time derivative of current state
- actx       - Landau context

  Output Parameter:
. F - The residual

  Level: beginner

.seealso: `DMPlexLandauCreateVelocitySpace()`, `DMPlexLandauIJacobian()`
 @*/
PetscErrorCode DMPlexLandauIFunction(TS ts, PetscReal time_dummy, Vec X, Vec X_t, Vec F, void *actx)
{
  LandauCtx *ctx = (LandauCtx *)actx;
  PetscInt   dim;
  DM         pack;
#if defined(PETSC_HAVE_THREADSAFETY)
  double starttime, endtime;
#endif
  PetscObjectState state;

  PetscFunctionBegin;
  PetscCall(TSGetDM(ts, &pack));
  PetscCall(DMGetApplicationContext(pack, &ctx));
  PetscCheck(ctx, PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
  if (ctx->stage) PetscCall(PetscLogStagePush(ctx->stage));
  PetscCall(PetscLogEventBegin(ctx->events[11], 0, 0, 0, 0));
  PetscCall(PetscLogEventBegin(ctx->events[0], 0, 0, 0, 0));
#if defined(PETSC_HAVE_THREADSAFETY)
  starttime = MPI_Wtime();
#endif
  PetscCall(DMGetDimension(pack, &dim));
  PetscCall(PetscObjectStateGet((PetscObject)ctx->J, &state));
  if (state != ctx->norm_state) {
    PetscCall(PetscInfo(ts, "Create Landau Jacobian t=%g J.state %" PetscInt64_FMT " --> %" PetscInt64_FMT "\n", (double)time_dummy, ctx->norm_state, state));
    PetscCall(MatZeroEntries(ctx->J));
    PetscCall(LandauFormJacobian_Internal(X, ctx->J, dim, 0.0, (void *)ctx));
    PetscCall(MatViewFromOptions(ctx->J, NULL, "-dm_landau_jacobian_view"));
    PetscCall(PetscObjectStateGet((PetscObject)ctx->J, &state));
    ctx->norm_state = state;
  } else {
    PetscCall(PetscInfo(ts, "WARNING Skip forming Jacobian, has not changed %" PetscInt64_FMT "\n", state));
  }
  /* mat vec for op */
  PetscCall(MatMult(ctx->J, X, F)); /* C*f */
  /* add time term */
  if (X_t) PetscCall(MatMultAdd(ctx->M, X_t, F, F));
#if defined(PETSC_HAVE_THREADSAFETY)
  if (ctx->stage) {
    endtime = MPI_Wtime();
    ctx->times[LANDAU_OPERATOR] += (endtime - starttime);
    ctx->times[LANDAU_JACOBIAN] += (endtime - starttime);
    ctx->times[LANDAU_MATRIX_TOTAL] += (endtime - starttime);
    ctx->times[LANDAU_JACOBIAN_COUNT] += 1;
  }
#endif
  PetscCall(PetscLogEventEnd(ctx->events[0], 0, 0, 0, 0));
  PetscCall(PetscLogEventEnd(ctx->events[11], 0, 0, 0, 0));
  if (ctx->stage) PetscCall(PetscLogStagePop());
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexLandauIJacobian - `TS` Jacobian construction, confusingly this adds mass

  Collective

  Input Parameters:
+ ts         - The time stepping context
. time_dummy - current time (not used)
. X          - Current state
. U_tdummy   - Time derivative of current state (not used)
. shift      - shift for du/dt term
- actx       - Landau context

  Output Parameters:
+ Amat - Jacobian
- Pmat - same as Amat

  Level: beginner

.seealso: `DMPlexLandauCreateVelocitySpace()`, `DMPlexLandauIFunction()`
 @*/
PetscErrorCode DMPlexLandauIJacobian(TS ts, PetscReal time_dummy, Vec X, Vec U_tdummy, PetscReal shift, Mat Amat, Mat Pmat, void *actx)
{
  LandauCtx *ctx = NULL;
  PetscInt   dim;
  DM         pack;
#if defined(PETSC_HAVE_THREADSAFETY)
  double starttime, endtime;
#endif
  PetscObjectState state;

  PetscFunctionBegin;
  PetscCall(TSGetDM(ts, &pack));
  PetscCall(DMGetApplicationContext(pack, &ctx));
  PetscCheck(ctx, PETSC_COMM_SELF, PETSC_ERR_PLIB, "no context");
  PetscCheck(Amat == Pmat && Amat == ctx->J, ctx->comm, PETSC_ERR_PLIB, "Amat!=Pmat || Amat!=ctx->J");
  PetscCall(DMGetDimension(pack, &dim));
  /* get collision Jacobian into A */
  if (ctx->stage) PetscCall(PetscLogStagePush(ctx->stage));
  PetscCall(PetscLogEventBegin(ctx->events[11], 0, 0, 0, 0));
  PetscCall(PetscLogEventBegin(ctx->events[9], 0, 0, 0, 0));
#if defined(PETSC_HAVE_THREADSAFETY)
  starttime = MPI_Wtime();
#endif
  PetscCall(PetscInfo(ts, "Adding mass to Jacobian t=%g, shift=%g\n", (double)time_dummy, (double)shift));
  PetscCheck(shift != 0.0, ctx->comm, PETSC_ERR_PLIB, "zero shift");
  PetscCall(PetscObjectStateGet((PetscObject)ctx->J, &state));
  PetscCheck(state == ctx->norm_state, ctx->comm, PETSC_ERR_PLIB, "wrong state, %" PetscInt64_FMT " %" PetscInt64_FMT "", ctx->norm_state, state);
  if (!ctx->use_matrix_mass) {
    PetscCall(LandauFormJacobian_Internal(X, ctx->J, dim, shift, (void *)ctx));
  } else { /* add mass */
    PetscCall(MatAXPY(Pmat, shift, ctx->M, SAME_NONZERO_PATTERN));
  }
#if defined(PETSC_HAVE_THREADSAFETY)
  if (ctx->stage) {
    endtime = MPI_Wtime();
    ctx->times[LANDAU_OPERATOR] += (endtime - starttime);
    ctx->times[LANDAU_MASS] += (endtime - starttime);
    ctx->times[LANDAU_MATRIX_TOTAL] += (endtime - starttime);
  }
#endif
  PetscCall(PetscLogEventEnd(ctx->events[9], 0, 0, 0, 0));
  PetscCall(PetscLogEventEnd(ctx->events[11], 0, 0, 0, 0));
  if (ctx->stage) PetscCall(PetscLogStagePop());
  PetscFunctionReturn(PETSC_SUCCESS);
}