// Copyright (c) 2010-2023, 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 "../../general/forall.hpp"
#include "../bilininteg.hpp"
#include "../gridfunc.hpp"
#include "../qfunction.hpp"
#include "bilininteg_diffusion_kernels.hpp"

namespace mfem
{

// Apply to x corresponding to DOFs in H^1 (trial), whose gradients are
// integrated against H(curl) test functions corresponding to y.
static void PAHcurlH1Apply2D(const int D1D,
                             const int Q1D,
                             const int NE,
                             const Array<double> &bc,
                             const Array<double> &gc,
                             const Array<double> &bot,
                             const Array<double> &bct,
                             const Vector &pa_data,
                             const Vector &x,
                             Vector &y)
{
   auto Bc = Reshape(bc.Read(), Q1D, D1D);
   auto Gc = Reshape(gc.Read(), Q1D, D1D);
   auto Bot = Reshape(bot.Read(), D1D-1, Q1D);
   auto Bct = Reshape(bct.Read(), D1D, Q1D);
   auto op = Reshape(pa_data.Read(), Q1D, Q1D, 3, NE);
   auto X = Reshape(x.Read(), D1D, D1D, NE);
   auto Y = Reshape(y.ReadWrite(), 2*(D1D-1)*D1D, NE);

   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
   {
      constexpr static int VDIM = 2;
      constexpr static int MAX_D1D = DofQuadLimits::HCURL_MAX_D1D;
      constexpr static int MAX_Q1D = DofQuadLimits::HCURL_MAX_Q1D;

      double mass[MAX_Q1D][MAX_Q1D][VDIM];

      for (int qy = 0; qy < Q1D; ++qy)
      {
         for (int qx = 0; qx < Q1D; ++qx)
         {
            for (int c = 0; c < VDIM; ++c)
            {
               mass[qy][qx][c] = 0.0;
            }
         }
      }

      for (int dy = 0; dy < D1D; ++dy)
      {
         double 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 double s = X(dx,dy,e);
            for (int qx = 0; qx < Q1D; ++qx)
            {
               gradX[qx][0] += s * Bc(qx,dx);
               gradX[qx][1] += s * Gc(qx,dx);
            }
         }
         for (int qy = 0; qy < Q1D; ++qy)
         {
            const double wy  = Bc(qy,dy);
            const double wDy = Gc(qy,dy);
            for (int qx = 0; qx < Q1D; ++qx)
            {
               const double wx  = gradX[qx][0];
               const double wDx = gradX[qx][1];
               mass[qy][qx][0] += wDx * wy;
               mass[qy][qx][1] += wx * wDy;
            }
         }
      }

      // Apply D operator.
      for (int qy = 0; qy < Q1D; ++qy)
      {
         for (int qx = 0; qx < Q1D; ++qx)
         {
            const double O11 = op(qx,qy,0,e);
            const double O12 = op(qx,qy,1,e);
            const double O22 = op(qx,qy,2,e);
            const double massX = mass[qy][qx][0];
            const double massY = mass[qy][qx][1];
            mass[qy][qx][0] = (O11*massX)+(O12*massY);
            mass[qy][qx][1] = (O12*massX)+(O22*massY);
         }
      }

      for (int qy = 0; qy < Q1D; ++qy)
      {
         int osc = 0;

         for (int c = 0; c < VDIM; ++c)  // loop over x, y components
         {
            const int D1Dy = (c == 1) ? D1D - 1 : D1D;
            const int D1Dx = (c == 0) ? D1D - 1 : D1D;

            double massX[MAX_D1D];
            for (int dx = 0; dx < D1Dx; ++dx)
            {
               massX[dx] = 0;
            }
            for (int qx = 0; qx < Q1D; ++qx)
            {
               for (int dx = 0; dx < D1Dx; ++dx)
               {
                  massX[dx] += mass[qy][qx][c] * ((c == 0) ? Bot(dx,qx) : Bct(dx,qx));
               }
            }

            for (int dy = 0; dy < D1Dy; ++dy)
            {
               const double wy = (c == 1) ? Bot(dy,qy) : Bct(dy,qy);

               for (int dx = 0; dx < D1Dx; ++dx)
               {
                  Y(dx + (dy * D1Dx) + osc, e) += massX[dx] * wy;
               }
            }

            osc += D1Dx * D1Dy;
         }  // loop c
      }
   }); // end of element loop
}

// Apply to x corresponding to DOFs in H(curl), integrated
// against gradients of H^1 functions corresponding to y.
static void PAHcurlH1ApplyTranspose2D(const int D1D,
                                      const int Q1D,
                                      const int NE,
                                      const Array<double> &bc,
                                      const Array<double> &bo,
                                      const Array<double> &bct,
                                      const Array<double> &gct,
                                      const Vector &pa_data,
                                      const Vector &x,
                                      Vector &y)
{
   auto Bc = Reshape(bc.Read(), Q1D, D1D);
   auto Bo = Reshape(bo.Read(), Q1D, D1D-1);
   auto Bt = Reshape(bct.Read(), D1D, Q1D);
   auto Gt = Reshape(gct.Read(), D1D, Q1D);
   auto op = Reshape(pa_data.Read(), Q1D, Q1D, 3, NE);
   auto X = Reshape(x.Read(), 2*(D1D-1)*D1D, NE);
   auto Y = Reshape(y.ReadWrite(), D1D, D1D, NE);

   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
   {
      constexpr static int VDIM = 2;
      constexpr static int MAX_D1D = DofQuadLimits::HCURL_MAX_D1D;
      constexpr static int MAX_Q1D = DofQuadLimits::HCURL_MAX_Q1D;

      double mass[MAX_Q1D][MAX_Q1D][VDIM];

      for (int qy = 0; qy < Q1D; ++qy)
      {
         for (int qx = 0; qx < Q1D; ++qx)
         {
            for (int c = 0; c < VDIM; ++c)
            {
               mass[qy][qx][c] = 0.0;
            }
         }
      }

      int osc = 0;

      for (int c = 0; c < VDIM; ++c)  // loop over x, y components
      {
         const int D1Dy = (c == 1) ? D1D - 1 : D1D;
         const int D1Dx = (c == 0) ? D1D - 1 : D1D;

         for (int dy = 0; dy < D1Dy; ++dy)
         {
            double massX[MAX_Q1D];
            for (int qx = 0; qx < Q1D; ++qx)
            {
               massX[qx] = 0.0;
            }

            for (int dx = 0; dx < D1Dx; ++dx)
            {
               const double t = X(dx + (dy * D1Dx) + osc, e);
               for (int qx = 0; qx < Q1D; ++qx)
               {
                  massX[qx] += t * ((c == 0) ? Bo(qx,dx) : Bc(qx,dx));
               }
            }

            for (int qy = 0; qy < Q1D; ++qy)
            {
               const double wy = (c == 1) ? Bo(qy,dy) : Bc(qy,dy);
               for (int qx = 0; qx < Q1D; ++qx)
               {
                  mass[qy][qx][c] += massX[qx] * wy;
               }
            }
         }

         osc += D1Dx * D1Dy;
      }  // loop (c) over components

      // Apply D operator.
      for (int qy = 0; qy < Q1D; ++qy)
      {
         for (int qx = 0; qx < Q1D; ++qx)
         {
            const double O11 = op(qx,qy,0,e);
            const double O12 = op(qx,qy,1,e);
            const double O22 = op(qx,qy,2,e);
            const double massX = mass[qy][qx][0];
            const double massY = mass[qy][qx][1];
            mass[qy][qx][0] = (O11*massX)+(O12*massY);
            mass[qy][qx][1] = (O12*massX)+(O22*massY);
         }
      }

      for (int qy = 0; qy < Q1D; ++qy)
      {
         double gradX[MAX_D1D][2];
         for (int dx = 0; dx < D1D; ++dx)
         {
            gradX[dx][0] = 0;
            gradX[dx][1] = 0;
         }
         for (int qx = 0; qx < Q1D; ++qx)
         {
            const double gX = mass[qy][qx][0];
            const double gY = mass[qy][qx][1];
            for (int dx = 0; dx < D1D; ++dx)
            {
               const double wx  = Bt(dx,qx);
               const double wDx = Gt(dx,qx);
               gradX[dx][0] += gX * wDx;
               gradX[dx][1] += gY * wx;
            }
         }
         for (int dy = 0; dy < D1D; ++dy)
         {
            const double wy  = Bt(dy,qy);
            const double wDy = Gt(dy,qy);
            for (int dx = 0; dx < D1D; ++dx)
            {
               Y(dx,dy,e) += ((gradX[dx][0] * wy) + (gradX[dx][1] * wDy));
            }
         }
      }
   }); // end of element loop
}

// Apply to x corresponding to DOFs in H^1 (trial), whose gradients are
// integrated against H(curl) test functions corresponding to y.
static void PAHcurlH1Apply3D(const int D1D,
                             const int Q1D,
                             const int NE,
                             const Array<double> &bc,
                             const Array<double> &gc,
                             const Array<double> &bot,
                             const Array<double> &bct,
                             const Vector &pa_data,
                             const Vector &x,
                             Vector &y)
{
   MFEM_VERIFY(D1D <= DeviceDofQuadLimits::Get().HCURL_MAX_D1D,
               "Error: D1D > MAX_D1D");
   MFEM_VERIFY(Q1D <= DeviceDofQuadLimits::Get().HCURL_MAX_Q1D,
               "Error: Q1D > MAX_Q1D");

   constexpr static int VDIM = 3;

   auto Bc = Reshape(bc.Read(), Q1D, D1D);
   auto Gc = Reshape(gc.Read(), Q1D, D1D);
   auto Bot = Reshape(bot.Read(), D1D-1, Q1D);
   auto Bct = Reshape(bct.Read(), D1D, Q1D);
   auto op = Reshape(pa_data.Read(), Q1D, Q1D, Q1D, 6, NE);
   auto X = Reshape(x.Read(), D1D, D1D, D1D, NE);
   auto Y = Reshape(y.ReadWrite(), 3*(D1D-1)*D1D*D1D, NE);

   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
   {
      constexpr static int MAX_D1D = DofQuadLimits::HCURL_MAX_D1D;
      constexpr static int MAX_Q1D = DofQuadLimits::HCURL_MAX_Q1D;

      double mass[MAX_Q1D][MAX_Q1D][MAX_Q1D][VDIM];

      for (int qz = 0; qz < Q1D; ++qz)
      {
         for (int qy = 0; qy < Q1D; ++qy)
         {
            for (int qx = 0; qx < Q1D; ++qx)
            {
               for (int c = 0; c < VDIM; ++c)
               {
                  mass[qz][qy][qx][c] = 0.0;
               }
            }
         }
      }

      for (int dz = 0; dz < D1D; ++dz)
      {
         double 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)
         {
            double 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 double s = X(dx,dy,dz,e);
               for (int qx = 0; qx < Q1D; ++qx)
               {
                  gradX[qx][0] += s * Bc(qx,dx);
                  gradX[qx][1] += s * Gc(qx,dx);
               }
            }
            for (int qy = 0; qy < Q1D; ++qy)
            {
               const double wy  = Bc(qy,dy);
               const double wDy = Gc(qy,dy);
               for (int qx = 0; qx < Q1D; ++qx)
               {
                  const double wx  = gradX[qx][0];
                  const double 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 double wz  = Bc(qz,dz);
            const double wDz = Gc(qz,dz);
            for (int qy = 0; qy < Q1D; ++qy)
            {
               for (int qx = 0; qx < Q1D; ++qx)
               {
                  mass[qz][qy][qx][0] += gradXY[qy][qx][0] * wz;
                  mass[qz][qy][qx][1] += gradXY[qy][qx][1] * wz;
                  mass[qz][qy][qx][2] += gradXY[qy][qx][2] * wDz;
               }
            }
         }
      }

      // Apply D operator.
      for (int qz = 0; qz < Q1D; ++qz)
      {
         for (int qy = 0; qy < Q1D; ++qy)
         {
            for (int qx = 0; qx < Q1D; ++qx)
            {
               const double O11 = op(qx,qy,qz,0,e);
               const double O12 = op(qx,qy,qz,1,e);
               const double O13 = op(qx,qy,qz,2,e);
               const double O22 = op(qx,qy,qz,3,e);
               const double O23 = op(qx,qy,qz,4,e);
               const double O33 = op(qx,qy,qz,5,e);
               const double massX = mass[qz][qy][qx][0];
               const double massY = mass[qz][qy][qx][1];
               const double massZ = mass[qz][qy][qx][2];
               mass[qz][qy][qx][0] = (O11*massX)+(O12*massY)+(O13*massZ);
               mass[qz][qy][qx][1] = (O12*massX)+(O22*massY)+(O23*massZ);
               mass[qz][qy][qx][2] = (O13*massX)+(O23*massY)+(O33*massZ);
            }
         }
      }

      for (int qz = 0; qz < Q1D; ++qz)
      {
         double massXY[MAX_D1D][MAX_D1D];

         int osc = 0;

         for (int c = 0; c < VDIM; ++c)  // loop over x, y, z components
         {
            const int D1Dz = (c == 2) ? D1D - 1 : D1D;
            const int D1Dy = (c == 1) ? D1D - 1 : D1D;
            const int D1Dx = (c == 0) ? D1D - 1 : D1D;

            for (int dy = 0; dy < D1Dy; ++dy)
            {
               for (int dx = 0; dx < D1Dx; ++dx)
               {
                  massXY[dy][dx] = 0.0;
               }
            }
            for (int qy = 0; qy < Q1D; ++qy)
            {
               double massX[MAX_D1D];
               for (int dx = 0; dx < D1Dx; ++dx)
               {
                  massX[dx] = 0;
               }
               for (int qx = 0; qx < Q1D; ++qx)
               {
                  for (int dx = 0; dx < D1Dx; ++dx)
                  {
                     massX[dx] += mass[qz][qy][qx][c] * ((c == 0) ? Bot(dx,qx) : Bct(dx,qx));
                  }
               }
               for (int dy = 0; dy < D1Dy; ++dy)
               {
                  const double wy = (c == 1) ? Bot(dy,qy) : Bct(dy,qy);
                  for (int dx = 0; dx < D1Dx; ++dx)
                  {
                     massXY[dy][dx] += massX[dx] * wy;
                  }
               }
            }

            for (int dz = 0; dz < D1Dz; ++dz)
            {
               const double wz = (c == 2) ? Bot(dz,qz) : Bct(dz,qz);
               for (int dy = 0; dy < D1Dy; ++dy)
               {
                  for (int dx = 0; dx < D1Dx; ++dx)
                  {
                     Y(dx + ((dy + (dz * D1Dy)) * D1Dx) + osc, e) += massXY[dy][dx] * wz;
                  }
               }
            }

            osc += D1Dx * D1Dy * D1Dz;
         }  // loop c
      }  // loop qz
   }); // end of element loop
}

// Apply to x corresponding to DOFs in H(curl), integrated
// against gradients of H^1 functions corresponding to y.
static void PAHcurlH1ApplyTranspose3D(const int D1D,
                                      const int Q1D,
                                      const int NE,
                                      const Array<double> &bc,
                                      const Array<double> &bo,
                                      const Array<double> &bct,
                                      const Array<double> &gct,
                                      const Vector &pa_data,
                                      const Vector &x,
                                      Vector &y)
{
   MFEM_VERIFY(D1D <= DeviceDofQuadLimits::Get().HCURL_MAX_D1D,
               "Error: D1D > MAX_D1D");
   MFEM_VERIFY(Q1D <= DeviceDofQuadLimits::Get().HCURL_MAX_Q1D,
               "Error: Q1D > MAX_Q1D");

   constexpr static int VDIM = 3;

   auto Bc = Reshape(bc.Read(), Q1D, D1D);
   auto Bo = Reshape(bo.Read(), Q1D, D1D-1);
   auto Bt = Reshape(bct.Read(), D1D, Q1D);
   auto Gt = Reshape(gct.Read(), D1D, Q1D);
   auto op = Reshape(pa_data.Read(), Q1D, Q1D, Q1D, 6, NE);
   auto X = Reshape(x.Read(), 3*(D1D-1)*D1D*D1D, NE);
   auto Y = Reshape(y.ReadWrite(), D1D, D1D, D1D, NE);

   mfem::forall(NE, [=] MFEM_HOST_DEVICE (int e)
   {
      constexpr static int MAX_D1D = DofQuadLimits::HCURL_MAX_D1D;
      constexpr static int MAX_Q1D = DofQuadLimits::HCURL_MAX_Q1D;

      double mass[MAX_Q1D][MAX_Q1D][MAX_Q1D][VDIM];

      for (int qz = 0; qz < Q1D; ++qz)
      {
         for (int qy = 0; qy < Q1D; ++qy)
         {
            for (int qx = 0; qx < Q1D; ++qx)
            {
               for (int c = 0; c < VDIM; ++c)
               {
                  mass[qz][qy][qx][c] = 0.0;
               }
            }
         }
      }

      int osc = 0;

      for (int c = 0; c < VDIM; ++c)  // loop over x, y, z components
      {
         const int D1Dz = (c == 2) ? D1D - 1 : D1D;
         const int D1Dy = (c == 1) ? D1D - 1 : D1D;
         const int D1Dx = (c == 0) ? D1D - 1 : D1D;

         for (int dz = 0; dz < D1Dz; ++dz)
         {
            double massXY[MAX_Q1D][MAX_Q1D];
            for (int qy = 0; qy < Q1D; ++qy)
            {
               for (int qx = 0; qx < Q1D; ++qx)
               {
                  massXY[qy][qx] = 0.0;
               }
            }

            for (int dy = 0; dy < D1Dy; ++dy)
            {
               double massX[MAX_Q1D];
               for (int qx = 0; qx < Q1D; ++qx)
               {
                  massX[qx] = 0.0;
               }

               for (int dx = 0; dx < D1Dx; ++dx)
               {
                  const double t = X(dx + ((dy + (dz * D1Dy)) * D1Dx) + osc, e);
                  for (int qx = 0; qx < Q1D; ++qx)
                  {
                     massX[qx] += t * ((c == 0) ? Bo(qx,dx) : Bc(qx,dx));
                  }
               }

               for (int qy = 0; qy < Q1D; ++qy)
               {
                  const double wy = (c == 1) ? Bo(qy,dy) : Bc(qy,dy);
                  for (int qx = 0; qx < Q1D; ++qx)
                  {
                     const double wx = massX[qx];
                     massXY[qy][qx] += wx * wy;
                  }
               }
            }

            for (int qz = 0; qz < Q1D; ++qz)
            {
               const double wz = (c == 2) ? Bo(qz,dz) : Bc(qz,dz);
               for (int qy = 0; qy < Q1D; ++qy)
               {
                  for (int qx = 0; qx < Q1D; ++qx)
                  {
                     mass[qz][qy][qx][c] += massXY[qy][qx] * wz;
                  }
               }
            }
         }

         osc += D1Dx * D1Dy * D1Dz;
      }  // loop (c) over components

      // Apply D operator.
      for (int qz = 0; qz < Q1D; ++qz)
      {
         for (int qy = 0; qy < Q1D; ++qy)
         {
            for (int qx = 0; qx < Q1D; ++qx)
            {
               const double O11 = op(qx,qy,qz,0,e);
               const double O12 = op(qx,qy,qz,1,e);
               const double O13 = op(qx,qy,qz,2,e);
               const double O22 = op(qx,qy,qz,3,e);
               const double O23 = op(qx,qy,qz,4,e);
               const double O33 = op(qx,qy,qz,5,e);
               const double massX = mass[qz][qy][qx][0];
               const double massY = mass[qz][qy][qx][1];
               const double massZ = mass[qz][qy][qx][2];
               mass[qz][qy][qx][0] = (O11*massX)+(O12*massY)+(O13*massZ);
               mass[qz][qy][qx][1] = (O12*massX)+(O22*massY)+(O23*massZ);
               mass[qz][qy][qx][2] = (O13*massX)+(O23*massY)+(O33*massZ);
            }
         }
      }

      for (int qz = 0; qz < Q1D; ++qz)
      {
         double 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)
         {
            double 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 double gX = mass[qz][qy][qx][0];
               const double gY = mass[qz][qy][qx][1];
               const double gZ = mass[qz][qy][qx][2];
               for (int dx = 0; dx < D1D; ++dx)
               {
                  const double wx  = Bt(dx,qx);
                  const double 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 double wy  = Bt(dy,qy);
               const double 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 double wz  = Bt(dz,qz);
            const double wDz = Gt(dz,qz);
            for (int dy = 0; dy < D1D; ++dy)
            {
               for (int dx = 0; dx < D1D; ++dx)
               {
                  Y(dx,dy,dz,e) +=
                     ((gradXY[dy][dx][0] * wz) +
                      (gradXY[dy][dx][1] * wz) +
                      (gradXY[dy][dx][2] * wDz));
               }
            }
         }
      }  // loop qz
   }); // end of element loop
}

void MixedVectorGradientIntegrator::AssemblePA(const FiniteElementSpace
                                               &trial_fes,
                                               const FiniteElementSpace &test_fes)
{
   // Assumes tensor-product elements, with a vector test space and H^1 trial space.
   Mesh *mesh = trial_fes.GetMesh();
   const FiniteElement *trial_fel = trial_fes.GetFE(0);
   const FiniteElement *test_fel = test_fes.GetFE(0);

   const NodalTensorFiniteElement *trial_el =
      dynamic_cast<const NodalTensorFiniteElement*>(trial_fel);
   MFEM_VERIFY(trial_el != NULL, "Only NodalTensorFiniteElement is supported!");

   const VectorTensorFiniteElement *test_el =
      dynamic_cast<const VectorTensorFiniteElement*>(test_fel);
   MFEM_VERIFY(test_el != NULL, "Only VectorTensorFiniteElement is supported!");

   const IntegrationRule *ir
      = IntRule ? IntRule : &MassIntegrator::GetRule(*trial_el, *trial_el,
                                                     *mesh->GetElementTransformation(0));
   const int dims = trial_el->GetDim();
   MFEM_VERIFY(dims == 2 || dims == 3, "");

   const int symmDims = (dims * (dims + 1)) / 2; // 1x1: 1, 2x2: 3, 3x3: 6
   const int nq = ir->GetNPoints();
   dim = mesh->Dimension();
   MFEM_VERIFY(dim == 2 || dim == 3, "");

   MFEM_VERIFY(trial_el->GetOrder() == test_el->GetOrder(), "");

   ne = trial_fes.GetNE();
   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
   mapsC = &test_el->GetDofToQuad(*ir, DofToQuad::TENSOR);
   mapsO = &test_el->GetDofToQuadOpen(*ir, DofToQuad::TENSOR);
   dofs1D = mapsC->ndof;
   quad1D = mapsC->nqpt;

   MFEM_VERIFY(dofs1D == mapsO->ndof + 1 && quad1D == mapsO->nqpt, "");

   pa_data.SetSize(symmDims * nq * ne, Device::GetMemoryType());

   QuadratureSpace qs(*mesh, *ir);
   CoefficientVector coeff(Q, qs, CoefficientStorage::FULL);

   // Use the same setup functions as VectorFEMassIntegrator.
   if (test_el->GetDerivType() == mfem::FiniteElement::CURL && dim == 3)
   {
      internal::PADiffusionSetup3D(quad1D, 1, ne, ir->GetWeights(), geom->J,
                                   coeff, pa_data);
   }
   else if (test_el->GetDerivType() == mfem::FiniteElement::CURL && dim == 2)
   {
      internal::PADiffusionSetup2D<2>(quad1D, 1, ne, ir->GetWeights(), geom->J,
                                      coeff, pa_data);
   }
   else
   {
      MFEM_ABORT("Unknown kernel.");
   }
}

void MixedVectorGradientIntegrator::AddMultPA(const Vector &x, Vector &y) const
{
   if (dim == 3)
   {
      PAHcurlH1Apply3D(dofs1D, quad1D, ne, mapsC->B, mapsC->G,
                       mapsO->Bt, mapsC->Bt, pa_data, x, y);
   }
   else if (dim == 2)
   {
      PAHcurlH1Apply2D(dofs1D, quad1D, ne, mapsC->B, mapsC->G,
                       mapsO->Bt, mapsC->Bt, pa_data, x, y);
   }
   else
   {
      MFEM_ABORT("Unsupported dimension!");
   }
}

void MixedVectorGradientIntegrator::AddMultTransposePA(const Vector &x,
                                                       Vector &y) const
{
   if (dim == 3)
   {
      PAHcurlH1ApplyTranspose3D(dofs1D, quad1D, ne, mapsC->B, mapsO->B,
                                mapsC->Bt, mapsC->Gt, pa_data, x, y);
   }
   else if (dim == 2)
   {
      PAHcurlH1ApplyTranspose2D(dofs1D, quad1D, ne, mapsC->B, mapsO->B,
                                mapsC->Bt, mapsC->Gt, pa_data, x, y);
   }
   else
   {
      MFEM_ABORT("Unsupported dimension!");
   }
}

} // namespace mfem