#include /*I "petscdmplex.h" I*/ #include /*I "petscsnes.h" I*/ #include #include #include static void pressure_Private(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 p[]) { p[0] = u[uOff[1]]; } /* SNESCorrectDiscretePressure_Private - Add a vector in the nullspace to make the continuum integral of the pressure field equal to zero. This is normally used only to evaluate convergence rates for the pressure accurately. Collective Input Parameters: + snes - The SNES . pfield - The field number for pressure . nullspace - The pressure nullspace . u - The solution vector - ctx - An optional user context Output Parameter: . u - The solution with a continuum pressure integral of zero Level: developer Notes: If int(u) = a and int(n) = b, then int(u - a/b n) = a - a/b b = 0. We assume that the nullspace is a single vector given explicitly. .seealso: `SNESConvergedCorrectPressure()` */ static PetscErrorCode SNESCorrectDiscretePressure_Private(SNES snes, PetscInt pfield, MatNullSpace nullspace, Vec u, void *ctx) { DM dm; PetscDS ds; const Vec *nullvecs; PetscScalar pintd, *intc, *intn; MPI_Comm comm; PetscInt Nf, Nv; PetscFunctionBegin; PetscCall(PetscObjectGetComm((PetscObject)snes, &comm)); PetscCall(SNESGetDM(snes, &dm)); PetscCheck(dm, comm, PETSC_ERR_ARG_WRONG, "Cannot compute test without a SNES DM"); PetscCheck(nullspace, comm, PETSC_ERR_ARG_WRONG, "Cannot compute test without a Jacobian nullspace"); PetscCall(DMGetDS(dm, &ds)); PetscCall(PetscDSSetObjective(ds, pfield, pressure_Private)); PetscCall(MatNullSpaceGetVecs(nullspace, NULL, &Nv, &nullvecs)); PetscCheck(Nv == 1, comm, PETSC_ERR_ARG_OUTOFRANGE, "Can only handle a single null vector for pressure, not %" PetscInt_FMT, Nv); PetscCall(VecDot(nullvecs[0], u, &pintd)); PetscCheck(PetscAbsScalar(pintd) <= PETSC_SMALL, comm, PETSC_ERR_ARG_WRONG, "Discrete integral of pressure: %g", (double)PetscRealPart(pintd)); PetscCall(PetscDSGetNumFields(ds, &Nf)); PetscCall(PetscMalloc2(Nf, &intc, Nf, &intn)); PetscCall(DMPlexComputeIntegralFEM(dm, nullvecs[0], intn, ctx)); PetscCall(DMPlexComputeIntegralFEM(dm, u, intc, ctx)); PetscCall(VecAXPY(u, -intc[pfield] / intn[pfield], nullvecs[0])); #if defined(PETSC_USE_DEBUG) PetscCall(DMPlexComputeIntegralFEM(dm, u, intc, ctx)); PetscCheck(PetscAbsScalar(intc[pfield]) <= PETSC_SMALL, comm, PETSC_ERR_ARG_WRONG, "Continuum integral of pressure after correction: %g", (double)PetscRealPart(intc[pfield])); #endif PetscCall(PetscFree2(intc, intn)); PetscFunctionReturn(PETSC_SUCCESS); } /*@C SNESConvergedCorrectPressure - Convergence test that adds a vector in the nullspace to make the continuum integral of the pressure field equal to zero. This is normally used only to evaluate convergence rates for the pressure accurately. The convergence test itself just mimics `SNESConvergedDefault()`. Logically Collective Input Parameters: + snes - the `SNES` context . it - the iteration (0 indicates before any Newton steps) . xnorm - 2-norm of current iterate . snorm - 2-norm of current step . fnorm - 2-norm of function at current iterate - ctx - Optional user context Output Parameter: . reason - `SNES_CONVERGED_ITERATING`, `SNES_CONVERGED_ITS`, or `SNES_DIVERGED_FNORM_NAN` Options Database Key: . -snes_convergence_test correct_pressure - see `SNESSetFromOptions()` Level: advanced Notes: In order to use this convergence test, you must set up several PETSc structures. First fields must be added to the `DM`, and a `PetscDS` must be created with discretizations of those fields. We currently assume that the pressure field has index 1. The pressure field must have a nullspace, likely created using the `DMSetNullSpaceConstructor()` interface. Last we must be able to integrate the pressure over the domain, so the `DM` attached to the SNES `must` be a `DMPLEX` at this time. .seealso: `SNES`, `DM`, `SNESConvergedDefault()`, `SNESSetConvergenceTest()`, `DMSetNullSpaceConstructor()`, `DMSetNullSpaceConstructor()` @*/ PetscErrorCode SNESConvergedCorrectPressure(SNES snes, PetscInt it, PetscReal xnorm, PetscReal gnorm, PetscReal f, SNESConvergedReason *reason, void *ctx) { PetscBool monitorIntegral = PETSC_FALSE; PetscFunctionBegin; PetscCall(SNESConvergedDefault(snes, it, xnorm, gnorm, f, reason, ctx)); if (monitorIntegral) { Mat J; Vec u; MatNullSpace nullspace; const Vec *nullvecs; PetscScalar pintd; PetscCall(SNESGetSolution(snes, &u)); PetscCall(SNESGetJacobian(snes, &J, NULL, NULL, NULL)); PetscCall(MatGetNullSpace(J, &nullspace)); PetscCall(MatNullSpaceGetVecs(nullspace, NULL, NULL, &nullvecs)); PetscCall(VecDot(nullvecs[0], u, &pintd)); PetscCall(PetscInfo(snes, "SNES: Discrete integral of pressure: %g\n", (double)PetscRealPart(pintd))); } if (*reason > 0) { Mat J; Vec u; MatNullSpace nullspace; PetscInt pfield = 1; PetscCall(SNESGetSolution(snes, &u)); PetscCall(SNESGetJacobian(snes, &J, NULL, NULL, NULL)); PetscCall(MatGetNullSpace(J, &nullspace)); PetscCall(SNESCorrectDiscretePressure_Private(snes, pfield, nullspace, u, ctx)); } PetscFunctionReturn(PETSC_SUCCESS); } /************************** Interpolation *******************************/ static PetscErrorCode DMSNESConvertPlex(DM dm, DM *plex, PetscBool copy) { PetscBool isPlex; PetscFunctionBegin; PetscCall(PetscObjectTypeCompare((PetscObject)dm, DMPLEX, &isPlex)); if (isPlex) { *plex = dm; PetscCall(PetscObjectReference((PetscObject)dm)); } else { PetscCall(PetscObjectQuery((PetscObject)dm, "dm_plex", (PetscObject *)plex)); if (!*plex) { PetscCall(DMConvert(dm, DMPLEX, plex)); PetscCall(PetscObjectCompose((PetscObject)dm, "dm_plex", (PetscObject)*plex)); if (copy) { PetscCall(DMCopyDMSNES(dm, *plex)); PetscCall(DMCopyAuxiliaryVec(dm, *plex)); } } else { PetscCall(PetscObjectReference((PetscObject)*plex)); } } PetscFunctionReturn(PETSC_SUCCESS); } /*@C DMInterpolationCreate - Creates a `DMInterpolationInfo` context Collective Input Parameter: . comm - the communicator Output Parameter: . ctx - the context Level: beginner .seealso: `DMInterpolationInfo`, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()`, `DMInterpolationDestroy()` @*/ PetscErrorCode DMInterpolationCreate(MPI_Comm comm, DMInterpolationInfo *ctx) { PetscFunctionBegin; PetscValidPointer(ctx, 2); PetscCall(PetscNew(ctx)); (*ctx)->comm = comm; (*ctx)->dim = -1; (*ctx)->nInput = 0; (*ctx)->points = NULL; (*ctx)->cells = NULL; (*ctx)->n = -1; (*ctx)->coords = NULL; PetscFunctionReturn(PETSC_SUCCESS); } /*@C DMInterpolationSetDim - Sets the spatial dimension for the interpolation context Not Collective Input Parameters: + ctx - the context - dim - the spatial dimension Level: intermediate .seealso: `DMInterpolationInfo`, `DMInterpolationGetDim()`, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()` @*/ PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo ctx, PetscInt dim) { PetscFunctionBegin; PetscCheck(!(dim < 1) && !(dim > 3), ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension for points: %" PetscInt_FMT, dim); ctx->dim = dim; PetscFunctionReturn(PETSC_SUCCESS); } /*@C DMInterpolationGetDim - Gets the spatial dimension for the interpolation context Not Collective Input Parameter: . ctx - the context Output Parameter: . dim - the spatial dimension Level: intermediate .seealso: `DMInterpolationInfo`, `DMInterpolationSetDim()`, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()` @*/ PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo ctx, PetscInt *dim) { PetscFunctionBegin; PetscValidIntPointer(dim, 2); *dim = ctx->dim; PetscFunctionReturn(PETSC_SUCCESS); } /*@C DMInterpolationSetDof - Sets the number of fields interpolated at a point for the interpolation context Not Collective Input Parameters: + ctx - the context - dof - the number of fields Level: intermediate .seealso: `DMInterpolationInfo`, `DMInterpolationGetDof()`, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()` @*/ PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo ctx, PetscInt dof) { PetscFunctionBegin; PetscCheck(dof >= 1, ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid number of components: %" PetscInt_FMT, dof); ctx->dof = dof; PetscFunctionReturn(PETSC_SUCCESS); } /*@C DMInterpolationGetDof - Gets the number of fields interpolated at a point for the interpolation context Not Collective Input Parameter: . ctx - the context Output Parameter: . dof - the number of fields Level: intermediate .seealso: DMInterpolationInfo, `DMInterpolationSetDof()`, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()` @*/ PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo ctx, PetscInt *dof) { PetscFunctionBegin; PetscValidIntPointer(dof, 2); *dof = ctx->dof; PetscFunctionReturn(PETSC_SUCCESS); } /*@C DMInterpolationAddPoints - Add points at which we will interpolate the fields Not Collective Input Parameters: + ctx - the context . n - the number of points - points - the coordinates for each point, an array of size n * dim Level: intermediate Note: The coordinate information is copied. .seealso: `DMInterpolationInfo`, `DMInterpolationSetDim()`, `DMInterpolationEvaluate()`, `DMInterpolationCreate()` @*/ PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo ctx, PetscInt n, PetscReal points[]) { PetscFunctionBegin; PetscCheck(ctx->dim >= 0, ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set"); PetscCheck(!ctx->points, ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "Cannot add points multiple times yet"); ctx->nInput = n; PetscCall(PetscMalloc1(n * ctx->dim, &ctx->points)); PetscCall(PetscArraycpy(ctx->points, points, n * ctx->dim)); PetscFunctionReturn(PETSC_SUCCESS); } /*@C DMInterpolationSetUp - Compute spatial indices for point location during interpolation Collective Input Parameters: + ctx - the context . dm - the `DM` for the function space used for interpolation . redundantPoints - If `PETSC_TRUE`, all processes are passing in the same array of points. Otherwise, points need to be communicated among processes. - ignoreOutsideDomain - If `PETSC_TRUE`, ignore points outside the domain, otherwise return an error Level: intermediate .seealso: DMInterpolationInfo, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()`, `DMInterpolationCreate()` @*/ PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo ctx, DM dm, PetscBool redundantPoints, PetscBool ignoreOutsideDomain) { MPI_Comm comm = ctx->comm; PetscScalar *a; PetscInt p, q, i; PetscMPIInt rank, size; Vec pointVec; PetscSF cellSF; PetscLayout layout; PetscReal *globalPoints; PetscScalar *globalPointsScalar; const PetscInt *ranges; PetscMPIInt *counts, *displs; const PetscSFNode *foundCells; const PetscInt *foundPoints; PetscMPIInt *foundProcs, *globalProcs; PetscInt n, N, numFound; PetscFunctionBegin; PetscValidHeaderSpecific(dm, DM_CLASSID, 2); PetscCallMPI(MPI_Comm_size(comm, &size)); PetscCallMPI(MPI_Comm_rank(comm, &rank)); PetscCheck(ctx->dim >= 0, comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set"); /* Locate points */ n = ctx->nInput; if (!redundantPoints) { PetscCall(PetscLayoutCreate(comm, &layout)); PetscCall(PetscLayoutSetBlockSize(layout, 1)); PetscCall(PetscLayoutSetLocalSize(layout, n)); PetscCall(PetscLayoutSetUp(layout)); PetscCall(PetscLayoutGetSize(layout, &N)); /* Communicate all points to all processes */ PetscCall(PetscMalloc3(N * ctx->dim, &globalPoints, size, &counts, size, &displs)); PetscCall(PetscLayoutGetRanges(layout, &ranges)); for (p = 0; p < size; ++p) { counts[p] = (ranges[p + 1] - ranges[p]) * ctx->dim; displs[p] = ranges[p] * ctx->dim; } PetscCallMPI(MPI_Allgatherv(ctx->points, n * ctx->dim, MPIU_REAL, globalPoints, counts, displs, MPIU_REAL, comm)); } else { N = n; globalPoints = ctx->points; counts = displs = NULL; layout = NULL; } #if 0 PetscCall(PetscMalloc3(N,&foundCells,N,&foundProcs,N,&globalProcs)); /* foundCells[p] = m->locatePoint(&globalPoints[p*ctx->dim]); */ #else #if defined(PETSC_USE_COMPLEX) PetscCall(PetscMalloc1(N * ctx->dim, &globalPointsScalar)); for (i = 0; i < N * ctx->dim; i++) globalPointsScalar[i] = globalPoints[i]; #else globalPointsScalar = globalPoints; #endif PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, ctx->dim, N * ctx->dim, globalPointsScalar, &pointVec)); PetscCall(PetscMalloc2(N, &foundProcs, N, &globalProcs)); for (p = 0; p < N; ++p) foundProcs[p] = size; cellSF = NULL; PetscCall(DMLocatePoints(dm, pointVec, DM_POINTLOCATION_REMOVE, &cellSF)); PetscCall(PetscSFGetGraph(cellSF, NULL, &numFound, &foundPoints, &foundCells)); #endif for (p = 0; p < numFound; ++p) { if (foundCells[p].index >= 0) foundProcs[foundPoints ? foundPoints[p] : p] = rank; } /* Let the lowest rank process own each point */ PetscCall(MPIU_Allreduce(foundProcs, globalProcs, N, MPI_INT, MPI_MIN, comm)); ctx->n = 0; for (p = 0; p < N; ++p) { if (globalProcs[p] == size) { PetscCheck(ignoreOutsideDomain, comm, PETSC_ERR_PLIB, "Point %" PetscInt_FMT ": %g %g %g not located in mesh", p, (double)globalPoints[p * ctx->dim + 0], (double)(ctx->dim > 1 ? globalPoints[p * ctx->dim + 1] : 0.0), (double)(ctx->dim > 2 ? globalPoints[p * ctx->dim + 2] : 0.0)); if (rank == 0) ++ctx->n; } else if (globalProcs[p] == rank) ++ctx->n; } /* Create coordinates vector and array of owned cells */ PetscCall(PetscMalloc1(ctx->n, &ctx->cells)); PetscCall(VecCreate(comm, &ctx->coords)); PetscCall(VecSetSizes(ctx->coords, ctx->n * ctx->dim, PETSC_DECIDE)); PetscCall(VecSetBlockSize(ctx->coords, ctx->dim)); PetscCall(VecSetType(ctx->coords, VECSTANDARD)); PetscCall(VecGetArray(ctx->coords, &a)); for (p = 0, q = 0, i = 0; p < N; ++p) { if (globalProcs[p] == rank) { PetscInt d; for (d = 0; d < ctx->dim; ++d, ++i) a[i] = globalPoints[p * ctx->dim + d]; ctx->cells[q] = foundCells[q].index; ++q; } if (globalProcs[p] == size && rank == 0) { PetscInt d; for (d = 0; d < ctx->dim; ++d, ++i) a[i] = 0.; ctx->cells[q] = -1; ++q; } } PetscCall(VecRestoreArray(ctx->coords, &a)); #if 0 PetscCall(PetscFree3(foundCells,foundProcs,globalProcs)); #else PetscCall(PetscFree2(foundProcs, globalProcs)); PetscCall(PetscSFDestroy(&cellSF)); PetscCall(VecDestroy(&pointVec)); #endif if ((void *)globalPointsScalar != (void *)globalPoints) PetscCall(PetscFree(globalPointsScalar)); if (!redundantPoints) PetscCall(PetscFree3(globalPoints, counts, displs)); PetscCall(PetscLayoutDestroy(&layout)); PetscFunctionReturn(PETSC_SUCCESS); } /*@C DMInterpolationGetCoordinates - Gets a `Vec` with the coordinates of each interpolation point Collective Input Parameter: . ctx - the context Output Parameter: . coordinates - the coordinates of interpolation points Level: intermediate Note: The local vector entries correspond to interpolation points lying on this process, according to the associated `DM`. This is a borrowed vector that the user should not destroy. .seealso: `DMInterpolationInfo`, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()`, `DMInterpolationCreate()` @*/ PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo ctx, Vec *coordinates) { PetscFunctionBegin; PetscValidPointer(coordinates, 2); PetscCheck(ctx->coords, ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup."); *coordinates = ctx->coords; PetscFunctionReturn(PETSC_SUCCESS); } /*@C DMInterpolationGetVector - Gets a `Vec` which can hold all the interpolated field values Collective Input Parameter: . ctx - the context Output Parameter: . v - a vector capable of holding the interpolated field values Level: intermediate Note: This vector should be returned using `DMInterpolationRestoreVector()`. .seealso: `DMInterpolationInfo`, `DMInterpolationRestoreVector()`, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()`, `DMInterpolationCreate()` @*/ PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo ctx, Vec *v) { PetscFunctionBegin; PetscValidPointer(v, 2); PetscCheck(ctx->coords, ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup."); PetscCall(VecCreate(ctx->comm, v)); PetscCall(VecSetSizes(*v, ctx->n * ctx->dof, PETSC_DECIDE)); PetscCall(VecSetBlockSize(*v, ctx->dof)); PetscCall(VecSetType(*v, VECSTANDARD)); PetscFunctionReturn(PETSC_SUCCESS); } /*@C DMInterpolationRestoreVector - Returns a `Vec` which can hold all the interpolated field values Collective Input Parameters: + ctx - the context - v - a vector capable of holding the interpolated field values Level: intermediate .seealso: `DMInterpolationInfo`, `DMInterpolationGetVector()`, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()`, `DMInterpolationCreate()` @*/ PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo ctx, Vec *v) { PetscFunctionBegin; PetscValidPointer(v, 2); PetscCheck(ctx->coords, ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup."); PetscCall(VecDestroy(v)); PetscFunctionReturn(PETSC_SUCCESS); } static inline PetscErrorCode DMInterpolate_Segment_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v) { PetscReal v0, J, invJ, detJ; const PetscInt dof = ctx->dof; const PetscScalar *coords; PetscScalar *a; PetscInt p; PetscFunctionBegin; PetscCall(VecGetArrayRead(ctx->coords, &coords)); PetscCall(VecGetArray(v, &a)); for (p = 0; p < ctx->n; ++p) { PetscInt c = ctx->cells[p]; PetscScalar *x = NULL; PetscReal xir[1]; PetscInt xSize, comp; PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, &v0, &J, &invJ, &detJ)); PetscCheck(detJ > 0.0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %" PetscInt_FMT, (double)detJ, c); xir[0] = invJ * PetscRealPart(coords[p] - v0); PetscCall(DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x)); if (2 * dof == xSize) { for (comp = 0; comp < dof; ++comp) a[p * dof + comp] = x[0 * dof + comp] * (1 - xir[0]) + x[1 * dof + comp] * xir[0]; } else if (dof == xSize) { for (comp = 0; comp < dof; ++comp) a[p * dof + comp] = x[0 * dof + comp]; } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Input closure size %" PetscInt_FMT " must be either %" PetscInt_FMT " or %" PetscInt_FMT, xSize, 2 * dof, dof); PetscCall(DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x)); } PetscCall(VecRestoreArray(v, &a)); PetscCall(VecRestoreArrayRead(ctx->coords, &coords)); PetscFunctionReturn(PETSC_SUCCESS); } static inline PetscErrorCode DMInterpolate_Triangle_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v) { PetscReal *v0, *J, *invJ, detJ; const PetscScalar *coords; PetscScalar *a; PetscInt p; PetscFunctionBegin; PetscCall(PetscMalloc3(ctx->dim, &v0, ctx->dim * ctx->dim, &J, ctx->dim * ctx->dim, &invJ)); PetscCall(VecGetArrayRead(ctx->coords, &coords)); PetscCall(VecGetArray(v, &a)); for (p = 0; p < ctx->n; ++p) { PetscInt c = ctx->cells[p]; PetscScalar *x = NULL; PetscReal xi[4]; PetscInt d, f, comp; PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ)); PetscCheck(detJ > 0.0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %" PetscInt_FMT, (double)detJ, c); PetscCall(DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x)); for (comp = 0; comp < ctx->dof; ++comp) a[p * ctx->dof + comp] = x[0 * ctx->dof + comp]; for (d = 0; d < ctx->dim; ++d) { xi[d] = 0.0; for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d * ctx->dim + f] * 0.5 * PetscRealPart(coords[p * ctx->dim + f] - v0[f]); for (comp = 0; comp < ctx->dof; ++comp) a[p * ctx->dof + comp] += PetscRealPart(x[(d + 1) * ctx->dof + comp] - x[0 * ctx->dof + comp]) * xi[d]; } PetscCall(DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x)); } PetscCall(VecRestoreArray(v, &a)); PetscCall(VecRestoreArrayRead(ctx->coords, &coords)); PetscCall(PetscFree3(v0, J, invJ)); PetscFunctionReturn(PETSC_SUCCESS); } static inline PetscErrorCode DMInterpolate_Tetrahedron_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v) { PetscReal *v0, *J, *invJ, detJ; const PetscScalar *coords; PetscScalar *a; PetscInt p; PetscFunctionBegin; PetscCall(PetscMalloc3(ctx->dim, &v0, ctx->dim * ctx->dim, &J, ctx->dim * ctx->dim, &invJ)); PetscCall(VecGetArrayRead(ctx->coords, &coords)); PetscCall(VecGetArray(v, &a)); for (p = 0; p < ctx->n; ++p) { PetscInt c = ctx->cells[p]; const PetscInt order[3] = {2, 1, 3}; PetscScalar *x = NULL; PetscReal xi[4]; PetscInt d, f, comp; PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ)); PetscCheck(detJ > 0.0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %" PetscInt_FMT, (double)detJ, c); PetscCall(DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x)); for (comp = 0; comp < ctx->dof; ++comp) a[p * ctx->dof + comp] = x[0 * ctx->dof + comp]; for (d = 0; d < ctx->dim; ++d) { xi[d] = 0.0; for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d * ctx->dim + f] * 0.5 * PetscRealPart(coords[p * ctx->dim + f] - v0[f]); for (comp = 0; comp < ctx->dof; ++comp) a[p * ctx->dof + comp] += PetscRealPart(x[order[d] * ctx->dof + comp] - x[0 * ctx->dof + comp]) * xi[d]; } PetscCall(DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x)); } PetscCall(VecRestoreArray(v, &a)); PetscCall(VecRestoreArrayRead(ctx->coords, &coords)); PetscCall(PetscFree3(v0, J, invJ)); PetscFunctionReturn(PETSC_SUCCESS); } static inline PetscErrorCode QuadMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx) { const PetscScalar *vertices = (const PetscScalar *)ctx; const PetscScalar x0 = vertices[0]; const PetscScalar y0 = vertices[1]; const PetscScalar x1 = vertices[2]; const PetscScalar y1 = vertices[3]; const PetscScalar x2 = vertices[4]; const PetscScalar y2 = vertices[5]; const PetscScalar x3 = vertices[6]; const PetscScalar y3 = vertices[7]; const PetscScalar f_1 = x1 - x0; const PetscScalar g_1 = y1 - y0; const PetscScalar f_3 = x3 - x0; const PetscScalar g_3 = y3 - y0; const PetscScalar f_01 = x2 - x1 - x3 + x0; const PetscScalar g_01 = y2 - y1 - y3 + y0; const PetscScalar *ref; PetscScalar *real; PetscFunctionBegin; PetscCall(VecGetArrayRead(Xref, &ref)); PetscCall(VecGetArray(Xreal, &real)); { const PetscScalar p0 = ref[0]; const PetscScalar p1 = ref[1]; real[0] = x0 + f_1 * p0 + f_3 * p1 + f_01 * p0 * p1; real[1] = y0 + g_1 * p0 + g_3 * p1 + g_01 * p0 * p1; } PetscCall(PetscLogFlops(28)); PetscCall(VecRestoreArrayRead(Xref, &ref)); PetscCall(VecRestoreArray(Xreal, &real)); PetscFunctionReturn(PETSC_SUCCESS); } #include static inline PetscErrorCode QuadJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx) { const PetscScalar *vertices = (const PetscScalar *)ctx; const PetscScalar x0 = vertices[0]; const PetscScalar y0 = vertices[1]; const PetscScalar x1 = vertices[2]; const PetscScalar y1 = vertices[3]; const PetscScalar x2 = vertices[4]; const PetscScalar y2 = vertices[5]; const PetscScalar x3 = vertices[6]; const PetscScalar y3 = vertices[7]; const PetscScalar f_01 = x2 - x1 - x3 + x0; const PetscScalar g_01 = y2 - y1 - y3 + y0; const PetscScalar *ref; PetscFunctionBegin; PetscCall(VecGetArrayRead(Xref, &ref)); { const PetscScalar x = ref[0]; const PetscScalar y = ref[1]; const PetscInt rows[2] = {0, 1}; PetscScalar values[4]; values[0] = (x1 - x0 + f_01 * y) * 0.5; values[1] = (x3 - x0 + f_01 * x) * 0.5; values[2] = (y1 - y0 + g_01 * y) * 0.5; values[3] = (y3 - y0 + g_01 * x) * 0.5; PetscCall(MatSetValues(J, 2, rows, 2, rows, values, INSERT_VALUES)); } PetscCall(PetscLogFlops(30)); PetscCall(VecRestoreArrayRead(Xref, &ref)); PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY)); PetscFunctionReturn(PETSC_SUCCESS); } static inline PetscErrorCode DMInterpolate_Quad_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v) { DM dmCoord; PetscFE fem = NULL; SNES snes; KSP ksp; PC pc; Vec coordsLocal, r, ref, real; Mat J; PetscTabulation T = NULL; const PetscScalar *coords; PetscScalar *a; PetscReal xir[2] = {0., 0.}; PetscInt Nf, p; const PetscInt dof = ctx->dof; PetscFunctionBegin; PetscCall(DMGetNumFields(dm, &Nf)); if (Nf) { PetscObject obj; PetscClassId id; PetscCall(DMGetField(dm, 0, NULL, &obj)); PetscCall(PetscObjectGetClassId(obj, &id)); if (id == PETSCFE_CLASSID) { fem = (PetscFE)obj; PetscCall(PetscFECreateTabulation(fem, 1, 1, xir, 0, &T)); } } PetscCall(DMGetCoordinatesLocal(dm, &coordsLocal)); PetscCall(DMGetCoordinateDM(dm, &dmCoord)); PetscCall(SNESCreate(PETSC_COMM_SELF, &snes)); PetscCall(SNESSetOptionsPrefix(snes, "quad_interp_")); PetscCall(VecCreate(PETSC_COMM_SELF, &r)); PetscCall(VecSetSizes(r, 2, 2)); PetscCall(VecSetType(r, dm->vectype)); PetscCall(VecDuplicate(r, &ref)); PetscCall(VecDuplicate(r, &real)); PetscCall(MatCreate(PETSC_COMM_SELF, &J)); PetscCall(MatSetSizes(J, 2, 2, 2, 2)); PetscCall(MatSetType(J, MATSEQDENSE)); PetscCall(MatSetUp(J)); PetscCall(SNESSetFunction(snes, r, QuadMap_Private, NULL)); PetscCall(SNESSetJacobian(snes, J, J, QuadJacobian_Private, NULL)); PetscCall(SNESGetKSP(snes, &ksp)); PetscCall(KSPGetPC(ksp, &pc)); PetscCall(PCSetType(pc, PCLU)); PetscCall(SNESSetFromOptions(snes)); PetscCall(VecGetArrayRead(ctx->coords, &coords)); PetscCall(VecGetArray(v, &a)); for (p = 0; p < ctx->n; ++p) { PetscScalar *x = NULL, *vertices = NULL; PetscScalar *xi; PetscInt c = ctx->cells[p], comp, coordSize, xSize; /* Can make this do all points at once */ PetscCall(DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices)); PetscCheck(4 * 2 == coordSize, ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %" PetscInt_FMT " should be %d", coordSize, 4 * 2); PetscCall(DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x)); PetscCall(SNESSetFunction(snes, NULL, NULL, vertices)); PetscCall(SNESSetJacobian(snes, NULL, NULL, NULL, vertices)); PetscCall(VecGetArray(real, &xi)); xi[0] = coords[p * ctx->dim + 0]; xi[1] = coords[p * ctx->dim + 1]; PetscCall(VecRestoreArray(real, &xi)); PetscCall(SNESSolve(snes, real, ref)); PetscCall(VecGetArray(ref, &xi)); xir[0] = PetscRealPart(xi[0]); xir[1] = PetscRealPart(xi[1]); if (4 * dof == xSize) { for (comp = 0; comp < dof; ++comp) a[p * dof + comp] = x[0 * dof + comp] * (1 - xir[0]) * (1 - xir[1]) + x[1 * dof + comp] * xir[0] * (1 - xir[1]) + x[2 * dof + comp] * xir[0] * xir[1] + x[3 * dof + comp] * (1 - xir[0]) * xir[1]; } else if (dof == xSize) { for (comp = 0; comp < dof; ++comp) a[p * dof + comp] = x[0 * dof + comp]; } else { PetscInt d; PetscCheck(fem, ctx->comm, PETSC_ERR_ARG_WRONG, "Cannot have a higher order interpolant if the discretization is not PetscFE"); xir[0] = 2.0 * xir[0] - 1.0; xir[1] = 2.0 * xir[1] - 1.0; PetscCall(PetscFEComputeTabulation(fem, 1, xir, 0, T)); for (comp = 0; comp < dof; ++comp) { a[p * dof + comp] = 0.0; for (d = 0; d < xSize / dof; ++d) a[p * dof + comp] += x[d * dof + comp] * T->T[0][d * dof + comp]; } } PetscCall(VecRestoreArray(ref, &xi)); PetscCall(DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices)); PetscCall(DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x)); } PetscCall(PetscTabulationDestroy(&T)); PetscCall(VecRestoreArray(v, &a)); PetscCall(VecRestoreArrayRead(ctx->coords, &coords)); PetscCall(SNESDestroy(&snes)); PetscCall(VecDestroy(&r)); PetscCall(VecDestroy(&ref)); PetscCall(VecDestroy(&real)); PetscCall(MatDestroy(&J)); PetscFunctionReturn(PETSC_SUCCESS); } static inline PetscErrorCode HexMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx) { const PetscScalar *vertices = (const PetscScalar *)ctx; const PetscScalar x0 = vertices[0]; const PetscScalar y0 = vertices[1]; const PetscScalar z0 = vertices[2]; const PetscScalar x1 = vertices[9]; const PetscScalar y1 = vertices[10]; const PetscScalar z1 = vertices[11]; const PetscScalar x2 = vertices[6]; const PetscScalar y2 = vertices[7]; const PetscScalar z2 = vertices[8]; const PetscScalar x3 = vertices[3]; const PetscScalar y3 = vertices[4]; const PetscScalar z3 = vertices[5]; const PetscScalar x4 = vertices[12]; const PetscScalar y4 = vertices[13]; const PetscScalar z4 = vertices[14]; const PetscScalar x5 = vertices[15]; const PetscScalar y5 = vertices[16]; const PetscScalar z5 = vertices[17]; const PetscScalar x6 = vertices[18]; const PetscScalar y6 = vertices[19]; const PetscScalar z6 = vertices[20]; const PetscScalar x7 = vertices[21]; const PetscScalar y7 = vertices[22]; const PetscScalar z7 = vertices[23]; const PetscScalar f_1 = x1 - x0; const PetscScalar g_1 = y1 - y0; const PetscScalar h_1 = z1 - z0; const PetscScalar f_3 = x3 - x0; const PetscScalar g_3 = y3 - y0; const PetscScalar h_3 = z3 - z0; const PetscScalar f_4 = x4 - x0; const PetscScalar g_4 = y4 - y0; const PetscScalar h_4 = z4 - z0; const PetscScalar f_01 = x2 - x1 - x3 + x0; const PetscScalar g_01 = y2 - y1 - y3 + y0; const PetscScalar h_01 = z2 - z1 - z3 + z0; const PetscScalar f_12 = x7 - x3 - x4 + x0; const PetscScalar g_12 = y7 - y3 - y4 + y0; const PetscScalar h_12 = z7 - z3 - z4 + z0; const PetscScalar f_02 = x5 - x1 - x4 + x0; const PetscScalar g_02 = y5 - y1 - y4 + y0; const PetscScalar h_02 = z5 - z1 - z4 + z0; const PetscScalar f_012 = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7; const PetscScalar g_012 = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7; const PetscScalar h_012 = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7; const PetscScalar *ref; PetscScalar *real; PetscFunctionBegin; PetscCall(VecGetArrayRead(Xref, &ref)); PetscCall(VecGetArray(Xreal, &real)); { const PetscScalar p0 = ref[0]; const PetscScalar p1 = ref[1]; const PetscScalar p2 = ref[2]; real[0] = x0 + f_1 * p0 + f_3 * p1 + f_4 * p2 + f_01 * p0 * p1 + f_12 * p1 * p2 + f_02 * p0 * p2 + f_012 * p0 * p1 * p2; real[1] = y0 + g_1 * p0 + g_3 * p1 + g_4 * p2 + g_01 * p0 * p1 + g_01 * p0 * p1 + g_12 * p1 * p2 + g_02 * p0 * p2 + g_012 * p0 * p1 * p2; real[2] = z0 + h_1 * p0 + h_3 * p1 + h_4 * p2 + h_01 * p0 * p1 + h_01 * p0 * p1 + h_12 * p1 * p2 + h_02 * p0 * p2 + h_012 * p0 * p1 * p2; } PetscCall(PetscLogFlops(114)); PetscCall(VecRestoreArrayRead(Xref, &ref)); PetscCall(VecRestoreArray(Xreal, &real)); PetscFunctionReturn(PETSC_SUCCESS); } static inline PetscErrorCode HexJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx) { const PetscScalar *vertices = (const PetscScalar *)ctx; const PetscScalar x0 = vertices[0]; const PetscScalar y0 = vertices[1]; const PetscScalar z0 = vertices[2]; const PetscScalar x1 = vertices[9]; const PetscScalar y1 = vertices[10]; const PetscScalar z1 = vertices[11]; const PetscScalar x2 = vertices[6]; const PetscScalar y2 = vertices[7]; const PetscScalar z2 = vertices[8]; const PetscScalar x3 = vertices[3]; const PetscScalar y3 = vertices[4]; const PetscScalar z3 = vertices[5]; const PetscScalar x4 = vertices[12]; const PetscScalar y4 = vertices[13]; const PetscScalar z4 = vertices[14]; const PetscScalar x5 = vertices[15]; const PetscScalar y5 = vertices[16]; const PetscScalar z5 = vertices[17]; const PetscScalar x6 = vertices[18]; const PetscScalar y6 = vertices[19]; const PetscScalar z6 = vertices[20]; const PetscScalar x7 = vertices[21]; const PetscScalar y7 = vertices[22]; const PetscScalar z7 = vertices[23]; const PetscScalar f_xy = x2 - x1 - x3 + x0; const PetscScalar g_xy = y2 - y1 - y3 + y0; const PetscScalar h_xy = z2 - z1 - z3 + z0; const PetscScalar f_yz = x7 - x3 - x4 + x0; const PetscScalar g_yz = y7 - y3 - y4 + y0; const PetscScalar h_yz = z7 - z3 - z4 + z0; const PetscScalar f_xz = x5 - x1 - x4 + x0; const PetscScalar g_xz = y5 - y1 - y4 + y0; const PetscScalar h_xz = z5 - z1 - z4 + z0; const PetscScalar f_xyz = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7; const PetscScalar g_xyz = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7; const PetscScalar h_xyz = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7; const PetscScalar *ref; PetscFunctionBegin; PetscCall(VecGetArrayRead(Xref, &ref)); { const PetscScalar x = ref[0]; const PetscScalar y = ref[1]; const PetscScalar z = ref[2]; const PetscInt rows[3] = {0, 1, 2}; PetscScalar values[9]; values[0] = (x1 - x0 + f_xy * y + f_xz * z + f_xyz * y * z) / 2.0; values[1] = (x3 - x0 + f_xy * x + f_yz * z + f_xyz * x * z) / 2.0; values[2] = (x4 - x0 + f_yz * y + f_xz * x + f_xyz * x * y) / 2.0; values[3] = (y1 - y0 + g_xy * y + g_xz * z + g_xyz * y * z) / 2.0; values[4] = (y3 - y0 + g_xy * x + g_yz * z + g_xyz * x * z) / 2.0; values[5] = (y4 - y0 + g_yz * y + g_xz * x + g_xyz * x * y) / 2.0; values[6] = (z1 - z0 + h_xy * y + h_xz * z + h_xyz * y * z) / 2.0; values[7] = (z3 - z0 + h_xy * x + h_yz * z + h_xyz * x * z) / 2.0; values[8] = (z4 - z0 + h_yz * y + h_xz * x + h_xyz * x * y) / 2.0; PetscCall(MatSetValues(J, 3, rows, 3, rows, values, INSERT_VALUES)); } PetscCall(PetscLogFlops(152)); PetscCall(VecRestoreArrayRead(Xref, &ref)); PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY)); PetscFunctionReturn(PETSC_SUCCESS); } static inline PetscErrorCode DMInterpolate_Hex_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v) { DM dmCoord; SNES snes; KSP ksp; PC pc; Vec coordsLocal, r, ref, real; Mat J; const PetscScalar *coords; PetscScalar *a; PetscInt p; PetscFunctionBegin; PetscCall(DMGetCoordinatesLocal(dm, &coordsLocal)); PetscCall(DMGetCoordinateDM(dm, &dmCoord)); PetscCall(SNESCreate(PETSC_COMM_SELF, &snes)); PetscCall(SNESSetOptionsPrefix(snes, "hex_interp_")); PetscCall(VecCreate(PETSC_COMM_SELF, &r)); PetscCall(VecSetSizes(r, 3, 3)); PetscCall(VecSetType(r, dm->vectype)); PetscCall(VecDuplicate(r, &ref)); PetscCall(VecDuplicate(r, &real)); PetscCall(MatCreate(PETSC_COMM_SELF, &J)); PetscCall(MatSetSizes(J, 3, 3, 3, 3)); PetscCall(MatSetType(J, MATSEQDENSE)); PetscCall(MatSetUp(J)); PetscCall(SNESSetFunction(snes, r, HexMap_Private, NULL)); PetscCall(SNESSetJacobian(snes, J, J, HexJacobian_Private, NULL)); PetscCall(SNESGetKSP(snes, &ksp)); PetscCall(KSPGetPC(ksp, &pc)); PetscCall(PCSetType(pc, PCLU)); PetscCall(SNESSetFromOptions(snes)); PetscCall(VecGetArrayRead(ctx->coords, &coords)); PetscCall(VecGetArray(v, &a)); for (p = 0; p < ctx->n; ++p) { PetscScalar *x = NULL, *vertices = NULL; PetscScalar *xi; PetscReal xir[3]; PetscInt c = ctx->cells[p], comp, coordSize, xSize; /* Can make this do all points at once */ PetscCall(DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices)); PetscCheck(8 * 3 == coordSize, ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid coordinate closure size %" PetscInt_FMT " should be %d", coordSize, 8 * 3); PetscCall(DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x)); PetscCheck((8 * ctx->dof == xSize) || (ctx->dof == xSize), ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid input closure size %" PetscInt_FMT " should be %" PetscInt_FMT " or %" PetscInt_FMT, xSize, 8 * ctx->dof, ctx->dof); PetscCall(SNESSetFunction(snes, NULL, NULL, vertices)); PetscCall(SNESSetJacobian(snes, NULL, NULL, NULL, vertices)); PetscCall(VecGetArray(real, &xi)); xi[0] = coords[p * ctx->dim + 0]; xi[1] = coords[p * ctx->dim + 1]; xi[2] = coords[p * ctx->dim + 2]; PetscCall(VecRestoreArray(real, &xi)); PetscCall(SNESSolve(snes, real, ref)); PetscCall(VecGetArray(ref, &xi)); xir[0] = PetscRealPart(xi[0]); xir[1] = PetscRealPart(xi[1]); xir[2] = PetscRealPart(xi[2]); if (8 * ctx->dof == xSize) { for (comp = 0; comp < ctx->dof; ++comp) { a[p * ctx->dof + comp] = x[0 * ctx->dof + comp] * (1 - xir[0]) * (1 - xir[1]) * (1 - xir[2]) + x[3 * ctx->dof + comp] * xir[0] * (1 - xir[1]) * (1 - xir[2]) + x[2 * ctx->dof + comp] * xir[0] * xir[1] * (1 - xir[2]) + x[1 * ctx->dof + comp] * (1 - xir[0]) * xir[1] * (1 - xir[2]) + x[4 * ctx->dof + comp] * (1 - xir[0]) * (1 - xir[1]) * xir[2] + x[5 * ctx->dof + comp] * xir[0] * (1 - xir[1]) * xir[2] + x[6 * ctx->dof + comp] * xir[0] * xir[1] * xir[2] + x[7 * ctx->dof + comp] * (1 - xir[0]) * xir[1] * xir[2]; } } else { for (comp = 0; comp < ctx->dof; ++comp) a[p * ctx->dof + comp] = x[0 * ctx->dof + comp]; } PetscCall(VecRestoreArray(ref, &xi)); PetscCall(DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices)); PetscCall(DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x)); } PetscCall(VecRestoreArray(v, &a)); PetscCall(VecRestoreArrayRead(ctx->coords, &coords)); PetscCall(SNESDestroy(&snes)); PetscCall(VecDestroy(&r)); PetscCall(VecDestroy(&ref)); PetscCall(VecDestroy(&real)); PetscCall(MatDestroy(&J)); PetscFunctionReturn(PETSC_SUCCESS); } /*@C DMInterpolationEvaluate - Using the input from dm and x, calculates interpolated field values at the interpolation points. Input Parameters: + ctx - The `DMInterpolationInfo` context . dm - The `DM` - x - The local vector containing the field to be interpolated Output Parameter: . v - The vector containing the interpolated values Level: beginner Note: A suitable `v` can be obtained using `DMInterpolationGetVector()`. .seealso: `DMInterpolationInfo`, `DMInterpolationGetVector()`, `DMInterpolationAddPoints()`, `DMInterpolationCreate()` @*/ PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo ctx, DM dm, Vec x, Vec v) { PetscDS ds; PetscInt n, p, Nf, field; PetscBool useDS = PETSC_FALSE; PetscFunctionBegin; PetscValidHeaderSpecific(dm, DM_CLASSID, 2); PetscValidHeaderSpecific(x, VEC_CLASSID, 3); PetscValidHeaderSpecific(v, VEC_CLASSID, 4); PetscCall(VecGetLocalSize(v, &n)); PetscCheck(n == ctx->n * ctx->dof, ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid input vector size %" PetscInt_FMT " should be %" PetscInt_FMT, n, ctx->n * ctx->dof); if (!n) PetscFunctionReturn(PETSC_SUCCESS); PetscCall(DMGetDS(dm, &ds)); if (ds) { useDS = PETSC_TRUE; PetscCall(PetscDSGetNumFields(ds, &Nf)); for (field = 0; field < Nf; ++field) { PetscObject obj; PetscClassId id; PetscCall(PetscDSGetDiscretization(ds, field, &obj)); PetscCall(PetscObjectGetClassId(obj, &id)); if (id != PETSCFE_CLASSID) { useDS = PETSC_FALSE; break; } } } if (useDS) { const PetscScalar *coords; PetscScalar *interpolant; PetscInt cdim, d; PetscCall(DMGetCoordinateDim(dm, &cdim)); PetscCall(VecGetArrayRead(ctx->coords, &coords)); PetscCall(VecGetArrayWrite(v, &interpolant)); for (p = 0; p < ctx->n; ++p) { PetscReal pcoords[3], xi[3]; PetscScalar *xa = NULL; PetscInt coff = 0, foff = 0, clSize; if (ctx->cells[p] < 0) continue; for (d = 0; d < cdim; ++d) pcoords[d] = PetscRealPart(coords[p * cdim + d]); PetscCall(DMPlexCoordinatesToReference(dm, ctx->cells[p], 1, pcoords, xi)); PetscCall(DMPlexVecGetClosure(dm, NULL, x, ctx->cells[p], &clSize, &xa)); for (field = 0; field < Nf; ++field) { PetscTabulation T; PetscFE fe; PetscCall(PetscDSGetDiscretization(ds, field, (PetscObject *)&fe)); PetscCall(PetscFECreateTabulation(fe, 1, 1, xi, 0, &T)); { const PetscReal *basis = T->T[0]; const PetscInt Nb = T->Nb; const PetscInt Nc = T->Nc; PetscInt f, fc; for (fc = 0; fc < Nc; ++fc) { interpolant[p * ctx->dof + coff + fc] = 0.0; for (f = 0; f < Nb; ++f) interpolant[p * ctx->dof + coff + fc] += xa[foff + f] * basis[(0 * Nb + f) * Nc + fc]; } coff += Nc; foff += Nb; } PetscCall(PetscTabulationDestroy(&T)); } PetscCall(DMPlexVecRestoreClosure(dm, NULL, x, ctx->cells[p], &clSize, &xa)); PetscCheck(coff == ctx->dof, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Total components %" PetscInt_FMT " != %" PetscInt_FMT " dof specified for interpolation", coff, ctx->dof); PetscCheck(foff == clSize, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Total FE space size %" PetscInt_FMT " != %" PetscInt_FMT " closure size", foff, clSize); } PetscCall(VecRestoreArrayRead(ctx->coords, &coords)); PetscCall(VecRestoreArrayWrite(v, &interpolant)); } else { DMPolytopeType ct; /* TODO Check each cell individually */ PetscCall(DMPlexGetCellType(dm, ctx->cells[0], &ct)); switch (ct) { case DM_POLYTOPE_SEGMENT: PetscCall(DMInterpolate_Segment_Private(ctx, dm, x, v)); break; case DM_POLYTOPE_TRIANGLE: PetscCall(DMInterpolate_Triangle_Private(ctx, dm, x, v)); break; case DM_POLYTOPE_QUADRILATERAL: PetscCall(DMInterpolate_Quad_Private(ctx, dm, x, v)); break; case DM_POLYTOPE_TETRAHEDRON: PetscCall(DMInterpolate_Tetrahedron_Private(ctx, dm, x, v)); break; case DM_POLYTOPE_HEXAHEDRON: PetscCall(DMInterpolate_Hex_Private(ctx, dm, x, v)); break; default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for cell type %s", DMPolytopeTypes[PetscMax(0, PetscMin(ct, DM_NUM_POLYTOPES))]); } } PetscFunctionReturn(PETSC_SUCCESS); } /*@C DMInterpolationDestroy - Destroys a `DMInterpolationInfo` context Collective Input Parameter: . ctx - the context Level: beginner .seealso: `DMInterpolationInfo`, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()`, `DMInterpolationCreate()` @*/ PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *ctx) { PetscFunctionBegin; PetscValidPointer(ctx, 1); PetscCall(VecDestroy(&(*ctx)->coords)); PetscCall(PetscFree((*ctx)->points)); PetscCall(PetscFree((*ctx)->cells)); PetscCall(PetscFree(*ctx)); *ctx = NULL; PetscFunctionReturn(PETSC_SUCCESS); } /*@C SNESMonitorFields - Monitors the residual for each field separately Collective Input Parameters: + snes - the `SNES` context . its - iteration number . fgnorm - 2-norm of residual - vf - `PetscViewerAndFormat` of `PetscViewerType` `PETSCVIEWERASCII` Level: intermediate Note: This routine prints the residual norm at each iteration. .seealso: `SNES`, `SNESMonitorSet()`, `SNESMonitorDefault()` @*/ PetscErrorCode SNESMonitorFields(SNES snes, PetscInt its, PetscReal fgnorm, PetscViewerAndFormat *vf) { PetscViewer viewer = vf->viewer; Vec res; DM dm; PetscSection s; const PetscScalar *r; PetscReal *lnorms, *norms; PetscInt numFields, f, pStart, pEnd, p; PetscFunctionBegin; PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 4); PetscCall(SNESGetFunction(snes, &res, NULL, NULL)); PetscCall(SNESGetDM(snes, &dm)); PetscCall(DMGetLocalSection(dm, &s)); PetscCall(PetscSectionGetNumFields(s, &numFields)); PetscCall(PetscSectionGetChart(s, &pStart, &pEnd)); PetscCall(PetscCalloc2(numFields, &lnorms, numFields, &norms)); PetscCall(VecGetArrayRead(res, &r)); for (p = pStart; p < pEnd; ++p) { for (f = 0; f < numFields; ++f) { PetscInt fdof, foff, d; PetscCall(PetscSectionGetFieldDof(s, p, f, &fdof)); PetscCall(PetscSectionGetFieldOffset(s, p, f, &foff)); for (d = 0; d < fdof; ++d) lnorms[f] += PetscRealPart(PetscSqr(r[foff + d])); } } PetscCall(VecRestoreArrayRead(res, &r)); PetscCall(MPIU_Allreduce(lnorms, norms, numFields, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)dm))); PetscCall(PetscViewerPushFormat(viewer, vf->format)); PetscCall(PetscViewerASCIIAddTab(viewer, ((PetscObject)snes)->tablevel)); PetscCall(PetscViewerASCIIPrintf(viewer, "%3" PetscInt_FMT " SNES Function norm %14.12e [", its, (double)fgnorm)); for (f = 0; f < numFields; ++f) { if (f > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ", ")); PetscCall(PetscViewerASCIIPrintf(viewer, "%14.12e", (double)PetscSqrtReal(norms[f]))); } PetscCall(PetscViewerASCIIPrintf(viewer, "]\n")); PetscCall(PetscViewerASCIISubtractTab(viewer, ((PetscObject)snes)->tablevel)); PetscCall(PetscViewerPopFormat(viewer)); PetscCall(PetscFree2(lnorms, norms)); PetscFunctionReturn(PETSC_SUCCESS); } /********************* Residual Computation **************************/ PetscErrorCode DMPlexGetAllCells_Internal(DM plex, IS *cellIS) { PetscInt depth; PetscFunctionBegin; PetscCall(DMPlexGetDepth(plex, &depth)); PetscCall(DMGetStratumIS(plex, "dim", depth, cellIS)); if (!*cellIS) PetscCall(DMGetStratumIS(plex, "depth", depth, cellIS)); PetscFunctionReturn(PETSC_SUCCESS); } /*@ DMPlexSNESComputeResidualFEM - Sums the local residual into vector F from the local input X using pointwise functions specified by the user Input Parameters: + dm - The mesh . X - Local solution - user - The user context Output Parameter: . F - Local output vector Level: developer Note: The residual is summed into F; the caller is responsible for using `VecZeroEntries()` or otherwise ensuring that any data in F is intentional. .seealso: `DM`, `DMPlexComputeJacobianAction()` @*/ PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user) { DM plex; IS allcellIS; PetscInt Nds, s; PetscFunctionBegin; PetscCall(DMSNESConvertPlex(dm, &plex, PETSC_TRUE)); PetscCall(DMPlexGetAllCells_Internal(plex, &allcellIS)); PetscCall(DMGetNumDS(dm, &Nds)); for (s = 0; s < Nds; ++s) { PetscDS ds; IS cellIS; PetscFormKey key; PetscCall(DMGetRegionNumDS(dm, s, &key.label, NULL, &ds, NULL)); key.value = 0; key.field = 0; key.part = 0; if (!key.label) { PetscCall(PetscObjectReference((PetscObject)allcellIS)); cellIS = allcellIS; } else { IS pointIS; key.value = 1; PetscCall(DMLabelGetStratumIS(key.label, key.value, &pointIS)); PetscCall(ISIntersect_Caching_Internal(allcellIS, pointIS, &cellIS)); PetscCall(ISDestroy(&pointIS)); } PetscCall(DMPlexComputeResidual_Internal(plex, key, cellIS, PETSC_MIN_REAL, X, NULL, 0.0, F, user)); PetscCall(ISDestroy(&cellIS)); } PetscCall(ISDestroy(&allcellIS)); PetscCall(DMDestroy(&plex)); PetscFunctionReturn(PETSC_SUCCESS); } PetscErrorCode DMSNESComputeResidual(DM dm, Vec X, Vec F, void *user) { DM plex; IS allcellIS; PetscInt Nds, s; PetscFunctionBegin; PetscCall(DMSNESConvertPlex(dm, &plex, PETSC_TRUE)); PetscCall(DMPlexGetAllCells_Internal(plex, &allcellIS)); PetscCall(DMGetNumDS(dm, &Nds)); for (s = 0; s < Nds; ++s) { PetscDS ds; DMLabel label; IS cellIS; PetscCall(DMGetRegionNumDS(dm, s, &label, NULL, &ds, NULL)); { PetscWeakFormKind resmap[2] = {PETSC_WF_F0, PETSC_WF_F1}; PetscWeakForm wf; PetscInt Nm = 2, m, Nk = 0, k, kp, off = 0; PetscFormKey *reskeys; /* Get unique residual keys */ for (m = 0; m < Nm; ++m) { PetscInt Nkm; PetscCall(PetscHMapFormGetSize(ds->wf->form[resmap[m]], &Nkm)); Nk += Nkm; } PetscCall(PetscMalloc1(Nk, &reskeys)); for (m = 0; m < Nm; ++m) PetscCall(PetscHMapFormGetKeys(ds->wf->form[resmap[m]], &off, reskeys)); PetscCheck(off == Nk, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number of keys %" PetscInt_FMT " should be %" PetscInt_FMT, off, Nk); PetscCall(PetscFormKeySort(Nk, reskeys)); for (k = 0, kp = 1; kp < Nk; ++kp) { if ((reskeys[k].label != reskeys[kp].label) || (reskeys[k].value != reskeys[kp].value)) { ++k; if (kp != k) reskeys[k] = reskeys[kp]; } } Nk = k; PetscCall(PetscDSGetWeakForm(ds, &wf)); for (k = 0; k < Nk; ++k) { DMLabel label = reskeys[k].label; PetscInt val = reskeys[k].value; if (!label) { PetscCall(PetscObjectReference((PetscObject)allcellIS)); cellIS = allcellIS; } else { IS pointIS; PetscCall(DMLabelGetStratumIS(label, val, &pointIS)); PetscCall(ISIntersect_Caching_Internal(allcellIS, pointIS, &cellIS)); PetscCall(ISDestroy(&pointIS)); } PetscCall(DMPlexComputeResidual_Internal(plex, reskeys[k], cellIS, PETSC_MIN_REAL, X, NULL, 0.0, F, user)); PetscCall(ISDestroy(&cellIS)); } PetscCall(PetscFree(reskeys)); } } PetscCall(ISDestroy(&allcellIS)); PetscCall(DMDestroy(&plex)); PetscFunctionReturn(PETSC_SUCCESS); } /*@ DMPlexSNESComputeBoundaryFEM - Form the boundary values for the local input X Input Parameters: + dm - The mesh - user - The user context Output Parameter: . X - Local solution Level: developer .seealso: `DMPLEX`, `DMPlexComputeJacobianAction()` @*/ PetscErrorCode DMPlexSNESComputeBoundaryFEM(DM dm, Vec X, void *user) { DM plex; PetscFunctionBegin; PetscCall(DMSNESConvertPlex(dm, &plex, PETSC_TRUE)); PetscCall(DMPlexInsertBoundaryValues(plex, PETSC_TRUE, X, PETSC_MIN_REAL, NULL, NULL, NULL)); PetscCall(DMDestroy(&plex)); PetscFunctionReturn(PETSC_SUCCESS); } /*@ DMSNESComputeJacobianAction - Compute the action of the Jacobian J(X) on Y Input Parameters: + dm - The `DM` . X - Local solution vector . Y - Local input vector - user - The user context Output Parameter: . F - local output vector Level: developer Notes: Users will typically use `DMSNESCreateJacobianMF()` followed by `MatMult()` instead of calling this routine directly. .seealso: `DM`, ``DMSNESCreateJacobianMF()`, `DMPlexSNESComputeResidualFEM()` @*/ PetscErrorCode DMSNESComputeJacobianAction(DM dm, Vec X, Vec Y, Vec F, void *user) { DM plex; IS allcellIS; PetscInt Nds, s; PetscFunctionBegin; PetscCall(DMSNESConvertPlex(dm, &plex, PETSC_TRUE)); PetscCall(DMPlexGetAllCells_Internal(plex, &allcellIS)); PetscCall(DMGetNumDS(dm, &Nds)); for (s = 0; s < Nds; ++s) { PetscDS ds; DMLabel label; IS cellIS; PetscCall(DMGetRegionNumDS(dm, s, &label, NULL, &ds, NULL)); { PetscWeakFormKind jacmap[4] = {PETSC_WF_G0, PETSC_WF_G1, PETSC_WF_G2, PETSC_WF_G3}; PetscWeakForm wf; PetscInt Nm = 4, m, Nk = 0, k, kp, off = 0; PetscFormKey *jackeys; /* Get unique Jacobian keys */ for (m = 0; m < Nm; ++m) { PetscInt Nkm; PetscCall(PetscHMapFormGetSize(ds->wf->form[jacmap[m]], &Nkm)); Nk += Nkm; } PetscCall(PetscMalloc1(Nk, &jackeys)); for (m = 0; m < Nm; ++m) PetscCall(PetscHMapFormGetKeys(ds->wf->form[jacmap[m]], &off, jackeys)); PetscCheck(off == Nk, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number of keys %" PetscInt_FMT " should be %" PetscInt_FMT, off, Nk); PetscCall(PetscFormKeySort(Nk, jackeys)); for (k = 0, kp = 1; kp < Nk; ++kp) { if ((jackeys[k].label != jackeys[kp].label) || (jackeys[k].value != jackeys[kp].value)) { ++k; if (kp != k) jackeys[k] = jackeys[kp]; } } Nk = k; PetscCall(PetscDSGetWeakForm(ds, &wf)); for (k = 0; k < Nk; ++k) { DMLabel label = jackeys[k].label; PetscInt val = jackeys[k].value; if (!label) { PetscCall(PetscObjectReference((PetscObject)allcellIS)); cellIS = allcellIS; } else { IS pointIS; PetscCall(DMLabelGetStratumIS(label, val, &pointIS)); PetscCall(ISIntersect_Caching_Internal(allcellIS, pointIS, &cellIS)); PetscCall(ISDestroy(&pointIS)); } PetscCall(DMPlexComputeJacobian_Action_Internal(plex, jackeys[k], cellIS, 0.0, 0.0, X, NULL, Y, F, user)); PetscCall(ISDestroy(&cellIS)); } PetscCall(PetscFree(jackeys)); } } PetscCall(ISDestroy(&allcellIS)); PetscCall(DMDestroy(&plex)); PetscFunctionReturn(PETSC_SUCCESS); } /*@ DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix `Jac` at the local solution `X` using pointwise functions specified by the user. Input Parameters: + dm - The `DM` . X - Local input vector - user - The user context Output Parameters: + Jac - Jacobian matrix - JacP - approximate Jacobian from which the preconditioner will be built, often `Jac` Level: developer Note: We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator, like a GPU, or vectorize on a multicore machine. .seealso: `DMPLEX`, `Mat` @*/ PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP, void *user) { DM plex; IS allcellIS; PetscBool hasJac, hasPrec; PetscInt Nds, s; PetscFunctionBegin; PetscCall(DMSNESConvertPlex(dm, &plex, PETSC_TRUE)); PetscCall(DMPlexGetAllCells_Internal(plex, &allcellIS)); PetscCall(DMGetNumDS(dm, &Nds)); for (s = 0; s < Nds; ++s) { PetscDS ds; IS cellIS; PetscFormKey key; PetscCall(DMGetRegionNumDS(dm, s, &key.label, NULL, &ds, NULL)); key.value = 0; key.field = 0; key.part = 0; if (!key.label) { PetscCall(PetscObjectReference((PetscObject)allcellIS)); cellIS = allcellIS; } else { IS pointIS; key.value = 1; PetscCall(DMLabelGetStratumIS(key.label, key.value, &pointIS)); PetscCall(ISIntersect_Caching_Internal(allcellIS, pointIS, &cellIS)); PetscCall(ISDestroy(&pointIS)); } if (!s) { PetscCall(PetscDSHasJacobian(ds, &hasJac)); PetscCall(PetscDSHasJacobianPreconditioner(ds, &hasPrec)); if (hasJac && hasPrec) PetscCall(MatZeroEntries(Jac)); PetscCall(MatZeroEntries(JacP)); } PetscCall(DMPlexComputeJacobian_Internal(plex, key, cellIS, 0.0, 0.0, X, NULL, Jac, JacP, user)); PetscCall(ISDestroy(&cellIS)); } PetscCall(ISDestroy(&allcellIS)); PetscCall(DMDestroy(&plex)); PetscFunctionReturn(PETSC_SUCCESS); } struct _DMSNESJacobianMFCtx { DM dm; Vec X; void *ctx; }; static PetscErrorCode DMSNESJacobianMF_Destroy_Private(Mat A) { struct _DMSNESJacobianMFCtx *ctx; PetscFunctionBegin; PetscCall(MatShellGetContext(A, &ctx)); PetscCall(MatShellSetContext(A, NULL)); PetscCall(DMDestroy(&ctx->dm)); PetscCall(VecDestroy(&ctx->X)); PetscCall(PetscFree(ctx)); PetscFunctionReturn(PETSC_SUCCESS); } static PetscErrorCode DMSNESJacobianMF_Mult_Private(Mat A, Vec Y, Vec Z) { struct _DMSNESJacobianMFCtx *ctx; PetscFunctionBegin; PetscCall(MatShellGetContext(A, &ctx)); PetscCall(DMSNESComputeJacobianAction(ctx->dm, ctx->X, Y, Z, ctx->ctx)); PetscFunctionReturn(PETSC_SUCCESS); } /*@ DMSNESCreateJacobianMF - Create a `Mat` which computes the action of the Jacobian matrix-free Collective Input Parameters: + dm - The `DM` . X - The evaluation point for the Jacobian - user - A user context, or `NULL` Output Parameter: . J - The `Mat` Level: advanced Note: Vec `X` is kept in `J`, so updating `X` then updates the evaluation point. .seealso: `DM`, `DMSNESComputeJacobianAction()` @*/ PetscErrorCode DMSNESCreateJacobianMF(DM dm, Vec X, void *user, Mat *J) { struct _DMSNESJacobianMFCtx *ctx; PetscInt n, N; PetscFunctionBegin; PetscCall(MatCreate(PetscObjectComm((PetscObject)dm), J)); PetscCall(MatSetType(*J, MATSHELL)); PetscCall(VecGetLocalSize(X, &n)); PetscCall(VecGetSize(X, &N)); PetscCall(MatSetSizes(*J, n, n, N, N)); PetscCall(PetscObjectReference((PetscObject)dm)); PetscCall(PetscObjectReference((PetscObject)X)); PetscCall(PetscMalloc1(1, &ctx)); ctx->dm = dm; ctx->X = X; ctx->ctx = user; PetscCall(MatShellSetContext(*J, ctx)); PetscCall(MatShellSetOperation(*J, MATOP_DESTROY, (void (*)(void))DMSNESJacobianMF_Destroy_Private)); PetscCall(MatShellSetOperation(*J, MATOP_MULT, (void (*)(void))DMSNESJacobianMF_Mult_Private)); PetscFunctionReturn(PETSC_SUCCESS); } /* MatComputeNeumannOverlap - Computes an unassembled (Neumann) local overlapping Mat in nonlinear context. Input Parameters: + X - `SNES` linearization point . ovl - index set of overlapping subdomains Output Parameter: . J - unassembled (Neumann) local matrix Level: intermediate .seealso: `DMCreateNeumannOverlap()`, `MATIS`, `PCHPDDMSetAuxiliaryMat()` */ static PetscErrorCode MatComputeNeumannOverlap_Plex(Mat J, PetscReal t, Vec X, Vec X_t, PetscReal s, IS ovl, void *ctx) { SNES snes; Mat pJ; DM ovldm, origdm; DMSNES sdm; PetscErrorCode (*bfun)(DM, Vec, void *); PetscErrorCode (*jfun)(DM, Vec, Mat, Mat, void *); void *bctx, *jctx; PetscFunctionBegin; PetscCall(PetscObjectQuery((PetscObject)ovl, "_DM_Overlap_HPDDM_MATIS", (PetscObject *)&pJ)); PetscCheck(pJ, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing overlapping Mat"); PetscCall(PetscObjectQuery((PetscObject)ovl, "_DM_Original_HPDDM", (PetscObject *)&origdm)); PetscCheck(origdm, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing original DM"); PetscCall(MatGetDM(pJ, &ovldm)); PetscCall(DMSNESGetBoundaryLocal(origdm, &bfun, &bctx)); PetscCall(DMSNESSetBoundaryLocal(ovldm, bfun, bctx)); PetscCall(DMSNESGetJacobianLocal(origdm, &jfun, &jctx)); PetscCall(DMSNESSetJacobianLocal(ovldm, jfun, jctx)); PetscCall(PetscObjectQuery((PetscObject)ovl, "_DM_Overlap_HPDDM_SNES", (PetscObject *)&snes)); if (!snes) { PetscCall(SNESCreate(PetscObjectComm((PetscObject)ovl), &snes)); PetscCall(SNESSetDM(snes, ovldm)); PetscCall(PetscObjectCompose((PetscObject)ovl, "_DM_Overlap_HPDDM_SNES", (PetscObject)snes)); PetscCall(PetscObjectDereference((PetscObject)snes)); } PetscCall(DMGetDMSNES(ovldm, &sdm)); PetscCall(VecLockReadPush(X)); { void *ctx; PetscErrorCode (*J)(SNES, Vec, Mat, Mat, void *); PetscCall(DMSNESGetJacobian(ovldm, &J, &ctx)); PetscCallBack("SNES callback Jacobian", (*J)(snes, X, pJ, pJ, ctx)); } PetscCall(VecLockReadPop(X)); /* this is a no-hop, just in case we decide to change the placeholder for the local Neumann matrix */ { Mat locpJ; PetscCall(MatISGetLocalMat(pJ, &locpJ)); PetscCall(MatCopy(locpJ, J, SAME_NONZERO_PATTERN)); } PetscFunctionReturn(PETSC_SUCCESS); } /*@ DMPlexSetSNESLocalFEM - Use `DMPLEX`'s internal FEM routines to compute `SNES` boundary values, residual, and Jacobian. Input Parameters: + dm - The `DM` object . boundaryctx - the user context that will be passed to pointwise evaluation of boundary values (see `PetscDSAddBoundary()`) . residualctx - the user context that will be passed to pointwise evaluation of finite element residual computations (see `PetscDSSetResidual()`) - jacobianctx - the user context that will be passed to pointwise evaluation of finite element Jacobian construction (see `PetscDSSetJacobian()`) Level: developer .seealso: `DMPLEX`, `SNES` @*/ PetscErrorCode DMPlexSetSNESLocalFEM(DM dm, void *boundaryctx, void *residualctx, void *jacobianctx) { PetscFunctionBegin; PetscCall(DMSNESSetBoundaryLocal(dm, DMPlexSNESComputeBoundaryFEM, boundaryctx)); PetscCall(DMSNESSetFunctionLocal(dm, DMPlexSNESComputeResidualFEM, residualctx)); PetscCall(DMSNESSetJacobianLocal(dm, DMPlexSNESComputeJacobianFEM, jacobianctx)); PetscCall(PetscObjectComposeFunction((PetscObject)dm, "MatComputeNeumannOverlap_C", MatComputeNeumannOverlap_Plex)); PetscFunctionReturn(PETSC_SUCCESS); } /*@C DMSNESCheckDiscretization - Check the discretization error of the exact solution Input Parameters: + snes - the `SNES` object . dm - the `DM` . t - the time . u - a `DM` vector - tol - A tolerance for the check, or -1 to print the results instead Output Parameter: . error - An array which holds the discretization error in each field, or `NULL` Level: developer Note: The user must call `PetscDSSetExactSolution()` beforehand .seealso: `PetscDSSetExactSolution()`, `DNSNESCheckFromOptions()`, `DMSNESCheckResidual()`, `DMSNESCheckJacobian()`, `PetscDSSetExactSolution()` @*/ PetscErrorCode DMSNESCheckDiscretization(SNES snes, DM dm, PetscReal t, Vec u, PetscReal tol, PetscReal error[]) { PetscErrorCode (**exacts)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx); void **ectxs; PetscReal *err; MPI_Comm comm; PetscInt Nf, f; PetscFunctionBegin; PetscValidHeaderSpecific(snes, SNES_CLASSID, 1); PetscValidHeaderSpecific(dm, DM_CLASSID, 2); PetscValidHeaderSpecific(u, VEC_CLASSID, 4); if (error) PetscValidRealPointer(error, 6); PetscCall(DMComputeExactSolution(dm, t, u, NULL)); PetscCall(VecViewFromOptions(u, NULL, "-vec_view")); PetscCall(PetscObjectGetComm((PetscObject)snes, &comm)); PetscCall(DMGetNumFields(dm, &Nf)); PetscCall(PetscCalloc3(Nf, &exacts, Nf, &ectxs, PetscMax(1, Nf), &err)); { PetscInt Nds, s; PetscCall(DMGetNumDS(dm, &Nds)); for (s = 0; s < Nds; ++s) { PetscDS ds; DMLabel label; IS fieldIS; const PetscInt *fields; PetscInt dsNf, f; PetscCall(DMGetRegionNumDS(dm, s, &label, &fieldIS, &ds, NULL)); PetscCall(PetscDSGetNumFields(ds, &dsNf)); PetscCall(ISGetIndices(fieldIS, &fields)); for (f = 0; f < dsNf; ++f) { const PetscInt field = fields[f]; PetscCall(PetscDSGetExactSolution(ds, field, &exacts[field], &ectxs[field])); } PetscCall(ISRestoreIndices(fieldIS, &fields)); } } if (Nf > 1) { PetscCall(DMComputeL2FieldDiff(dm, t, exacts, ectxs, u, err)); if (tol >= 0.0) { for (f = 0; f < Nf; ++f) PetscCheck(err[f] <= tol, comm, PETSC_ERR_ARG_WRONG, "L_2 Error %g for field %" PetscInt_FMT " exceeds tolerance %g", (double)err[f], f, (double)tol); } else if (error) { for (f = 0; f < Nf; ++f) error[f] = err[f]; } else { PetscCall(PetscPrintf(comm, "L_2 Error: [")); for (f = 0; f < Nf; ++f) { if (f) PetscCall(PetscPrintf(comm, ", ")); PetscCall(PetscPrintf(comm, "%g", (double)err[f])); } PetscCall(PetscPrintf(comm, "]\n")); } } else { PetscCall(DMComputeL2Diff(dm, t, exacts, ectxs, u, &err[0])); if (tol >= 0.0) { PetscCheck(err[0] <= tol, comm, PETSC_ERR_ARG_WRONG, "L_2 Error %g exceeds tolerance %g", (double)err[0], (double)tol); } else if (error) { error[0] = err[0]; } else { PetscCall(PetscPrintf(comm, "L_2 Error: %g\n", (double)err[0])); } } PetscCall(PetscFree3(exacts, ectxs, err)); PetscFunctionReturn(PETSC_SUCCESS); } /*@C DMSNESCheckResidual - Check the residual of the exact solution Input Parameters: + snes - the `SNES` object . dm - the `DM` . u - a `DM` vector - tol - A tolerance for the check, or -1 to print the results instead Output Parameter: . residual - The residual norm of the exact solution, or `NULL` Level: developer .seealso: `DNSNESCheckFromOptions()`, `DMSNESCheckDiscretization()`, `DMSNESCheckJacobian()` @*/ PetscErrorCode DMSNESCheckResidual(SNES snes, DM dm, Vec u, PetscReal tol, PetscReal *residual) { MPI_Comm comm; Vec r; PetscReal res; PetscFunctionBegin; PetscValidHeaderSpecific(snes, SNES_CLASSID, 1); PetscValidHeaderSpecific(dm, DM_CLASSID, 2); PetscValidHeaderSpecific(u, VEC_CLASSID, 3); if (residual) PetscValidRealPointer(residual, 5); PetscCall(PetscObjectGetComm((PetscObject)snes, &comm)); PetscCall(DMComputeExactSolution(dm, 0.0, u, NULL)); PetscCall(VecDuplicate(u, &r)); PetscCall(SNESComputeFunction(snes, u, r)); PetscCall(VecNorm(r, NORM_2, &res)); if (tol >= 0.0) { PetscCheck(res <= tol, comm, PETSC_ERR_ARG_WRONG, "L_2 Residual %g exceeds tolerance %g", (double)res, (double)tol); } else if (residual) { *residual = res; } else { PetscCall(PetscPrintf(comm, "L_2 Residual: %g\n", (double)res)); PetscCall(VecChop(r, 1.0e-10)); PetscCall(PetscObjectSetName((PetscObject)r, "Initial Residual")); PetscCall(PetscObjectSetOptionsPrefix((PetscObject)r, "res_")); PetscCall(VecViewFromOptions(r, NULL, "-vec_view")); } PetscCall(VecDestroy(&r)); PetscFunctionReturn(PETSC_SUCCESS); } /*@C DMSNESCheckJacobian - Check the Jacobian of the exact solution against the residual using the Taylor Test Input Parameters: + snes - the `SNES` object . dm - the `DM` . u - a `DM` vector - tol - A tolerance for the check, or -1 to print the results instead Output Parameters: + isLinear - Flag indicaing that the function looks linear, or `NULL` - convRate - The rate of convergence of the linear model, or `NULL` Level: developer .seealso: `DNSNESCheckFromOptions()`, `DMSNESCheckDiscretization()`, `DMSNESCheckResidual()` @*/ PetscErrorCode DMSNESCheckJacobian(SNES snes, DM dm, Vec u, PetscReal tol, PetscBool *isLinear, PetscReal *convRate) { MPI_Comm comm; PetscDS ds; Mat J, M; MatNullSpace nullspace; PetscReal slope, intercept; PetscBool hasJac, hasPrec, isLin = PETSC_FALSE; PetscFunctionBegin; PetscValidHeaderSpecific(snes, SNES_CLASSID, 1); PetscValidHeaderSpecific(dm, DM_CLASSID, 2); PetscValidHeaderSpecific(u, VEC_CLASSID, 3); if (isLinear) PetscValidBoolPointer(isLinear, 5); if (convRate) PetscValidRealPointer(convRate, 6); PetscCall(PetscObjectGetComm((PetscObject)snes, &comm)); PetscCall(DMComputeExactSolution(dm, 0.0, u, NULL)); /* Create and view matrices */ PetscCall(DMCreateMatrix(dm, &J)); PetscCall(DMGetDS(dm, &ds)); PetscCall(PetscDSHasJacobian(ds, &hasJac)); PetscCall(PetscDSHasJacobianPreconditioner(ds, &hasPrec)); if (hasJac && hasPrec) { PetscCall(DMCreateMatrix(dm, &M)); PetscCall(SNESComputeJacobian(snes, u, J, M)); PetscCall(PetscObjectSetName((PetscObject)M, "Preconditioning Matrix")); PetscCall(PetscObjectSetOptionsPrefix((PetscObject)M, "jacpre_")); PetscCall(MatViewFromOptions(M, NULL, "-mat_view")); PetscCall(MatDestroy(&M)); } else { PetscCall(SNESComputeJacobian(snes, u, J, J)); } PetscCall(PetscObjectSetName((PetscObject)J, "Jacobian")); PetscCall(PetscObjectSetOptionsPrefix((PetscObject)J, "jac_")); PetscCall(MatViewFromOptions(J, NULL, "-mat_view")); /* Check nullspace */ PetscCall(MatGetNullSpace(J, &nullspace)); if (nullspace) { PetscBool isNull; PetscCall(MatNullSpaceTest(nullspace, J, &isNull)); PetscCheck(isNull, comm, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid."); } /* Taylor test */ { PetscRandom rand; Vec du, uhat, r, rhat, df; PetscReal h; PetscReal *es, *hs, *errors; PetscReal hMax = 1.0, hMin = 1e-6, hMult = 0.1; PetscInt Nv, v; /* Choose a perturbation direction */ PetscCall(PetscRandomCreate(comm, &rand)); PetscCall(VecDuplicate(u, &du)); PetscCall(VecSetRandom(du, rand)); PetscCall(PetscRandomDestroy(&rand)); PetscCall(VecDuplicate(u, &df)); PetscCall(MatMult(J, du, df)); /* Evaluate residual at u, F(u), save in vector r */ PetscCall(VecDuplicate(u, &r)); PetscCall(SNESComputeFunction(snes, u, r)); /* Look at the convergence of our Taylor approximation as we approach u */ for (h = hMax, Nv = 0; h >= hMin; h *= hMult, ++Nv) ; PetscCall(PetscCalloc3(Nv, &es, Nv, &hs, Nv, &errors)); PetscCall(VecDuplicate(u, &uhat)); PetscCall(VecDuplicate(u, &rhat)); for (h = hMax, Nv = 0; h >= hMin; h *= hMult, ++Nv) { PetscCall(VecWAXPY(uhat, h, du, u)); /* F(\hat u) \approx F(u) + J(u) (uhat - u) = F(u) + h * J(u) du */ PetscCall(SNESComputeFunction(snes, uhat, rhat)); PetscCall(VecAXPBYPCZ(rhat, -1.0, -h, 1.0, r, df)); PetscCall(VecNorm(rhat, NORM_2, &errors[Nv])); es[Nv] = PetscLog10Real(errors[Nv]); hs[Nv] = PetscLog10Real(h); } PetscCall(VecDestroy(&uhat)); PetscCall(VecDestroy(&rhat)); PetscCall(VecDestroy(&df)); PetscCall(VecDestroy(&r)); PetscCall(VecDestroy(&du)); for (v = 0; v < Nv; ++v) { if ((tol >= 0) && (errors[v] > tol)) break; else if (errors[v] > PETSC_SMALL) break; } if (v == Nv) isLin = PETSC_TRUE; PetscCall(PetscLinearRegression(Nv, hs, es, &slope, &intercept)); PetscCall(PetscFree3(es, hs, errors)); /* Slope should be about 2 */ if (tol >= 0) { PetscCheck(isLin || PetscAbsReal(2 - slope) <= tol, comm, PETSC_ERR_ARG_WRONG, "Taylor approximation convergence rate should be 2, not %0.2f", (double)slope); } else if (isLinear || convRate) { if (isLinear) *isLinear = isLin; if (convRate) *convRate = slope; } else { if (!isLin) PetscCall(PetscPrintf(comm, "Taylor approximation converging at order %3.2f\n", (double)slope)); else PetscCall(PetscPrintf(comm, "Function appears to be linear\n")); } } PetscCall(MatDestroy(&J)); PetscFunctionReturn(PETSC_SUCCESS); } PetscErrorCode DMSNESCheck_Internal(SNES snes, DM dm, Vec u) { PetscFunctionBegin; PetscCall(DMSNESCheckDiscretization(snes, dm, 0.0, u, -1.0, NULL)); PetscCall(DMSNESCheckResidual(snes, dm, u, -1.0, NULL)); PetscCall(DMSNESCheckJacobian(snes, dm, u, -1.0, NULL, NULL)); PetscFunctionReturn(PETSC_SUCCESS); } /*@C DMSNESCheckFromOptions - Check the residual and Jacobian functions using the exact solution by outputting some diagnostic information Input Parameters: + snes - the `SNES` object - u - representative `SNES` vector Level: developer Note: The user must call `PetscDSSetExactSolution()` beforehand .seealso: `SNES`, `DM` @*/ PetscErrorCode DMSNESCheckFromOptions(SNES snes, Vec u) { DM dm; Vec sol; PetscBool check; PetscFunctionBegin; PetscCall(PetscOptionsHasName(((PetscObject)snes)->options, ((PetscObject)snes)->prefix, "-dmsnes_check", &check)); if (!check) PetscFunctionReturn(PETSC_SUCCESS); PetscCall(SNESGetDM(snes, &dm)); PetscCall(VecDuplicate(u, &sol)); PetscCall(SNESSetSolution(snes, sol)); PetscCall(DMSNESCheck_Internal(snes, dm, sol)); PetscCall(VecDestroy(&sol)); PetscFunctionReturn(PETSC_SUCCESS); }