552 lines
22 KiB
C++
552 lines
22 KiB
C++
// Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
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// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
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// LICENSE and NOTICE for details. LLNL-CODE-806117.
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//
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// This file is part of the MFEM library. For more information and source code
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// availability visit https://mfem.org.
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//
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// MFEM is free software; you can redistribute it and/or modify it under the
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// terms of the BSD-3 license. We welcome feedback and contributions, see file
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// CONTRIBUTING.md for details.
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#include "lor_h1.hpp"
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#include "lor_util.hpp"
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#include "../../linalg/dtensor.hpp"
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#include "../../general/forall.hpp"
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namespace mfem
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{
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template <int ORDER>
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void BatchedLOR_H1::Assemble2D()
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{
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const int nel_ho = fes_ho.GetNE();
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static constexpr int nv = 4;
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static constexpr int dim = 2;
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static constexpr int ddm2 = (dim*(dim+1))/2;
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static constexpr int nd1d = ORDER + 1;
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static constexpr int ndof_per_el = nd1d*nd1d;
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static constexpr int nnz_per_row = 9;
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static constexpr int sz_local_mat = nv*nv;
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const bool const_mq = c1.Size() == 1;
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const auto MQ = const_mq
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? Reshape(c1.Read(), 1, 1, 1)
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: Reshape(c1.Read(), nd1d, nd1d, nel_ho);
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const bool const_dq = c2.Size() == 1;
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const auto DQ = const_dq
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? Reshape(c2.Read(), 1, 1, 1)
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: Reshape(c2.Read(), nd1d, nd1d, nel_ho);
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sparse_ij.SetSize(nnz_per_row*ndof_per_el*nel_ho);
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auto V = Reshape(sparse_ij.Write(), nnz_per_row, nd1d, nd1d, nel_ho);
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auto X = X_vert.Read();
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MFEM_FORALL_2D(iel_ho, nel_ho, ORDER, ORDER, 1,
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{
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// Assemble a sparse matrix over the macro-element by looping over each
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// subelement.
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// V(j,ix,iy) stores the jth nonzero in the row of the sparse matrix
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// corresponding to local DOF (ix, iy).
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MFEM_FOREACH_THREAD(iy,y,nd1d)
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{
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MFEM_FOREACH_THREAD(ix,x,nd1d)
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{
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for (int j=0; j<nnz_per_row; ++j)
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{
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V(j,ix,iy,iel_ho) = 0.0;
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}
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}
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}
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MFEM_SYNC_THREAD;
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// Compute geometric factors at quadrature points
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MFEM_FOREACH_THREAD(ky,y,ORDER)
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{
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MFEM_FOREACH_THREAD(kx,x,ORDER)
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{
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double Q_[(ddm2 + 1)*nv];
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double local_mat_[sz_local_mat];
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DeviceTensor<3> Q(Q_, ddm2 + 1, 2, 2);
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DeviceTensor<2> local_mat(local_mat_, nv, nv);
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for (int i=0; i<sz_local_mat; ++i) { local_mat[i] = 0.0; }
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double vx[4], vy[4];
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LORVertexCoordinates2D<ORDER>(X, iel_ho, kx, ky, vx, vy);
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for (int iqy=0; iqy<2; ++iqy)
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{
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for (int iqx=0; iqx<2; ++iqx)
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{
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const double x = iqx;
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const double y = iqy;
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const double w = 1.0/4.0;
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double J_[2*2];
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DeviceTensor<2> J(J_, 2, 2);
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Jacobian2D(x, y, vx, vy, J);
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const double detJ = Det2D(J);
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const double w_detJ = w/detJ;
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Q(0,iqy,iqx) = w_detJ * (J(0,1)*J(0,1) + J(1,1)*J(1,1)); // 1,1
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Q(1,iqy,iqx) = -w_detJ * (J(0,1)*J(0,0) + J(1,1)*J(1,0)); // 1,2
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Q(2,iqy,iqx) = w_detJ * (J(0,0)*J(0,0) + J(1,0)*J(1,0)); // 2,2
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Q(3,iqy,iqx) = w*detJ;
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}
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}
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for (int iqx=0; iqx<2; ++iqx)
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{
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for (int iqy=0; iqy<2; ++iqy)
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{
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const double mq = const_mq ? MQ(0,0,0) : MQ(kx+iqx, ky+iqy, iel_ho);
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const double dq = const_dq ? DQ(0,0,0) : DQ(kx+iqx, ky+iqy, iel_ho);
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for (int jy=0; jy<2; ++jy)
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{
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const double bjy = (jy == iqy) ? 1.0 : 0.0;
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const double gjy = (jy == 0) ? -1.0 : 1.0;
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for (int jx=0; jx<2; ++jx)
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{
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const double bjx = (jx == iqx) ? 1.0 : 0.0;
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const double gjx = (jx == 0) ? -1.0 : 1.0;
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const double djx = gjx*bjy;
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const double djy = bjx*gjy;
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int jj_loc = jx + 2*jy;
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for (int iy=0; iy<2; ++iy)
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{
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const double biy = (iy == iqy) ? 1.0 : 0.0;
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const double giy = (iy == 0) ? -1.0 : 1.0;
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for (int ix=0; ix<2; ++ix)
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{
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const double bix = (ix == iqx) ? 1.0 : 0.0;
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const double gix = (ix == 0) ? -1.0 : 1.0;
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const double dix = gix*biy;
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const double diy = bix*giy;
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int ii_loc = ix + 2*iy;
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// Only store the lower-triangular part of
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// the matrix (by symmetry).
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if (jj_loc > ii_loc) { continue; }
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double val = 0.0;
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val += dix*djx*Q(0,iqy,iqx);
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val += (dix*djy + diy*djx)*Q(1,iqy,iqx);
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val += diy*djy*Q(2,iqy,iqx);
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val *= dq;
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val += mq*bix*biy*bjx*bjy*Q(3,iqy,iqx);
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local_mat(ii_loc, jj_loc) += val;
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}
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}
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}
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}
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}
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}
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// Assemble the local matrix into the macro-element sparse matrix
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// in a format similar to coordinate format. The (I,J) arrays
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// are implicit (not stored explicitly).
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for (int ii_loc=0; ii_loc<nv; ++ii_loc)
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{
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const int ix = ii_loc%2;
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const int iy = ii_loc/2;
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for (int jj_loc=0; jj_loc<nv; ++jj_loc)
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{
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const int jx = jj_loc%2;
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const int jy = jj_loc/2;
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const int jj_off = (jx-ix+1) + 3*(jy-iy+1);
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// Symmetry
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if (jj_loc <= ii_loc)
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{
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AtomicAdd(V(jj_off, ix+kx, iy+ky, iel_ho), local_mat(ii_loc, jj_loc));
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}
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else
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{
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AtomicAdd(V(jj_off, ix+kx, iy+ky, iel_ho), local_mat(jj_loc, ii_loc));
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}
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}
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}
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}
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}
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});
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sparse_mapping.SetSize(nnz_per_row*ndof_per_el);
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sparse_mapping = -1;
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auto map = Reshape(sparse_mapping.HostReadWrite(), nnz_per_row, ndof_per_el);
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for (int iy=0; iy<nd1d; ++iy)
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{
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const int jy_begin = (iy > 0) ? iy - 1 : 0;
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const int jy_end = (iy < ORDER) ? iy + 1 : ORDER;
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for (int ix=0; ix<nd1d; ++ix)
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{
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const int jx_begin = (ix > 0) ? ix - 1 : 0;
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const int jx_end = (ix < ORDER) ? ix + 1 : ORDER;
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const int ii_el = ix + nd1d*iy;
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for (int jy=jy_begin; jy<=jy_end; ++jy)
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{
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for (int jx=jx_begin; jx<=jx_end; ++jx)
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{
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const int jj_off = (jx-ix+1) + 3*(jy-iy+1);
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const int jj_el = jx + nd1d*jy;
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map(jj_off, ii_el) = jj_el;
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}
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}
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}
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}
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}
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template <int ORDER>
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void BatchedLOR_H1::Assemble3D()
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{
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const int nel_ho = fes_ho.GetNE();
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static constexpr int nv = 8;
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static constexpr int dim = 3;
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static constexpr int ddm2 = (dim*(dim+1))/2;
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static constexpr int nd1d = ORDER + 1;
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static constexpr int ndof_per_el = nd1d*nd1d*nd1d;
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static constexpr int nnz_per_row = 27;
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static constexpr int sz_grad_A = 3*3*2*2*2*2;
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static constexpr int sz_grad_B = sz_grad_A*2;
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static constexpr int sz_mass_A = 2*2*2*2;
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static constexpr int sz_mass_B = sz_mass_A*2;
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static constexpr int sz_local_mat = nv*nv;
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const bool const_mq = c1.Size() == 1;
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const auto MQ = const_mq
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? Reshape(c1.Read(), 1, 1, 1, 1)
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: Reshape(c1.Read(), nd1d, nd1d, nd1d, nel_ho);
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const bool const_dq = c2.Size() == 1;
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const auto DQ = const_dq
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? Reshape(c2.Read(), 1, 1, 1, 1)
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: Reshape(c2.Read(), nd1d, nd1d, nd1d, nel_ho);
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sparse_ij.SetSize(nel_ho*ndof_per_el*nnz_per_row);
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auto V = Reshape(sparse_ij.Write(), nnz_per_row, nd1d, nd1d, nd1d, nel_ho);
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auto X = X_vert.Read();
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// Last thread dimension is lowered to avoid "too many resources" error
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MFEM_FORALL_3D(iel_ho, nel_ho, ORDER, ORDER, (ORDER>6)?4:ORDER,
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{
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// Assemble a sparse matrix over the macro-element by looping over each
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// subelement.
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// V(j,i) stores the jth nonzero in the ith row of the sparse matrix.
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MFEM_FOREACH_THREAD(iz,z,nd1d)
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{
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MFEM_FOREACH_THREAD(iy,y,nd1d)
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{
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MFEM_FOREACH_THREAD(ix,x,nd1d)
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{
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MFEM_UNROLL(nnz_per_row)
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for (int j=0; j<nnz_per_row; ++j)
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{
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V(j,ix,iy,iz,iel_ho) = 0.0;
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}
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}
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}
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}
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MFEM_SYNC_THREAD;
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// Compute geometric factors at quadrature points
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MFEM_FOREACH_THREAD(kz,z,ORDER)
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{
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MFEM_FOREACH_THREAD(ky,y,ORDER)
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{
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MFEM_FOREACH_THREAD(kx,x,ORDER)
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{
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double Q_[(ddm2 + 1)*nv];
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double grad_A_[sz_grad_A];
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double grad_B_[sz_grad_B];
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double mass_A_[sz_mass_A];
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double mass_B_[sz_mass_B];
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double local_mat_[sz_local_mat];
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DeviceTensor<4> Q(Q_, ddm2 + 1, 2, 2, 2);
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DeviceTensor<2> local_mat(local_mat_, nv, nv);
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DeviceTensor<6> grad_A(grad_A_, 3, 3, 2, 2, 2, 2);
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DeviceTensor<7> grad_B(grad_B_, 3, 3, 2, 2, 2, 2, 2);
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DeviceTensor<4> mass_A(mass_A_, 2, 2, 2, 2);
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DeviceTensor<5> mass_B(mass_B_, 2, 2, 2, 2, 2);
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// local_mat is the local (dense) stiffness matrix
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for (int i=0; i<sz_local_mat; ++i) { local_mat[i] = 0.0; }
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// Intermediate quantities
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// (see e.g. Mora and Demkowicz for notation).
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for (int i=0; i<sz_grad_A; ++i) { grad_A[i] = 0.0; }
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for (int i=0; i<sz_grad_B; ++i) { grad_B[i] = 0.0; }
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for (int i=0; i<sz_mass_A; ++i) { mass_A[i] = 0.0; }
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for (int i=0; i<sz_mass_B; ++i) { mass_B[i] = 0.0; }
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double vx[8], vy[8], vz[8];
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LORVertexCoordinates3D<ORDER>(X, iel_ho, kx, ky, kz, vx, vy, vz);
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//MFEM_UNROLL(2)
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for (int iqz=0; iqz<2; ++iqz)
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{
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//MFEM_UNROLL(2)
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for (int iqy=0; iqy<2; ++iqy)
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{
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//MFEM_UNROLL(2)
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for (int iqx=0; iqx<2; ++iqx)
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{
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const double x = iqx;
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const double y = iqy;
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const double z = iqz;
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const double w = 1.0/8.0;
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double J_[3*3];
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DeviceTensor<2> J(J_, 3, 3);
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Jacobian3D(x, y, z, vx, vy, vz, J);
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const double detJ = Det3D(J);
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const double w_detJ = w/detJ;
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// adj(J)
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double A_[3*3];
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DeviceTensor<2> A(A_, 3, 3);
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Adjugate3D(J, A);
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Q(0,iqz,iqy,iqx) = w_detJ*(A(0,0)*A(0,0)+A(0,1)*A(0,1)+A(0,2)*A(0,2)); // 1,1
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Q(1,iqz,iqy,iqx) = w_detJ*(A(0,0)*A(1,0)+A(0,1)*A(1,1)+A(0,2)*A(1,2)); // 2,1
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Q(2,iqz,iqy,iqx) = w_detJ*(A(0,0)*A(2,0)+A(0,1)*A(2,1)+A(0,2)*A(2,2)); // 3,1
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Q(3,iqz,iqy,iqx) = w_detJ*(A(1,0)*A(1,0)+A(1,1)*A(1,1)+A(1,2)*A(1,2)); // 2,2
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Q(4,iqz,iqy,iqx) = w_detJ*(A(1,0)*A(2,0)+A(1,1)*A(2,1)+A(1,2)*A(2,2)); // 3,2
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Q(5,iqz,iqy,iqx) = w_detJ*(A(2,0)*A(2,0)+A(2,1)*A(2,1)+A(2,2)*A(2,2)); // 3,3
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Q(6,iqz,iqy,iqx) = w*detJ;
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}
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}
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}
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//MFEM_UNROLL(2)
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for (int iqx=0; iqx<2; ++iqx)
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{
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//MFEM_UNROLL(2)
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for (int jz=0; jz<2; ++jz)
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{
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// Note loop starts at iz=jz here, taking advantage of
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// symmetries.
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//MFEM_UNROLL(2)
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for (int iz=jz; iz<2; ++iz)
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{
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//MFEM_UNROLL(2)
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for (int iqy=0; iqy<2; ++iqy)
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{
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//MFEM_UNROLL(2)
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for (int iqz=0; iqz<2; ++iqz)
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{
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const double mq = const_mq ? MQ(0,0,0,0) : MQ(kx+iqx, ky+iqy, kz+iqz, iel_ho);
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const double dq = const_dq ? DQ(0,0,0,0) : DQ(kx+iqx, ky+iqy, kz+iqz, iel_ho);
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const double biz = (iz == iqz) ? 1.0 : 0.0;
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const double giz = (iz == 0) ? -1.0 : 1.0;
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const double bjz = (jz == iqz) ? 1.0 : 0.0;
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const double gjz = (jz == 0) ? -1.0 : 1.0;
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const double J11 = Q(0,iqz,iqy,iqx);
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const double J21 = Q(1,iqz,iqy,iqx);
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const double J31 = Q(2,iqz,iqy,iqx);
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const double J12 = J21;
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const double J22 = Q(3,iqz,iqy,iqx);
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const double J32 = Q(4,iqz,iqy,iqx);
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const double J13 = J31;
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const double J23 = J32;
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const double J33 = Q(5,iqz,iqy,iqx);
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grad_A(0,0,iqy,iz,jz,iqx) += dq*J11*biz*bjz;
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grad_A(1,0,iqy,iz,jz,iqx) += dq*J21*biz*bjz;
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grad_A(2,0,iqy,iz,jz,iqx) += dq*J31*giz*bjz;
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grad_A(0,1,iqy,iz,jz,iqx) += dq*J12*biz*bjz;
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grad_A(1,1,iqy,iz,jz,iqx) += dq*J22*biz*bjz;
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grad_A(2,1,iqy,iz,jz,iqx) += dq*J32*giz*bjz;
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grad_A(0,2,iqy,iz,jz,iqx) += dq*J13*biz*gjz;
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grad_A(1,2,iqy,iz,jz,iqx) += dq*J23*biz*gjz;
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grad_A(2,2,iqy,iz,jz,iqx) += dq*J33*giz*gjz;
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double wdetJ = Q(6,iqz,iqy,iqx);
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mass_A(iqy,iz,jz,iqx) += mq*wdetJ*biz*bjz;
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}
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//MFEM_UNROLL(2)
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for (int jy=0; jy<2; ++jy)
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{
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//MFEM_UNROLL(2)
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for (int iy=0; iy<2; ++iy)
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{
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const double biy = (iy == iqy) ? 1.0 : 0.0;
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const double giy = (iy == 0) ? -1.0 : 1.0;
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const double bjy = (jy == iqy) ? 1.0 : 0.0;
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const double gjy = (jy == 0) ? -1.0 : 1.0;
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grad_B(0,0,iy,jy,iz,jz,iqx) += biy*bjy*grad_A(0,0,iqy,iz,jz,iqx);
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grad_B(1,0,iy,jy,iz,jz,iqx) += giy*bjy*grad_A(1,0,iqy,iz,jz,iqx);
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grad_B(2,0,iy,jy,iz,jz,iqx) += biy*bjy*grad_A(2,0,iqy,iz,jz,iqx);
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grad_B(0,1,iy,jy,iz,jz,iqx) += biy*gjy*grad_A(0,1,iqy,iz,jz,iqx);
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grad_B(1,1,iy,jy,iz,jz,iqx) += giy*gjy*grad_A(1,1,iqy,iz,jz,iqx);
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grad_B(2,1,iy,jy,iz,jz,iqx) += biy*gjy*grad_A(2,1,iqy,iz,jz,iqx);
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grad_B(0,2,iy,jy,iz,jz,iqx) += biy*bjy*grad_A(0,2,iqy,iz,jz,iqx);
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grad_B(1,2,iy,jy,iz,jz,iqx) += giy*bjy*grad_A(1,2,iqy,iz,jz,iqx);
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grad_B(2,2,iy,jy,iz,jz,iqx) += biy*bjy*grad_A(2,2,iqy,iz,jz,iqx);
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|
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mass_B(iy,jy,iz,jz,iqx) += biy*bjy*mass_A(iqy,iz,jz,iqx);
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}
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|
}
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|
}
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|
//MFEM_UNROLL(2)
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for (int jy=0; jy<2; ++jy)
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|
{
|
|
//MFEM_UNROLL(2)
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|
for (int jx=0; jx<2; ++jx)
|
|
{
|
|
//MFEM_UNROLL(2)
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|
for (int iy=0; iy<2; ++iy)
|
|
{
|
|
//MFEM_UNROLL(2)
|
|
for (int ix=0; ix<2; ++ix)
|
|
{
|
|
const double bix = (ix == iqx) ? 1.0 : 0.0;
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|
const double gix = (ix == 0) ? -1.0 : 1.0;
|
|
|
|
const double bjx = (jx == iqx) ? 1.0 : 0.0;
|
|
const double gjx = (jx == 0) ? -1.0 : 1.0;
|
|
|
|
int ii_loc = ix + 2*iy + 4*iz;
|
|
int jj_loc = jx + 2*jy + 4*jz;
|
|
|
|
// Only store the lower-triangular part of
|
|
// the matrix (by symmetry).
|
|
if (jj_loc > ii_loc) { continue; }
|
|
|
|
double val = 0.0;
|
|
val += gix*gjx*grad_B(0,0,iy,jy,iz,jz,iqx);
|
|
val += bix*gjx*grad_B(1,0,iy,jy,iz,jz,iqx);
|
|
val += bix*gjx*grad_B(2,0,iy,jy,iz,jz,iqx);
|
|
val += gix*bjx*grad_B(0,1,iy,jy,iz,jz,iqx);
|
|
val += bix*bjx*grad_B(1,1,iy,jy,iz,jz,iqx);
|
|
val += bix*bjx*grad_B(2,1,iy,jy,iz,jz,iqx);
|
|
val += gix*bjx*grad_B(0,2,iy,jy,iz,jz,iqx);
|
|
val += bix*bjx*grad_B(2,2,iy,jy,iz,jz,iqx);
|
|
val += bix*bjx*grad_B(1,2,iy,jy,iz,jz,iqx);
|
|
|
|
val += bix*bjx*mass_B(iy,jy,iz,jz,iqx);
|
|
|
|
local_mat(ii_loc, jj_loc) += val;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
// Assemble the local matrix into the macro-element sparse matrix
|
|
// in a format similar to coordinate format. The (I,J) arrays
|
|
// are implicit (not stored explicitly).
|
|
//MFEM_UNROLL(8)
|
|
for (int ii_loc=0; ii_loc<nv; ++ii_loc)
|
|
{
|
|
const int ix = ii_loc%2;
|
|
const int iy = (ii_loc/2)%2;
|
|
const int iz = ii_loc/2/2;
|
|
|
|
for (int jj_loc=0; jj_loc<nv; ++jj_loc)
|
|
{
|
|
const int jx = jj_loc%2;
|
|
const int jy = (jj_loc/2)%2;
|
|
const int jz = jj_loc/2/2;
|
|
const int jj_off = (jx-ix+1) + 3*(jy-iy+1) + 9*(jz-iz+1);
|
|
|
|
if (jj_loc <= ii_loc)
|
|
{
|
|
AtomicAdd(V(jj_off, ix+kx, iy+ky, iz+kz, iel_ho), local_mat(ii_loc, jj_loc));
|
|
}
|
|
else
|
|
{
|
|
AtomicAdd(V(jj_off, ix+kx, iy+ky, iz+kz, iel_ho), local_mat(jj_loc, ii_loc));
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
});
|
|
|
|
sparse_mapping.SetSize(nnz_per_row*ndof_per_el);
|
|
sparse_mapping = -1;
|
|
auto map = Reshape(sparse_mapping.HostReadWrite(), nnz_per_row, ndof_per_el);
|
|
for (int iz=0; iz<nd1d; ++iz)
|
|
{
|
|
const int jz_begin = (iz > 0) ? iz - 1 : 0;
|
|
const int jz_end = (iz < ORDER) ? iz + 1 : ORDER;
|
|
for (int iy=0; iy<nd1d; ++iy)
|
|
{
|
|
const int jy_begin = (iy > 0) ? iy - 1 : 0;
|
|
const int jy_end = (iy < ORDER) ? iy + 1 : ORDER;
|
|
for (int ix=0; ix<nd1d; ++ix)
|
|
{
|
|
const int jx_begin = (ix > 0) ? ix - 1 : 0;
|
|
const int jx_end = (ix < ORDER) ? ix + 1 : ORDER;
|
|
|
|
const int ii_el = ix + nd1d*(iy + nd1d*iz);
|
|
|
|
for (int jz=jz_begin; jz<=jz_end; ++jz)
|
|
{
|
|
for (int jy=jy_begin; jy<=jy_end; ++jy)
|
|
{
|
|
for (int jx=jx_begin; jx<=jx_end; ++jx)
|
|
{
|
|
const int jj_off = (jx-ix+1) + 3*(jy-iy+1) + 9*(jz-iz+1);
|
|
const int jj_el = jx + nd1d*(jy + nd1d*jz);
|
|
map(jj_off, ii_el) = jj_el;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// Explicit template instantiations
|
|
template void BatchedLOR_H1::Assemble2D<1>();
|
|
template void BatchedLOR_H1::Assemble2D<2>();
|
|
template void BatchedLOR_H1::Assemble2D<3>();
|
|
template void BatchedLOR_H1::Assemble2D<4>();
|
|
template void BatchedLOR_H1::Assemble2D<5>();
|
|
template void BatchedLOR_H1::Assemble2D<6>();
|
|
template void BatchedLOR_H1::Assemble2D<7>();
|
|
template void BatchedLOR_H1::Assemble2D<8>();
|
|
|
|
template void BatchedLOR_H1::Assemble3D<1>();
|
|
template void BatchedLOR_H1::Assemble3D<2>();
|
|
template void BatchedLOR_H1::Assemble3D<3>();
|
|
template void BatchedLOR_H1::Assemble3D<4>();
|
|
template void BatchedLOR_H1::Assemble3D<5>();
|
|
template void BatchedLOR_H1::Assemble3D<6>();
|
|
template void BatchedLOR_H1::Assemble3D<7>();
|
|
template void BatchedLOR_H1::Assemble3D<8>();
|
|
|
|
BatchedLOR_H1::BatchedLOR_H1(BilinearForm &a,
|
|
FiniteElementSpace &fes_ho_,
|
|
Vector &X_vert_,
|
|
Vector &sparse_ij_,
|
|
Array<int> &sparse_mapping_)
|
|
: BatchedLORKernel(fes_ho_, X_vert_, sparse_ij_, sparse_mapping_)
|
|
{
|
|
ProjectLORCoefficient<MassIntegrator>(a, c1);
|
|
ProjectLORCoefficient<DiffusionIntegrator>(a, c2);
|
|
}
|
|
|
|
} // namespace mfem
|