xref: /libCEED/examples/mfem/bp3.hpp (revision ecf6354e9a1bfdf9b8a51c1eb1e730eaa037defc)

// Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at
// the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights
// reserved. See files LICENSE and NOTICE for details.
//
// This file is part of CEED, a collection of benchmarks, miniapps, software
// libraries and APIs for efficient high-order finite element and spectral
// element discretizations for exascale applications. For more information and
// source code availability see http://github.com/ceed.
//
// The CEED research is supported by the Exascale Computing Project 17-SC-20-SC,
// a collaborative effort of two U.S. Department of Energy organizations (Office
// of Science and the National Nuclear Security Administration) responsible for
// the planning and preparation of a capable exascale ecosystem, including
// software, applications, hardware, advanced system engineering and early
// testbed platforms, in support of the nation's exascale computing imperative.

/// @file
/// MFEM diffusion operator based on libCEED

#include <ceed.h>
#include <mfem.hpp>

/// A structure used to pass additional data to f_build_diff and f_apply_diff
struct BuildContext { CeedInt dim, space_dim; };

/// libCEED Q-function for building quadrature data for a diffusion operator
static int f_build_diff(void *ctx, CeedInt Q,
                        const CeedScalar *const *in, CeedScalar *const *out) {
  BuildContext *bc = (BuildContext*)ctx;
  // in[0] is Jacobians with shape [dim, nc=dim, Q]
  // in[1] is quadrature weights, size (Q)
  //
  // At every quadrature point, compute qw/det(J).adj(J).adj(J)^T and store
  // the symmetric part of the result.
  const CeedScalar *J = in[0], *qw = in[1];
  CeedScalar *qd = out[0];
  switch (bc->dim + 10*bc->space_dim) {
  case 11:
    for (CeedInt i=0; i<Q; i++) {
      qd[i] = qw[i] / J[i];
    }
    break;
  case 22:
    for (CeedInt i=0; i<Q; i++) {
      // J: 0 2   qd: 0 1   adj(J):  J22 -J12
      //    1 3       1 2           -J21  J11
      const CeedScalar J11 = J[i+Q*0];
      const CeedScalar J21 = J[i+Q*1];
      const CeedScalar J12 = J[i+Q*2];
      const CeedScalar J22 = J[i+Q*3];
      const CeedScalar w = qw[i] / (J11*J22 - J21*J12);
      qd[i+Q*0] =   w * (J12*J12 + J22*J22);
      qd[i+Q*1] = - w * (J11*J12 + J21*J22);
      qd[i+Q*2] =   w * (J11*J11 + J21*J21);
    }
    break;
  case 33:
    for (CeedInt i=0; i<Q; i++) {
      // J: 0 3 6   qd: 0 1 2
      //    1 4 7       1 3 4
      //    2 5 8       2 4 5
      const CeedScalar J11 = J[i+Q*0];
      const CeedScalar J21 = J[i+Q*1];
      const CeedScalar J31 = J[i+Q*2];
      const CeedScalar J12 = J[i+Q*3];
      const CeedScalar J22 = J[i+Q*4];
      const CeedScalar J32 = J[i+Q*5];
      const CeedScalar J13 = J[i+Q*6];
      const CeedScalar J23 = J[i+Q*7];
      const CeedScalar J33 = J[i+Q*8];
      const CeedScalar A11 = J22*J33 - J23*J32;
      const CeedScalar A12 = J13*J32 - J12*J33;
      const CeedScalar A13 = J12*J23 - J13*J22;
      const CeedScalar A21 = J23*J31 - J21*J33;
      const CeedScalar A22 = J11*J33 - J13*J31;
      const CeedScalar A23 = J13*J21 - J11*J23;
      const CeedScalar A31 = J21*J32 - J22*J31;
      const CeedScalar A32 = J12*J31 - J11*J32;
      const CeedScalar A33 = J11*J22 - J12*J21;
      const CeedScalar w = qw[i] / (J11*A11 + J21*A12 + J31*A13);
      qd[i+Q*0] = w * (A11*A11 + A12*A12 + A13*A13);
      qd[i+Q*1] = w * (A11*A21 + A12*A22 + A13*A23);
      qd[i+Q*2] = w * (A11*A31 + A12*A32 + A13*A33);
      qd[i+Q*3] = w * (A21*A21 + A22*A22 + A23*A23);
      qd[i+Q*4] = w * (A21*A31 + A22*A32 + A23*A33);
      qd[i+Q*5] = w * (A31*A31 + A32*A32 + A33*A33);
    }
    break;
  default:
    return CeedError(NULL, 1, "dim=%d, space_dim=%d is not supported",
                     bc->dim, bc->space_dim);
  }
  return 0;
}

/// libCEED Q-function for applying a diff operator
static int f_apply_diff(void *ctx, CeedInt Q,
                        const CeedScalar *const *in, CeedScalar *const *out) {
  BuildContext *bc = (BuildContext*)ctx;
  // in[0], out[0] have shape [dim, nc=1, Q]
  const CeedScalar *ug = in[0], *qd = in[1];
  CeedScalar *vg = out[0];
  switch (bc->dim) {
  case 1:
    for (CeedInt i=0; i<Q; i++) {
      vg[i] = ug[i] * qd[i];
    }
    break;
  case 2:
    for (CeedInt i=0; i<Q; i++) {
      const CeedScalar ug0 = ug[i+Q*0];
      const CeedScalar ug1 = ug[i+Q*1];
      vg[i+Q*0] = qd[i+Q*0]*ug0 + qd[i+Q*1]*ug1;
      vg[i+Q*1] = qd[i+Q*1]*ug0 + qd[i+Q*2]*ug1;
    }
    break;
  case 3:
    for (CeedInt i=0; i<Q; i++) {
      const CeedScalar ug0 = ug[i+Q*0];
      const CeedScalar ug1 = ug[i+Q*1];
      const CeedScalar ug2 = ug[i+Q*2];
      vg[i+Q*0] = qd[i+Q*0]*ug0 + qd[i+Q*1]*ug1 + qd[i+Q*2]*ug2;
      vg[i+Q*1] = qd[i+Q*1]*ug0 + qd[i+Q*3]*ug1 + qd[i+Q*4]*ug2;
      vg[i+Q*2] = qd[i+Q*2]*ug0 + qd[i+Q*4]*ug1 + qd[i+Q*5]*ug2;
    }
    break;
  default:
    return CeedError(NULL, 1, "topo_dim=%d is not supported", bc->dim);
  }
  return 0;
}

/// Wrapper for a diffusion CeedOperator as an mfem::Operator
class CeedDiffusionOperator : public mfem::Operator {
 protected:
  const mfem::FiniteElementSpace *fes;
  CeedOperator build_oper, oper;
  CeedBasis basis, mesh_basis;
  CeedElemRestriction restr, mesh_restr, restr_i, mesh_restr_i;
  CeedQFunction apply_qfunc, build_qfunc;
  CeedVector node_coords, rho;

  BuildContext build_ctx;

  CeedVector u, v;

  static void FESpace2Ceed(const mfem::FiniteElementSpace *fes,
                           const mfem::IntegrationRule &ir,
                           Ceed ceed, CeedBasis *basis,
                           CeedElemRestriction *restr) {
    mfem::Mesh *mesh = fes->GetMesh();
    const mfem::FiniteElement *fe = fes->GetFE(0);
    const int order = fes->GetOrder(0);
    mfem::Array<int> dof_map;
    switch (mesh->Dimension()) {
    case 1: {
      const mfem::H1_SegmentElement *h1_fe =
        dynamic_cast<const mfem::H1_SegmentElement*>(fe);
      MFEM_VERIFY(h1_fe, "invalid FE");
      h1_fe->GetDofMap().Copy(dof_map);
      break;
    }
    case 2: {
      const mfem::H1_QuadrilateralElement *h1_fe =
        dynamic_cast<const mfem::H1_QuadrilateralElement*>(fe);
      MFEM_VERIFY(h1_fe, "invalid FE");
      h1_fe->GetDofMap().Copy(dof_map);
      break;
    }
    case 3: {
      const mfem::H1_HexahedronElement *h1_fe =
        dynamic_cast<const mfem::H1_HexahedronElement*>(fe);
      MFEM_VERIFY(h1_fe, "invalid FE");
      h1_fe->GetDofMap().Copy(dof_map);
      break;
    }
    }
    const mfem::FiniteElement *fe1d =
      fes->FEColl()->FiniteElementForGeometry(mfem::Geometry::SEGMENT);
    mfem::DenseMatrix shape1d(fe1d->GetDof(), ir.GetNPoints());
    mfem::DenseMatrix grad1d(fe1d->GetDof(), ir.GetNPoints());
    mfem::Vector qref1d(ir.GetNPoints()), qweight1d(ir.GetNPoints());
    mfem::Vector shape_i(shape1d.Height());
    mfem::DenseMatrix grad_i(grad1d.Height(), 1);
    const mfem::H1_SegmentElement *h1_fe1d =
      dynamic_cast<const mfem::H1_SegmentElement*>(fe1d);
    MFEM_VERIFY(h1_fe1d, "invalid FE");
    const mfem::Array<int> &dof_map_1d = h1_fe1d->GetDofMap();
    for (int i = 0; i < ir.GetNPoints(); i++) {
      const mfem::IntegrationPoint &ip = ir.IntPoint(i);
      qref1d(i) = ip.x;
      qweight1d(i) = ip.weight;
      fe1d->CalcShape(ip, shape_i);
      fe1d->CalcDShape(ip, grad_i);
      for (int j = 0; j < shape1d.Height(); j++) {
        shape1d(j,i) = shape_i(dof_map_1d[j]);
        grad1d(j,i) = grad_i(dof_map_1d[j],0);
      }
    }
    CeedBasisCreateTensorH1(ceed, mesh->Dimension(), fes->GetVDim(), order+1,
                            ir.GetNPoints(), shape1d.GetData(),
                            grad1d.GetData(), qref1d.GetData(),
                            qweight1d.GetData(), basis);

    const mfem::Table &el_dof = fes->GetElementToDofTable();
    mfem::Array<int> tp_el_dof(el_dof.Size_of_connections());
    for (int i = 0; i < mesh->GetNE(); i++) {
      const int el_offset = fe->GetDof()*i;
      for (int j = 0; j < fe->GetDof(); j++) {
        tp_el_dof[j + el_offset] = el_dof.GetJ()[dof_map[j] + el_offset];
      }
    }
    CeedElemRestrictionCreate(ceed, mesh->GetNE(), fe->GetDof(),
                              fes->GetNDofs(), fes->GetVDim(), CEED_MEM_HOST, CEED_COPY_VALUES,
                              tp_el_dof.GetData(), restr);
  }

 public:
  /// Constructor. Assumes @a fes is a scalar FE space.
  CeedDiffusionOperator(Ceed ceed, const mfem::FiniteElementSpace *fes)
    : Operator(fes->GetNDofs()),
      fes(fes) {
    mfem::Mesh *mesh = fes->GetMesh();
    const int order = fes->GetOrder(0);
    const int ir_order = 2*(order + 2) - 1; // <-----
    const mfem::IntegrationRule &ir =
      mfem::IntRules.Get(mfem::Geometry::SEGMENT, ir_order);
    CeedInt nqpts, nelem = mesh->GetNE(), dim = mesh->SpaceDimension();

    FESpace2Ceed(fes, ir, ceed, &basis, &restr);

    const mfem::FiniteElementSpace *mesh_fes = mesh->GetNodalFESpace();
    MFEM_VERIFY(mesh_fes, "the Mesh has no nodal FE space");
    FESpace2Ceed(mesh_fes, ir, ceed, &mesh_basis, &mesh_restr);
    CeedBasisGetNumQuadraturePoints(basis, &nqpts);

    CeedElemRestrictionCreateIdentity(ceed, nelem, nqpts*dim*(dim+1)/2,
                              nqpts*nelem*dim*(dim+1)/2, 1, &restr_i);
    CeedElemRestrictionCreateIdentity(ceed, nelem, nqpts,
                              nqpts*nelem, 1, &mesh_restr_i);

    CeedVectorCreate(ceed, mesh->GetNodes()->Size(), &node_coords);
    CeedVectorSetArray(node_coords, CEED_MEM_HOST, CEED_USE_POINTER,
                       mesh->GetNodes()->GetData());

    CeedVectorCreate(ceed, nelem*nqpts*dim*(dim+1)/2, &rho);

    // Context data to be passed to the 'f_build_diff' Q-function.
    build_ctx.dim = mesh->Dimension();
    build_ctx.space_dim = mesh->SpaceDimension();

    // Create the Q-function that builds the diff operator (i.e. computes its
    // quadrature data) and set its context data.
    CeedQFunctionCreateInterior(ceed, 1, f_build_diff,
                                __FILE__":f_build_diff", &build_qfunc);
    CeedQFunctionAddInput(build_qfunc, "dx", dim, CEED_EVAL_GRAD);
    CeedQFunctionAddInput(build_qfunc, "weights", 1, CEED_EVAL_WEIGHT);
    CeedQFunctionAddOutput(build_qfunc, "rho", dim*(dim+1)/2, CEED_EVAL_NONE);
    CeedQFunctionSetContext(build_qfunc, &build_ctx, sizeof(build_ctx));

    // Create the operator that builds the quadrature data for the diff operator.
    CeedOperatorCreate(ceed, build_qfunc, NULL, NULL, &build_oper);
    CeedOperatorSetField(build_oper, "dx", mesh_restr, mesh_basis,
                         CEED_VECTOR_ACTIVE);
    CeedOperatorSetField(build_oper, "weights", mesh_restr_i,
                         mesh_basis, CEED_VECTOR_NONE);
    CeedOperatorSetField(build_oper, "rho", restr_i,
                         CEED_BASIS_COLOCATED, CEED_VECTOR_ACTIVE);

    // Compute the quadrature data for the diff operator.
    CeedOperatorApply(build_oper, node_coords, rho,
                      CEED_REQUEST_IMMEDIATE);

    // Create the Q-function that defines the action of the diff operator.
    CeedQFunctionCreateInterior(ceed, 1, f_apply_diff,
                                __FILE__":f_apply_diff", &apply_qfunc);
    CeedQFunctionAddInput(apply_qfunc, "u", 1, CEED_EVAL_GRAD);
    CeedQFunctionAddInput(apply_qfunc, "rho", dim*(dim+1)/2, CEED_EVAL_NONE);
    CeedQFunctionAddOutput(apply_qfunc, "v", 1, CEED_EVAL_GRAD);
    CeedQFunctionSetContext(apply_qfunc, &build_ctx, sizeof(build_ctx));

    // Create the diff operator.
    CeedOperatorCreate(ceed, apply_qfunc, NULL, NULL, &oper);
    CeedOperatorSetField(oper, "u", restr, basis, CEED_VECTOR_ACTIVE);
    CeedOperatorSetField(oper, "rho", restr_i,
                         CEED_BASIS_COLOCATED, rho);
    CeedOperatorSetField(oper, "v", restr, basis, CEED_VECTOR_ACTIVE);

    CeedVectorCreate(ceed, fes->GetNDofs(), &u);
    CeedVectorCreate(ceed, fes->GetNDofs(), &v);
  }

  /// Destructor
  ~CeedDiffusionOperator() {
    CeedVectorDestroy(&u);
    CeedVectorDestroy(&v);
    CeedVectorDestroy(&rho);
    CeedVectorDestroy(&node_coords);
    CeedElemRestrictionDestroy(&restr);
    CeedElemRestrictionDestroy(&mesh_restr);
    CeedElemRestrictionDestroy(&restr_i);
    CeedElemRestrictionDestroy(&mesh_restr_i);
    CeedBasisDestroy(&basis);
    CeedBasisDestroy(&mesh_basis);
    CeedQFunctionDestroy(&build_qfunc);
    CeedOperatorDestroy(&build_oper);
    CeedQFunctionDestroy(&apply_qfunc);
    CeedOperatorDestroy(&oper);
  }

  /// Operator action
  virtual void Mult(const mfem::Vector &x, mfem::Vector &y) const {
    CeedVectorSetArray(u, CEED_MEM_HOST, CEED_USE_POINTER, x.GetData());
    CeedVectorSetArray(v, CEED_MEM_HOST, CEED_USE_POINTER, y.GetData());

    CeedOperatorApply(oper, u, v, CEED_REQUEST_IMMEDIATE);
  }
};