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mfem/fem/quadinterpolator.cpp
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// Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
// LICENSE and NOTICE for details. LLNL-CODE-806117.
//
// This file is part of the MFEM library. For more information and source code
// availability visit https://mfem.org.
//
// MFEM is free software; you can redistribute it and/or modify it under the
// terms of the BSD-3 license. We welcome feedback and contributions, see file
// CONTRIBUTING.md for details.
#include "quadinterpolator.hpp"
#include "qinterp/dispatch.hpp"
#include "qspace.hpp"
#include "../general/forall.hpp"
#include "../linalg/dtensor.hpp"
#include "../linalg/kernels.hpp"
namespace mfem
{
QuadratureInterpolator::QuadratureInterpolator(const FiniteElementSpace &fes,
const IntegrationRule &ir):
fespace(&fes),
qspace(nullptr),
IntRule(&ir),
q_layout(QVectorLayout::byNODES),
use_tensor_products(UsesTensorBasis(fes))
{
d_buffer.UseDevice(true);
if (fespace->GetNE() == 0) { return; }
const FiniteElement *fe = fespace->GetFE(0);
MFEM_VERIFY(dynamic_cast<const ScalarFiniteElement*>(fe) != NULL,
"Only scalar finite elements are supported");
}
QuadratureInterpolator::QuadratureInterpolator(const FiniteElementSpace &fes,
const QuadratureSpace &qs):
fespace(&fes),
qspace(&qs),
IntRule(nullptr),
q_layout(QVectorLayout::byNODES),
use_tensor_products(UsesTensorBasis(fes))
{
d_buffer.UseDevice(true);
if (fespace->GetNE() == 0) { return; }
const FiniteElement *fe = fespace->GetFE(0);
MFEM_VERIFY(dynamic_cast<const ScalarFiniteElement*>(fe) != NULL,
"Only scalar finite elements are supported");
}
namespace internal
{
namespace quadrature_interpolator
{
// Template compute kernel for 2D quadrature interpolation:
// * non-tensor product version,
// * assumes 'e_vec' is using ElementDofOrdering::NATIVE,
// * assumes 'maps.mode == FULL'.
template<const int T_VDIM, const int T_ND, const int T_NQ>
static void Eval2D(const int NE,
const int vdim,
const QVectorLayout q_layout,
const GeometricFactors *geom,
const DofToQuad &maps,
const Vector &e_vec,
Vector &q_val,
Vector &q_der,
Vector &q_det,
const int eval_flags)
{
using QI = QuadratureInterpolator;
const int nd = maps.ndof;
const int nq = maps.nqpt;
const int ND = T_ND ? T_ND : nd;
const int NQ = T_NQ ? T_NQ : nq;
const int NMAX = NQ > ND ? NQ : ND;
const int VDIM = T_VDIM ? T_VDIM : vdim;
MFEM_ASSERT(maps.mode == DofToQuad::FULL, "internal error");
MFEM_ASSERT(!geom || geom->mesh->SpaceDimension() == 2, "");
MFEM_VERIFY(ND <= QI::MAX_ND2D, "");
MFEM_VERIFY(NQ <= QI::MAX_NQ2D, "");
MFEM_VERIFY(VDIM == 2 || !(eval_flags & QI::DETERMINANTS), "");
MFEM_VERIFY(bool(geom) == bool(eval_flags & QI::PHYSICAL_DERIVATIVES),
"'geom' must be given (non-null) only when evaluating physical"
" derivatives");
const auto B = Reshape(maps.B.Read(), NQ, ND);
const auto G = Reshape(maps.G.Read(), NQ, 2, ND);
const auto J = Reshape(geom ? geom->J.Read() : nullptr, NQ, 2, 2, NE);
const auto E = Reshape(e_vec.Read(), ND, VDIM, NE);
auto val = q_layout == QVectorLayout::byNODES ?
Reshape(q_val.Write(), NQ, VDIM, NE):
Reshape(q_val.Write(), VDIM, NQ, NE);
auto der = q_layout == QVectorLayout::byNODES ?
Reshape(q_der.Write(), NQ, VDIM, 2, NE):
Reshape(q_der.Write(), VDIM, 2, NQ, NE);
auto det = Reshape(q_det.Write(), NQ, NE);
MFEM_FORALL_2D(e, NE, NMAX, 1, 1,
{
const int ND = T_ND ? T_ND : nd;
const int NQ = T_NQ ? T_NQ : nq;
const int VDIM = T_VDIM ? T_VDIM : vdim;
constexpr int max_ND = T_ND ? T_ND : QI::MAX_ND2D;
constexpr int max_VDIM = T_VDIM ? T_VDIM : QI::MAX_VDIM2D;
MFEM_SHARED double s_E[max_VDIM*max_ND];
MFEM_FOREACH_THREAD(d, x, ND)
{
for (int c = 0; c < VDIM; c++)
{
s_E[c+d*VDIM] = E(d,c,e);
}
}
MFEM_SYNC_THREAD;
MFEM_FOREACH_THREAD(q, x, NQ)
{
if (eval_flags & QI::VALUES)
{
double ed[max_VDIM];
for (int c = 0; c < VDIM; c++) { ed[c] = 0.0; }
for (int d = 0; d < ND; ++d)
{
const double b = B(q,d);
for (int c = 0; c < VDIM; c++) { ed[c] += b*s_E[c+d*VDIM]; }
}
for (int c = 0; c < VDIM; c++)
{
if (q_layout == QVectorLayout::byVDIM) { val(c,q,e) = ed[c]; }
if (q_layout == QVectorLayout::byNODES) { val(q,c,e) = ed[c]; }
}
}
if ((eval_flags & QI::DERIVATIVES) ||
(eval_flags & QI::PHYSICAL_DERIVATIVES) ||
(eval_flags & QI::DETERMINANTS))
{
// use MAX_VDIM2D to avoid "subscript out of range" warnings
double D[QI::MAX_VDIM2D*2];
for (int i = 0; i < 2*VDIM; i++) { D[i] = 0.0; }
for (int d = 0; d < ND; ++d)
{
const double wx = G(q,0,d);
const double wy = G(q,1,d);
for (int c = 0; c < VDIM; c++)
{
double s_e = s_E[c+d*VDIM];
D[c+VDIM*0] += s_e * wx;
D[c+VDIM*1] += s_e * wy;
}
}
if (eval_flags & QI::DERIVATIVES)
{
for (int c = 0; c < VDIM; c++)
{
if (q_layout == QVectorLayout::byVDIM)
{
der(c,0,q,e) = D[c+VDIM*0];
der(c,1,q,e) = D[c+VDIM*1];
}
if (q_layout == QVectorLayout::byNODES)
{
der(q,c,0,e) = D[c+VDIM*0];
der(q,c,1,e) = D[c+VDIM*1];
}
}
}
if (eval_flags & QI::PHYSICAL_DERIVATIVES)
{
double Jloc[4], Jinv[4];
Jloc[0] = J(q,0,0,e);
Jloc[1] = J(q,1,0,e);
Jloc[2] = J(q,0,1,e);
Jloc[3] = J(q,1,1,e);
kernels::CalcInverse<2>(Jloc, Jinv);
for (int c = 0; c < VDIM; c++)
{
const double u = D[c+VDIM*0];
const double v = D[c+VDIM*1];
const double JiU = Jinv[0]*u + Jinv[1]*v;
const double JiV = Jinv[2]*u + Jinv[3]*v;
if (q_layout == QVectorLayout::byVDIM)
{
der(c,0,q,e) = JiU;
der(c,1,q,e) = JiV;
}
if (q_layout == QVectorLayout::byNODES)
{
der(q,c,0,e) = JiU;
der(q,c,1,e) = JiV;
}
}
}
if (VDIM == 2 && (eval_flags & QI::DETERMINANTS))
{
// The check (VDIM == 2) should eliminate this block when VDIM is
// known at compile time and (VDIM != 2).
det(q,e) = kernels::Det<2>(D);
}
}
}
});
}
// Template compute kernel for 3D quadrature interpolation:
// * non-tensor product version,
// * assumes 'e_vec' is using ElementDofOrdering::NATIVE,
// * assumes 'maps.mode == FULL'.
template<const int T_VDIM, const int T_ND, const int T_NQ>
static void Eval3D(const int NE,
const int vdim,
const QVectorLayout q_layout,
const GeometricFactors *geom,
const DofToQuad &maps,
const Vector &e_vec,
Vector &q_val,
Vector &q_der,
Vector &q_det,
const int eval_flags)
{
using QI = QuadratureInterpolator;
const int nd = maps.ndof;
const int nq = maps.nqpt;
const int ND = T_ND ? T_ND : nd;
const int NQ = T_NQ ? T_NQ : nq;
const int NMAX = NQ > ND ? NQ : ND;
const int VDIM = T_VDIM ? T_VDIM : vdim;
MFEM_ASSERT(maps.mode == DofToQuad::FULL, "internal error");
MFEM_ASSERT(!geom || geom->mesh->SpaceDimension() == 3, "");
MFEM_VERIFY(ND <= QI::MAX_ND3D, "");
MFEM_VERIFY(NQ <= QI::MAX_NQ3D, "");
MFEM_VERIFY(VDIM == 3 || !(eval_flags & QI::DETERMINANTS), "");
MFEM_VERIFY(bool(geom) == bool(eval_flags & QI::PHYSICAL_DERIVATIVES),
"'geom' must be given (non-null) only when evaluating physical"
" derivatives");
const auto B = Reshape(maps.B.Read(), NQ, ND);
const auto G = Reshape(maps.G.Read(), NQ, 3, ND);
const auto J = Reshape(geom ? geom->J.Read() : nullptr, NQ, 3, 3, NE);
const auto E = Reshape(e_vec.Read(), ND, VDIM, NE);
auto val = q_layout == QVectorLayout::byNODES ?
Reshape(q_val.Write(), NQ, VDIM, NE):
Reshape(q_val.Write(), VDIM, NQ, NE);
auto der = q_layout == QVectorLayout::byNODES ?
Reshape(q_der.Write(), NQ, VDIM, 3, NE):
Reshape(q_der.Write(), VDIM, 3, NQ, NE);
auto det = Reshape(q_det.Write(), NQ, NE);
MFEM_FORALL_2D(e, NE, NMAX, 1, 1,
{
const int ND = T_ND ? T_ND : nd;
const int NQ = T_NQ ? T_NQ : nq;
const int VDIM = T_VDIM ? T_VDIM : vdim;
constexpr int max_ND = T_ND ? T_ND : QI::MAX_ND3D;
constexpr int max_VDIM = T_VDIM ? T_VDIM : QI::MAX_VDIM3D;
MFEM_SHARED double s_E[max_VDIM*max_ND];
MFEM_FOREACH_THREAD(d, x, ND)
{
for (int c = 0; c < VDIM; c++)
{
s_E[c+d*VDIM] = E(d,c,e);
}
}
MFEM_SYNC_THREAD;
MFEM_FOREACH_THREAD(q, x, NQ)
{
if (eval_flags & QI::VALUES)
{
double ed[max_VDIM];
for (int c = 0; c < VDIM; c++) { ed[c] = 0.0; }
for (int d = 0; d < ND; ++d)
{
const double b = B(q,d);
for (int c = 0; c < VDIM; c++) { ed[c] += b*s_E[c+d*VDIM]; }
}
for (int c = 0; c < VDIM; c++)
{
if (q_layout == QVectorLayout::byVDIM) { val(c,q,e) = ed[c]; }
if (q_layout == QVectorLayout::byNODES) { val(q,c,e) = ed[c]; }
}
}
if ((eval_flags & QI::DERIVATIVES) ||
(eval_flags & QI::PHYSICAL_DERIVATIVES) ||
(eval_flags & QI::DETERMINANTS))
{
// use MAX_VDIM3D to avoid "subscript out of range" warnings
double D[QI::MAX_VDIM3D*3];
for (int i = 0; i < 3*VDIM; i++) { D[i] = 0.0; }
for (int d = 0; d < ND; ++d)
{
const double wx = G(q,0,d);
const double wy = G(q,1,d);
const double wz = G(q,2,d);
for (int c = 0; c < VDIM; c++)
{
double s_e = s_E[c+d*VDIM];
D[c+VDIM*0] += s_e * wx;
D[c+VDIM*1] += s_e * wy;
D[c+VDIM*2] += s_e * wz;
}
}
if (eval_flags & QI::DERIVATIVES)
{
for (int c = 0; c < VDIM; c++)
{
if (q_layout == QVectorLayout::byVDIM)
{
der(c,0,q,e) = D[c+VDIM*0];
der(c,1,q,e) = D[c+VDIM*1];
der(c,2,q,e) = D[c+VDIM*2];
}
if (q_layout == QVectorLayout::byNODES)
{
der(q,c,0,e) = D[c+VDIM*0];
der(q,c,1,e) = D[c+VDIM*1];
der(q,c,2,e) = D[c+VDIM*2];
}
}
}
if (eval_flags & QI::PHYSICAL_DERIVATIVES)
{
double Jloc[9], Jinv[9];
for (int col = 0; col < 3; col++)
{
for (int row = 0; row < 3; row++)
{
Jloc[row+3*col] = J(q,row,col,e);
}
}
kernels::CalcInverse<3>(Jloc, Jinv);
for (int c = 0; c < VDIM; c++)
{
const double u = D[c+VDIM*0];
const double v = D[c+VDIM*1];
const double w = D[c+VDIM*2];
const double JiU = Jinv[0]*u + Jinv[1]*v + Jinv[2]*w;
const double JiV = Jinv[3]*u + Jinv[4]*v + Jinv[5]*w;
const double JiW = Jinv[6]*u + Jinv[7]*v + Jinv[8]*w;
if (q_layout == QVectorLayout::byVDIM)
{
der(c,0,q,e) = JiU;
der(c,1,q,e) = JiV;
der(c,2,q,e) = JiW;
}
if (q_layout == QVectorLayout::byNODES)
{
der(q,c,0,e) = JiU;
der(q,c,1,e) = JiV;
der(q,c,2,e) = JiW;
}
}
}
if (VDIM == 3 && (eval_flags & QI::DETERMINANTS))
{
// The check (VDIM == 3) should eliminate this block when VDIM is
// known at compile time and (VDIM != 3).
det(q,e) = kernels::Det<3>(D);
}
}
}
});
}
} // namespace quadrature_interpolator
} // namespace internal
void QuadratureInterpolator::Mult(const Vector &e_vec,
unsigned eval_flags,
Vector &q_val,
Vector &q_der,
Vector &q_det) const
{
using namespace internal::quadrature_interpolator;
const int ne = fespace->GetNE();
if (ne == 0) { return; }
const int vdim = fespace->GetVDim();
const FiniteElement *fe = fespace->GetFE(0);
const bool use_tensor_eval =
use_tensor_products &&
dynamic_cast<const TensorBasisElement*>(fe) != nullptr;
const IntegrationRule *ir =
IntRule ? IntRule : &qspace->GetElementIntRule(0);
const DofToQuad::Mode mode =
use_tensor_eval ? DofToQuad::TENSOR : DofToQuad::FULL;
const DofToQuad &maps = fe->GetDofToQuad(*ir, mode);
const GeometricFactors *geom = nullptr;
if (eval_flags & PHYSICAL_DERIVATIVES)
{
const int jacobians = GeometricFactors::JACOBIANS;
geom = fespace->GetMesh()->GetGeometricFactors(*ir, jacobians);
}
MFEM_ASSERT(fespace->GetMesh()->GetNumGeometries(
fespace->GetMesh()->Dimension()) == 1,
"mixed meshes are not supported");
if (use_tensor_eval)
{
// TODO: use fused kernels
if (q_layout == QVectorLayout::byNODES)
{
if (eval_flags & VALUES)
{
TensorValues<QVectorLayout::byNODES>(ne, vdim, maps, e_vec, q_val);
}
if (eval_flags & DERIVATIVES)
{
TensorDerivatives<QVectorLayout::byNODES>(
ne, vdim, maps, e_vec, q_der);
}
if (eval_flags & PHYSICAL_DERIVATIVES)
{
TensorPhysDerivatives<QVectorLayout::byNODES>(
ne, vdim, maps, *geom, e_vec, q_der);
}
}
if (q_layout == QVectorLayout::byVDIM)
{
if (eval_flags & VALUES)
{
TensorValues<QVectorLayout::byVDIM>(ne, vdim, maps, e_vec, q_val);
}
if (eval_flags & DERIVATIVES)
{
TensorDerivatives<QVectorLayout::byVDIM>(
ne, vdim, maps, e_vec, q_der);
}
if (eval_flags & PHYSICAL_DERIVATIVES)
{
TensorPhysDerivatives<QVectorLayout::byVDIM>(
ne, vdim, maps, *geom, e_vec, q_der);
}
}
if (eval_flags & DETERMINANTS)
{
TensorDeterminants(ne, vdim, maps, e_vec, q_det, d_buffer);
}
}
else // use_tensor_eval == false
{
const int nd = maps.ndof;
const int nq = maps.nqpt;
const int dim = maps.FE->GetDim();
void (*mult)(const int NE,
const int vdim,
const QVectorLayout q_layout,
const GeometricFactors *geom,
const DofToQuad &maps,
const Vector &e_vec,
Vector &q_val,
Vector &q_der,
Vector &q_det,
const int eval_flags) = NULL;
if (vdim == 1)
{
if (dim == 2)
{
switch (100*nd + nq)
{
// Q0
case 101: mult = &Eval2D<1,1,1>; break;
case 104: mult = &Eval2D<1,1,4>; break;
// Q1
case 404: mult = &Eval2D<1,4,4>; break;
case 409: mult = &Eval2D<1,4,9>; break;
// Q2
case 909: mult = &Eval2D<1,9,9>; break;
case 916: mult = &Eval2D<1,9,16>; break;
// Q3
case 1616: mult = &Eval2D<1,16,16>; break;
case 1625: mult = &Eval2D<1,16,25>; break;
case 1636: mult = &Eval2D<1,16,36>; break;
// Q4
case 2525: mult = &Eval2D<1,25,25>; break;
case 2536: mult = &Eval2D<1,25,36>; break;
case 2549: mult = &Eval2D<1,25,49>; break;
case 2564: mult = &Eval2D<1,25,64>; break;
}
if (nq >= 100 || !mult)
{
mult = &Eval2D<1,0,0>;
}
}
else if (dim == 3)
{
switch (1000*nd + nq)
{
// Q0
case 1001: mult = &Eval3D<1,1,1>; break;
case 1008: mult = &Eval3D<1,1,8>; break;
// Q1
case 8008: mult = &Eval3D<1,8,8>; break;
case 8027: mult = &Eval3D<1,8,27>; break;
// Q2
case 27027: mult = &Eval3D<1,27,27>; break;
case 27064: mult = &Eval3D<1,27,64>; break;
// Q3
case 64064: mult = &Eval3D<1,64,64>; break;
case 64125: mult = &Eval3D<1,64,125>; break;
case 64216: mult = &Eval3D<1,64,216>; break;
// Q4
case 125125: mult = &Eval3D<1,125,125>; break;
case 125216: mult = &Eval3D<1,125,216>; break;
}
if (nq >= 1000 || !mult)
{
mult = &Eval3D<1,0,0>;
}
}
}
else if (vdim == 3 && dim == 2)
{
switch (100*nd + nq)
{
// Q0
case 101: mult = &Eval2D<3,1,1>; break;
case 104: mult = &Eval2D<3,1,4>; break;
// Q1
case 404: mult = &Eval2D<3,4,4>; break;
case 409: mult = &Eval2D<3,4,9>; break;
// Q2
case 904: mult = &Eval2D<3,9,4>; break;
case 909: mult = &Eval2D<3,9,9>; break;
case 916: mult = &Eval2D<3,9,16>; break;
case 925: mult = &Eval2D<3,9,25>; break;
// Q3
case 1616: mult = &Eval2D<3,16,16>; break;
case 1625: mult = &Eval2D<3,16,25>; break;
case 1636: mult = &Eval2D<3,16,36>; break;
// Q4
case 2525: mult = &Eval2D<3,25,25>; break;
case 2536: mult = &Eval2D<3,25,36>; break;
case 2549: mult = &Eval2D<3,25,49>; break;
case 2564: mult = &Eval2D<3,25,64>; break;
default: mult = &Eval2D<3,0,0>;
}
}
else if (vdim == dim)
{
if (dim == 2)
{
switch (100*nd + nq)
{
// Q1
case 404: mult = &Eval2D<2,4,4>; break;
case 409: mult = &Eval2D<2,4,9>; break;
// Q2
case 909: mult = &Eval2D<2,9,9>; break;
case 916: mult = &Eval2D<2,9,16>; break;
// Q3
case 1616: mult = &Eval2D<2,16,16>; break;
case 1625: mult = &Eval2D<2,16,25>; break;
case 1636: mult = &Eval2D<2,16,36>; break;
// Q4
case 2525: mult = &Eval2D<2,25,25>; break;
case 2536: mult = &Eval2D<2,25,36>; break;
case 2549: mult = &Eval2D<2,25,49>; break;
case 2564: mult = &Eval2D<2,25,64>; break;
}
if (nq >= 100 || !mult) { mult = &Eval2D<2,0,0>; }
}
else if (dim == 3)
{
switch (1000*nd + nq)
{
// Q1
case 8008: mult = &Eval3D<3,8,8>; break;
case 8027: mult = &Eval3D<3,8,27>; break;
// Q2
case 27027: mult = &Eval3D<3,27,27>; break;
case 27064: mult = &Eval3D<3,27,64>; break;
case 27125: mult = &Eval3D<3,27,125>; break;
// Q3
case 64064: mult = &Eval3D<3,64,64>; break;
case 64125: mult = &Eval3D<3,64,125>; break;
case 64216: mult = &Eval3D<3,64,216>; break;
// Q4
case 125125: mult = &Eval3D<3,125,125>; break;
case 125216: mult = &Eval3D<3,125,216>; break;
}
if (nq >= 1000 || !mult) { mult = &Eval3D<3,0,0>; }
}
}
if (mult)
{
mult(ne,vdim,q_layout,geom,maps,e_vec,q_val,q_der,q_det,eval_flags);
}
else { MFEM_ABORT("case not supported yet"); }
}
}
void QuadratureInterpolator::MultTranspose(unsigned eval_flags,
const Vector &q_val,
const Vector &q_der,
Vector &e_vec) const
{
MFEM_CONTRACT_VAR(eval_flags);
MFEM_CONTRACT_VAR(q_val);
MFEM_CONTRACT_VAR(q_der);
MFEM_CONTRACT_VAR(e_vec);
MFEM_ABORT("this method is not implemented yet");
}
void QuadratureInterpolator::Values(const Vector &e_vec,
Vector &q_val) const
{
Vector empty;
Mult(e_vec, VALUES, q_val, empty, empty);
}
void QuadratureInterpolator::Derivatives(const Vector &e_vec,
Vector &q_der) const
{
Vector empty;
Mult(e_vec, DERIVATIVES, empty, q_der, empty);
}
void QuadratureInterpolator::PhysDerivatives(const Vector &e_vec,
Vector &q_der) const
{
Vector empty;
Mult(e_vec, PHYSICAL_DERIVATIVES, empty, q_der, empty);
}
void QuadratureInterpolator::Determinants(const Vector &e_vec,
Vector &q_det) const
{
Vector empty;
Mult(e_vec, DETERMINANTS, empty, empty, q_det);
}
} // namespace mfem