bilininteg_vecdiffusion_kernels.hpp

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// Copyright (c) 2010-2026, 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.
 
#ifndef MFEM_BILININTEG_VECDIFFUSION_KERNELS_HPP
#define MFEM_BILININTEG_VECDIFFUSION_KERNELS_HPP
 
#include "../../general/forall.hpp"
#include "../bilininteg.hpp"
#include "../ceed/integrators/diffusion/diffusion.hpp"
#include "../gridfunc.hpp"
#include "../qfunction.hpp"
 
/// \cond DO_NOT_DOCUMENT
namespace mfem::internal
{
 
// PA Diffusion Apply 2D kernel
template <int T_D1D = 0, int T_Q1D = 0, int T_VDIM = 0>
void PAVectorDiffusionApply2D(const int NE, const Array<real_t> &b,
                              const Array<real_t> &g, const Array<real_t> &bt,
                              const Array<real_t> &gt, const Vector &d_,
                              const Vector &x_, Vector &y_, const int d1d = 0,
                              const int q1d = 0, const int vdim = 0)
{
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
   const int VDIM = T_VDIM ? T_VDIM : vdim;
   MFEM_VERIFY(D1D <= DeviceDofQuadLimits::Get().MAX_D1D, "");
   MFEM_VERIFY(Q1D <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
   auto B = Reshape(b.Read(), Q1D, D1D);
   auto G = Reshape(g.Read(), Q1D, D1D);
   auto Bt = Reshape(bt.Read(), D1D, Q1D);
   auto Gt = Reshape(gt.Read(), D1D, Q1D);
   auto D = Reshape(d_.Read(), Q1D * Q1D, 3, NE);
   auto x = Reshape(x_.Read(), D1D, D1D, VDIM, NE);
   auto y = Reshape(y_.ReadWrite(), D1D, D1D, VDIM, NE);
   mfem::forall(NE, [=] MFEM_HOST_DEVICE(int e)
   {
      const int D1D = T_D1D ? T_D1D : d1d;
      const int Q1D = T_Q1D ? T_Q1D : q1d;
      const int VDIM = T_VDIM ? T_VDIM : vdim;
      constexpr int max_D1D = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
      constexpr int max_Q1D = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
 
      real_t grad[max_Q1D][max_Q1D][2];
      for (int c = 0; c < VDIM; c++)
      {
         for (int qy = 0; qy < Q1D; ++qy)
         {
            for (int qx = 0; qx < Q1D; ++qx)
            {
               grad[qy][qx][0] = 0.0;
               grad[qy][qx][1] = 0.0;
            }
         }
         for (int dy = 0; dy < D1D; ++dy)
         {
            real_t gradX[max_Q1D][2];
            for (int qx = 0; qx < Q1D; ++qx)
            {
               gradX[qx][0] = 0.0;
               gradX[qx][1] = 0.0;
            }
            for (int dx = 0; dx < D1D; ++dx)
            {
               const real_t s = x(dx, dy, c, e);
               for (int qx = 0; qx < Q1D; ++qx)
               {
                  gradX[qx][0] += s * B(qx, dx);
                  gradX[qx][1] += s * G(qx, dx);
               }
            }
            for (int qy = 0; qy < Q1D; ++qy)
            {
               const real_t wy = B(qy, dy);
               const real_t wDy = G(qy, dy);
               for (int qx = 0; qx < Q1D; ++qx)
               {
                  grad[qy][qx][0] += gradX[qx][1] * wy;
                  grad[qy][qx][1] += gradX[qx][0] * wDy;
               }
            }
         }
         // Calculate Dxy, xDy in plane
         for (int qy = 0; qy < Q1D; ++qy)
         {
            for (int qx = 0; qx < Q1D; ++qx)
            {
               const int q = qx + qy * Q1D;
               const real_t O11 = D(q, 0, e);
               const real_t O12 = D(q, 1, e);
               const real_t O22 = D(q, 2, e);
               const real_t gradX = grad[qy][qx][0];
               const real_t gradY = grad[qy][qx][1];
               grad[qy][qx][0] = (O11 * gradX) + (O12 * gradY);
               grad[qy][qx][1] = (O12 * gradX) + (O22 * gradY);
            }
         }
         for (int qy = 0; qy < Q1D; ++qy)
         {
            real_t gradX[max_D1D][2];
            for (int dx = 0; dx < D1D; ++dx)
            {
               gradX[dx][0] = 0.0;
               gradX[dx][1] = 0.0;
            }
            for (int qx = 0; qx < Q1D; ++qx)
            {
               const real_t gX = grad[qy][qx][0];
               const real_t gY = grad[qy][qx][1];
               for (int dx = 0; dx < D1D; ++dx)
               {
                  const real_t wx = Bt(dx, qx);
                  const real_t wDx = Gt(dx, qx);
                  gradX[dx][0] += gX * wDx;
                  gradX[dx][1] += gY * wx;
               }
            }
            for (int dy = 0; dy < D1D; ++dy)
            {
               const real_t wy = Bt(dy, qy);
               const real_t wDy = Gt(dy, qy);
               for (int dx = 0; dx < D1D; ++dx)
               {
                  y(dx, dy, c, e) +=
                     ((gradX[dx][0] * wy) + (gradX[dx][1] * wDy));
               }
            }
         }
      }
   });
}
 
// PA Diffusion Apply 3D kernel
template <const int T_D1D = 0, const int T_Q1D = 0>
void PAVectorDiffusionApply3D(const int NE, const Array<real_t> &b,
                              const Array<real_t> &g, const Array<real_t> &bt,
                              const Array<real_t> &gt, const Vector &op_,
                              const Vector &x_, Vector &y_, const int d1d = 0,
                              const int q1d = 0, const int sdim = 0)
{
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
   constexpr int VDIM = 3;
   MFEM_VERIFY(D1D <= DeviceDofQuadLimits::Get().MAX_D1D, "");
   MFEM_VERIFY(Q1D <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
   auto B = Reshape(b.Read(), Q1D, D1D);
   auto G = Reshape(g.Read(), Q1D, D1D);
   auto Bt = Reshape(bt.Read(), D1D, Q1D);
   auto Gt = Reshape(gt.Read(), D1D, Q1D);
   auto op = Reshape(op_.Read(), Q1D * Q1D * Q1D, 6, NE);
   auto x = Reshape(x_.Read(), D1D, D1D, D1D, VDIM, NE);
   auto y = Reshape(y_.ReadWrite(), D1D, D1D, D1D, VDIM, NE);
   mfem::forall(NE, [=] MFEM_HOST_DEVICE(int e)
   {
      const int D1D = T_D1D ? T_D1D : d1d;
      const int Q1D = T_Q1D ? T_Q1D : q1d;
      constexpr int max_D1D = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
      constexpr int max_Q1D = T_Q1D ? T_Q1D : DofQuadLimits::MAX_Q1D;
      for (int c = 0; c < VDIM; ++c)
      {
         real_t grad[max_Q1D][max_Q1D][max_Q1D][3];
         for (int qz = 0; qz < Q1D; ++qz)
         {
            for (int qy = 0; qy < Q1D; ++qy)
            {
               for (int qx = 0; qx < Q1D; ++qx)
               {
                  grad[qz][qy][qx][0] = 0.0;
                  grad[qz][qy][qx][1] = 0.0;
                  grad[qz][qy][qx][2] = 0.0;
               }
            }
         }
         for (int dz = 0; dz < D1D; ++dz)
         {
            real_t gradXY[max_Q1D][max_Q1D][3];
            for (int qy = 0; qy < Q1D; ++qy)
            {
               for (int qx = 0; qx < Q1D; ++qx)
               {
                  gradXY[qy][qx][0] = 0.0;
                  gradXY[qy][qx][1] = 0.0;
                  gradXY[qy][qx][2] = 0.0;
               }
            }
            for (int dy = 0; dy < D1D; ++dy)
            {
               real_t gradX[max_Q1D][2];
               for (int qx = 0; qx < Q1D; ++qx)
               {
                  gradX[qx][0] = 0.0;
                  gradX[qx][1] = 0.0;
               }
               for (int dx = 0; dx < D1D; ++dx)
               {
                  const real_t s = x(dx, dy, dz, c, e);
                  for (int qx = 0; qx < Q1D; ++qx)
                  {
                     gradX[qx][0] += s * B(qx, dx);
                     gradX[qx][1] += s * G(qx, dx);
                  }
               }
               for (int qy = 0; qy < Q1D; ++qy)
               {
                  const real_t wy = B(qy, dy);
                  const real_t wDy = G(qy, dy);
                  for (int qx = 0; qx < Q1D; ++qx)
                  {
                     const real_t wx = gradX[qx][0];
                     const real_t wDx = gradX[qx][1];
                     gradXY[qy][qx][0] += wDx * wy;
                     gradXY[qy][qx][1] += wx * wDy;
                     gradXY[qy][qx][2] += wx * wy;
                  }
               }
            }
            for (int qz = 0; qz < Q1D; ++qz)
            {
               const real_t wz = B(qz, dz);
               const real_t wDz = G(qz, dz);
               for (int qy = 0; qy < Q1D; ++qy)
               {
                  for (int qx = 0; qx < Q1D; ++qx)
                  {
                     grad[qz][qy][qx][0] += gradXY[qy][qx][0] * wz;
                     grad[qz][qy][qx][1] += gradXY[qy][qx][1] * wz;
                     grad[qz][qy][qx][2] += gradXY[qy][qx][2] * wDz;
                  }
               }
            }
         }
         // Calculate Dxyz, xDyz, xyDz in plane
         for (int qz = 0; qz < Q1D; ++qz)
         {
            for (int qy = 0; qy < Q1D; ++qy)
            {
               for (int qx = 0; qx < Q1D; ++qx)
               {
                  const int q = qx + (qy + qz * Q1D) * Q1D;
                  const real_t O11 = op(q, 0, e);
                  const real_t O12 = op(q, 1, e);
                  const real_t O13 = op(q, 2, e);
                  const real_t O22 = op(q, 3, e);
                  const real_t O23 = op(q, 4, e);
                  const real_t O33 = op(q, 5, e);
                  const real_t gradX = grad[qz][qy][qx][0];
                  const real_t gradY = grad[qz][qy][qx][1];
                  const real_t gradZ = grad[qz][qy][qx][2];
                  grad[qz][qy][qx][0] =
                     (O11 * gradX) + (O12 * gradY) + (O13 * gradZ);
                  grad[qz][qy][qx][1] =
                     (O12 * gradX) + (O22 * gradY) + (O23 * gradZ);
                  grad[qz][qy][qx][2] =
                     (O13 * gradX) + (O23 * gradY) + (O33 * gradZ);
               }
            }
         }
         for (int qz = 0; qz < Q1D; ++qz)
         {
            real_t gradXY[max_D1D][max_D1D][3];
            for (int dy = 0; dy < D1D; ++dy)
            {
               for (int dx = 0; dx < D1D; ++dx)
               {
                  gradXY[dy][dx][0] = 0;
                  gradXY[dy][dx][1] = 0;
                  gradXY[dy][dx][2] = 0;
               }
            }
            for (int qy = 0; qy < Q1D; ++qy)
            {
               real_t gradX[max_D1D][3];
               for (int dx = 0; dx < D1D; ++dx)
               {
                  gradX[dx][0] = 0;
                  gradX[dx][1] = 0;
                  gradX[dx][2] = 0;
               }
               for (int qx = 0; qx < Q1D; ++qx)
               {
                  const real_t gX = grad[qz][qy][qx][0];
                  const real_t gY = grad[qz][qy][qx][1];
                  const real_t gZ = grad[qz][qy][qx][2];
                  for (int dx = 0; dx < D1D; ++dx)
                  {
                     const real_t wx = Bt(dx, qx);
                     const real_t wDx = Gt(dx, qx);
                     gradX[dx][0] += gX * wDx;
                     gradX[dx][1] += gY * wx;
                     gradX[dx][2] += gZ * wx;
                  }
               }
               for (int dy = 0; dy < D1D; ++dy)
               {
                  const real_t wy = Bt(dy, qy);
                  const real_t wDy = Gt(dy, qy);
                  for (int dx = 0; dx < D1D; ++dx)
                  {
                     gradXY[dy][dx][0] += gradX[dx][0] * wy;
                     gradXY[dy][dx][1] += gradX[dx][1] * wDy;
                     gradXY[dy][dx][2] += gradX[dx][2] * wy;
                  }
               }
            }
            for (int dz = 0; dz < D1D; ++dz)
            {
               const real_t wz = Bt(dz, qz);
               const real_t wDz = Gt(dz, qz);
               for (int dy = 0; dy < D1D; ++dy)
               {
                  for (int dx = 0; dx < D1D; ++dx)
                  {
                     y(dx, dy, dz, c, e) +=
                        ((gradXY[dy][dx][0] * wz) + (gradXY[dy][dx][1] * wz) +
                         (gradXY[dy][dx][2] * wDz));
                  }
               }
            }
         }
      }
   });
}
} // namespace mfem::internal
 
/// \endcond DO_NOT_DOCUMENT
 
#endif // MFEM_BILININTEG_VECDIFFUSION_KERNELS_HPP