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// *****************************************************************************
/*!
  \file      src/PDE/Integrate/Surface.cpp
  \copyright 2012-2015 J. Bakosi,
             2016-2018 Los Alamos National Security, LLC.,
             2019-2021 Triad National Security, LLC.
             All rights reserved. See the LICENSE file for details.
  \brief     Functions for computing internal surface integrals of a system
     of PDEs in DG methods
  \details   This file contains functionality for computing internal surface
     integrals of a system of PDEs used in discontinuous Galerkin methods for
     various orders of numerical representation.
*/
// *****************************************************************************

#include <array>

#include "Surface.hpp"
#include "Vector.hpp"
#include "Quadrature.hpp"
#include "Reconstruction.hpp"

namespace tk {

void
surfInt( ncomp_t system,
         std::size_t nmat,
         ncomp_t offset,
         real t,
         const std::size_t ndof,
         const std::size_t rdof,
         const std::vector< std::size_t >& inpoel,
         const UnsMesh::Coords& coord,
         const inciter::FaceData& fd,
         const Fields& geoFace,
         const Fields& geoElem,
         const RiemannFluxFn& flux,
         const VelFn& vel,
         const Fields& U,
         const Fields& P,
         const std::vector< std::size_t >& ndofel,
         Fields& R,
         std::vector< std::vector< tk::real > >& vriem,
         std::vector< std::vector< tk::real > >& riemannLoc,
         std::vector< std::vector< tk::real > >& riemannDeriv,
         int intsharp )
// *****************************************************************************
//  Compute internal surface flux integrals
//! \param[in] system Equation system index
//! \param[in] nmat Number of materials in this PDE system
//! \param[in] offset Offset this PDE system operates from
//! \param[in] t Physical time
//! \param[in] ndof Maximum number of degrees of freedom
//! \param[in] rdof Maximum number of reconstructed degrees of freedom
//! \param[in] inpoel Element-node connectivity
//! \param[in] coord Array of nodal coordinates
//! \param[in] fd Face connectivity and boundary conditions object
//! \param[in] geoFace Face geometry array
//! \param[in] geoElem Element geometry array
//! \param[in] flux Riemann flux function to use
//! \param[in] vel Function to use to query prescribed velocity (if any)
//! \param[in] U Solution vector at recent time step
//! \param[in] P Vector of primitives at recent time step
//! \param[in] ndofel Vector of local number of degrees of freedome
//! \param[in,out] R Right-hand side vector computed
//! \param[in,out] vriem Vector of the riemann velocity
//! \param[in,out] riemannLoc Vector of coordinates where Riemann velocity data
//!   is available
//! \param[in,out] riemannDeriv Derivatives of partial-pressures and velocities
//!   computed from the Riemann solver for use in the non-conservative terms.
//!   These derivatives are used only for multi-material hydro and unused for
//!   single-material compflow and linear transport.
//! \param[in] intsharp Interface compression tag, an optional argument, with
//!   default 0, so that it is unused for single-material and transport.
// *****************************************************************************
{
  const auto& esuf = fd.Esuf();
  const auto& inpofa = fd.Inpofa();

  const auto& cx = coord[0];
  const auto& cy = coord[1];
  const auto& cz = coord[2];

  auto ncomp = U.nprop()/rdof;<--- Variable 'ncomp' is assigned a value that is never used.
  auto nprim = P.nprop()/rdof;<--- Variable 'nprim' is assigned a value that is never used.

  Assert( (nmat==1 ? riemannDeriv.empty() : true), "Non-empty Riemann "
          "derivative vector for single material compflow" );

  // compute internal surface flux integrals
  for (auto f=fd.Nbfac(); f<esuf.size()/2; ++f)
  {
    Assert( esuf[2*f] > -1 && esuf[2*f+1] > -1, "Interior element detected "
            "as -1" );

    std::size_t el = static_cast< std::size_t >(esuf[2*f]);
    std::size_t er = static_cast< std::size_t >(esuf[2*f+1]);

    auto ng_l = tk::NGfa(ndofel[el]);
    auto ng_r = tk::NGfa(ndofel[er]);

    // When the number of gauss points for the left and right element are
    // different, choose the larger ng
    auto ng = std::max( ng_l, ng_r );

    // arrays for quadrature points
    std::array< std::vector< real >, 2 > coordgp;
    std::vector< real > wgp;

    coordgp[0].resize( ng );
    coordgp[1].resize( ng );
    wgp.resize( ng );

    // get quadrature point weights and coordinates for triangle
    GaussQuadratureTri( ng, coordgp, wgp );

    // Extract the element coordinates
    std::array< std::array< tk::real, 3>, 4 > coordel_l {{ 
      {{ cx[ inpoel[4*el  ] ], cy[ inpoel[4*el  ] ], cz[ inpoel[4*el  ] ] }},
      {{ cx[ inpoel[4*el+1] ], cy[ inpoel[4*el+1] ], cz[ inpoel[4*el+1] ] }},
      {{ cx[ inpoel[4*el+2] ], cy[ inpoel[4*el+2] ], cz[ inpoel[4*el+2] ] }},
      {{ cx[ inpoel[4*el+3] ], cy[ inpoel[4*el+3] ], cz[ inpoel[4*el+3] ] }} }};

    std::array< std::array< tk::real, 3>, 4 > coordel_r {{ 
      {{ cx[ inpoel[4*er  ] ], cy[ inpoel[4*er  ] ], cz[ inpoel[4*er  ] ] }},
      {{ cx[ inpoel[4*er+1] ], cy[ inpoel[4*er+1] ], cz[ inpoel[4*er+1] ] }},
      {{ cx[ inpoel[4*er+2] ], cy[ inpoel[4*er+2] ], cz[ inpoel[4*er+2] ] }},
      {{ cx[ inpoel[4*er+3] ], cy[ inpoel[4*er+3] ], cz[ inpoel[4*er+3] ] }} }};

    // Compute the determinant of Jacobian matrix
    auto detT_l = 
      Jacobian( coordel_l[0], coordel_l[1], coordel_l[2], coordel_l[3] );
    auto detT_r =
      Jacobian( coordel_r[0], coordel_r[1], coordel_r[2], coordel_r[3] );

    // Extract the face coordinates
    std::array< std::array< tk::real, 3>, 3 > coordfa {{
      {{ cx[ inpofa[3*f  ] ], cy[ inpofa[3*f  ] ], cz[ inpofa[3*f  ] ] }},
      {{ cx[ inpofa[3*f+1] ], cy[ inpofa[3*f+1] ], cz[ inpofa[3*f+1] ] }},
      {{ cx[ inpofa[3*f+2] ], cy[ inpofa[3*f+2] ], cz[ inpofa[3*f+2] ] }} }};

    std::array< real, 3 >
      fn{{ geoFace(f,1,0), geoFace(f,2,0), geoFace(f,3,0) }};

    // Gaussian quadrature
    for (std::size_t igp=0; igp<ng; ++igp)
    {
      // Compute the coordinates of quadrature point at physical domain
      auto gp = eval_gp( igp, coordfa, coordgp );

      // In order to determine the high-order solution from the left and right
      // elements at the surface quadrature points, the basis functions from
      // the left and right elements are needed. For this, a transformation to
      // the reference coordinates is necessary, since the basis functions are
      // defined on the reference tetrahedron only.
      // The transformation relations are shown below:
      //  xi   = Jacobian( coordel[0], gp, coordel[2], coordel[3] ) / detT
      //  eta  = Jacobian( coordel[0], coordel[2], gp, coordel[3] ) / detT
      //  zeta = Jacobian( coordel[0], coordel[2], coordel[3], gp ) / detT

      // If an rDG method is set up (P0P1), then, currently we compute the P1
      // basis functions and solutions by default. This implies that P0P1 is
      // unsupported in the p-adaptive DG (PDG). This is a workaround until we
      // have rdofel, which is needed to distinguish between ndofs and rdofs per
      // element for pDG.
      std::size_t dof_el, dof_er;
      if (rdof > ndof)
      {
        dof_el = rdof;
        dof_er = rdof;
      }
      else
      {
        dof_el = ndofel[el];
        dof_er = ndofel[er];
      }

      std::array< tk::real, 3> ref_gp_l{
        Jacobian( coordel_l[0], gp, coordel_l[2], coordel_l[3] ) / detT_l,
        Jacobian( coordel_l[0], coordel_l[1], gp, coordel_l[3] ) / detT_l,
        Jacobian( coordel_l[0], coordel_l[1], coordel_l[2], gp ) / detT_l };
      std::array< tk::real, 3> ref_gp_r{
        Jacobian( coordel_r[0], gp, coordel_r[2], coordel_r[3] ) / detT_r,
        Jacobian( coordel_r[0], coordel_r[1], gp, coordel_r[3] ) / detT_r,
        Jacobian( coordel_r[0], coordel_r[1], coordel_r[2], gp ) / detT_r };

      //Compute the basis functions
      auto B_l = eval_basis( dof_el, ref_gp_l[0], ref_gp_l[1], ref_gp_l[2] );
      auto B_r = eval_basis( dof_er, ref_gp_r[0], ref_gp_r[1], ref_gp_r[2] );

      auto wt = wgp[igp] * geoFace(f,0,0);<--- Variable 'wt' is assigned a value that is never used.

      std::array< std::vector< real >, 2 > state;

      state[0] = evalPolynomialSol(system, offset, intsharp, ncomp, nprim, rdof,
        nmat, el, dof_el, inpoel, coord, geoElem, ref_gp_l, B_l, U, P);
      state[1] = evalPolynomialSol(system, offset, intsharp, ncomp, nprim, rdof,
        nmat, er, dof_er, inpoel, coord, geoElem, ref_gp_r, B_r, U, P);

      Assert( state[0].size() == ncomp+nprim, "Incorrect size for "
              "appended boundary state vector" );
      Assert( state[1].size() == ncomp+nprim, "Incorrect size for "
              "appended boundary state vector" );

      // evaluate prescribed velocity (if any)
      auto v = vel( system, ncomp, gp[0], gp[1], gp[2], t );

      // compute flux
      auto fl = flux( fn, state, v );

      // Add the surface integration term to the rhs
      update_rhs_fa( ncomp, nmat, offset, ndof, ndofel[el], ndofel[er], wt, fn,
                     el, er, fl, B_l, B_r, R, riemannDeriv );

      // Store the riemann velocity and coordinates data of quadrature point
      // used for velocity reconstruction if MulMat scheme is selected
      if (nmat > 1 && ndof > 1)
        tk::evaluRiemann( ncomp, esuf[2*f], esuf[2*f+1], nmat, fl, fn, gp,
                          state, vriem, riemannLoc );

    }
  }
}

void
update_rhs_fa( ncomp_t ncomp,
               std::size_t nmat,
               ncomp_t offset,
               const std::size_t ndof,
               const std::size_t ndof_l,
               const std::size_t ndof_r,
               const tk::real wt,
               const std::array< tk::real, 3 >& fn,
               const std::size_t el,
               const std::size_t er,
               const std::vector< tk::real >& fl,
               const std::vector< tk::real >& B_l,
               const std::vector< tk::real >& B_r,
               Fields& R,<--- Parameter 'R' can be declared with const
               std::vector< std::vector< tk::real > >& riemannDeriv )
// *****************************************************************************
//  Update the rhs by adding the surface integration term
//! \param[in] ncomp Number of scalar components in this PDE system
//! \param[in] nmat Number of materials in this PDE system
//! \param[in] offset Offset this PDE system operates from
//! \param[in] ndof Maximum number of degrees of freedom
//! \param[in] ndof_l Number of degrees of freedom for left element
//! \param[in] ndof_r Number of degrees of freedom for right element
//! \param[in] wt Weight of gauss quadrature point
//! \param[in] fn Face/Surface normal
//! \param[in] el Left element index
//! \param[in] er Right element index
//! \param[in] fl Surface flux
//! \param[in] B_l Basis function for the left element
//! \param[in] B_r Basis function for the right element
//! \param[in,out] R Right-hand side vector computed
//! \param[in,out] riemannDeriv Derivatives of partial-pressures and velocities
//!   computed from the Riemann solver for use in the non-conservative terms.
//!   These derivatives are used only for multi-material hydro and unused for
//!   single-material compflow and linear transport.
// *****************************************************************************
{
  // following lines commented until rdofel is made available.
  //Assert( B_l.size() == ndof_l, "Size mismatch" );
  //Assert( B_r.size() == ndof_r, "Size mismatch" );

  for (ncomp_t c=0; c<ncomp; ++c)
  {
    auto mark = c*ndof;
    R(el, mark, offset) -= wt * fl[c];
    R(er, mark, offset) += wt * fl[c];

    if(ndof_l > 1)          //DG(P1)
    {
      R(el, mark+1, offset) -= wt * fl[c] * B_l[1];
      R(el, mark+2, offset) -= wt * fl[c] * B_l[2];
      R(el, mark+3, offset) -= wt * fl[c] * B_l[3];
    }

    if(ndof_r > 1)          //DG(P1)
    {
      R(er, mark+1, offset) += wt * fl[c] * B_r[1];
      R(er, mark+2, offset) += wt * fl[c] * B_r[2];
      R(er, mark+3, offset) += wt * fl[c] * B_r[3];
    }

    if(ndof_l > 4)          //DG(P2)
    {
      R(el, mark+4, offset) -= wt * fl[c] * B_l[4];
      R(el, mark+5, offset) -= wt * fl[c] * B_l[5];
      R(el, mark+6, offset) -= wt * fl[c] * B_l[6];
      R(el, mark+7, offset) -= wt * fl[c] * B_l[7];
      R(el, mark+8, offset) -= wt * fl[c] * B_l[8];
      R(el, mark+9, offset) -= wt * fl[c] * B_l[9];
    }

    if(ndof_r > 4)          //DG(P2)
    {
      R(er, mark+4, offset) += wt * fl[c] * B_r[4];
      R(er, mark+5, offset) += wt * fl[c] * B_r[5];
      R(er, mark+6, offset) += wt * fl[c] * B_r[6];
      R(er, mark+7, offset) += wt * fl[c] * B_r[7];
      R(er, mark+8, offset) += wt * fl[c] * B_r[8];
      R(er, mark+9, offset) += wt * fl[c] * B_r[9];
    }
  }

  // Prep for non-conservative terms in multimat
  if (fl.size() > ncomp)
  {
    // Gradients of partial pressures
    for (std::size_t k=0; k<nmat; ++k)
    {
      for (std::size_t idir=0; idir<3; ++idir)
      {
        riemannDeriv[3*k+idir][el] += wt * fl[ncomp+k] * fn[idir];
        riemannDeriv[3*k+idir][er] -= wt * fl[ncomp+k] * fn[idir];
      }
    }

    // Divergence of velocity
    riemannDeriv[3*nmat][el] += wt * fl[ncomp+nmat];
    riemannDeriv[3*nmat][er] -= wt * fl[ncomp+nmat];
  }
}

void
surfIntFV( ncomp_t system,
  std::size_t nmat,
  ncomp_t offset,
  real t,
  const std::size_t rdof,
  const std::vector< std::size_t >& inpoel,
  const UnsMesh::Coords& coord,
  const inciter::FaceData& fd,
  const Fields& geoFace,
  const Fields& geoElem,
  const RiemannFluxFn& flux,
  const VelFn& vel,
  const Fields& U,
  const Fields& P,
  Fields& R,
  std::vector< std::vector< tk::real > >& riemannDeriv,
  int intsharp )
// *****************************************************************************
//  Compute internal surface flux integrals for second order FV
//! \param[in] system Equation system index
//! \param[in] nmat Number of materials in this PDE system
//! \param[in] offset Offset this PDE system operates from
//! \param[in] t Physical time
//! \param[in] rdof Maximum number of reconstructed degrees of freedom
//! \param[in] inpoel Element-node connectivity
//! \param[in] coord Array of nodal coordinates
//! \param[in] fd Face connectivity and boundary conditions object
//! \param[in] geoFace Face geometry array
//! \param[in] geoElem Element geometry array
//! \param[in] flux Riemann flux function to use
//! \param[in] vel Function to use to query prescribed velocity (if any)
//! \param[in] U Solution vector at recent time step
//! \param[in] P Vector of primitives at recent time step
//! \param[in,out] R Right-hand side vector computed
//! \param[in,out] riemannDeriv Derivatives of partial-pressures and velocities
//!   computed from the Riemann solver for use in the non-conservative terms.
//!   These derivatives are used only for multi-material hydro and unused for
//!   single-material compflow and linear transport.
//! \param[in] intsharp Interface compression tag, an optional argument, with
//!   default 0, so that it is unused for single-material and transport.
// *****************************************************************************
{
  const auto& esuf = fd.Esuf();

  const auto& cx = coord[0];
  const auto& cy = coord[1];
  const auto& cz = coord[2];

  auto ncomp = U.nprop()/rdof;<--- Variable 'ncomp' is assigned a value that is never used.
  auto nprim = P.nprop()/rdof;<--- Variable 'nprim' is assigned a value that is never used.

  Assert( (nmat==1 ? riemannDeriv.empty() : true), "Non-empty Riemann "
          "derivative vector for single material compflow" );

  // compute internal surface flux integrals
  for (auto f=fd.Nbfac(); f<esuf.size()/2; ++f)
  {
    Assert( esuf[2*f] > -1 && esuf[2*f+1] > -1, "Interior element detected "
            "as -1" );

    std::size_t el = static_cast< std::size_t >(esuf[2*f]);
    std::size_t er = static_cast< std::size_t >(esuf[2*f+1]);

    // Extract the element coordinates
    std::array< std::array< tk::real, 3>, 4 > coordel_l {{ 
      {{ cx[ inpoel[4*el  ] ], cy[ inpoel[4*el  ] ], cz[ inpoel[4*el  ] ] }},
      {{ cx[ inpoel[4*el+1] ], cy[ inpoel[4*el+1] ], cz[ inpoel[4*el+1] ] }},
      {{ cx[ inpoel[4*el+2] ], cy[ inpoel[4*el+2] ], cz[ inpoel[4*el+2] ] }},
      {{ cx[ inpoel[4*el+3] ], cy[ inpoel[4*el+3] ], cz[ inpoel[4*el+3] ] }} }};

    std::array< std::array< tk::real, 3>, 4 > coordel_r {{ 
      {{ cx[ inpoel[4*er  ] ], cy[ inpoel[4*er  ] ], cz[ inpoel[4*er  ] ] }},
      {{ cx[ inpoel[4*er+1] ], cy[ inpoel[4*er+1] ], cz[ inpoel[4*er+1] ] }},
      {{ cx[ inpoel[4*er+2] ], cy[ inpoel[4*er+2] ], cz[ inpoel[4*er+2] ] }},
      {{ cx[ inpoel[4*er+3] ], cy[ inpoel[4*er+3] ], cz[ inpoel[4*er+3] ] }} }};

    // Compute the determinant of Jacobian matrix
    auto detT_l = 
      Jacobian( coordel_l[0], coordel_l[1], coordel_l[2], coordel_l[3] );
    auto detT_r =
      Jacobian( coordel_r[0], coordel_r[1], coordel_r[2], coordel_r[3] );

    // face normal
    std::array< real, 3 > fn{{geoFace(f,1,0), geoFace(f,2,0), geoFace(f,3,0)}};

    // face centroid
    std::array< real, 3 > gp{{geoFace(f,4,0), geoFace(f,5,0), geoFace(f,6,0)}};

    // In order to determine the high-order solution from the left and right
    // elements at the surface quadrature points, the basis functions from
    // the left and right elements are needed. For this, a transformation to
    // the reference coordinates is necessary, since the basis functions are
    // defined on the reference tetrahedron only.
    // The transformation relations are shown below:
    //  xi   = Jacobian( coordel[0], gp, coordel[2], coordel[3] ) / detT
    //  eta  = Jacobian( coordel[0], coordel[2], gp, coordel[3] ) / detT
    //  zeta = Jacobian( coordel[0], coordel[2], coordel[3], gp ) / detT

    std::array< tk::real, 3> ref_gp_l{
      Jacobian( coordel_l[0], gp, coordel_l[2], coordel_l[3] ) / detT_l,
      Jacobian( coordel_l[0], coordel_l[1], gp, coordel_l[3] ) / detT_l,
      Jacobian( coordel_l[0], coordel_l[1], coordel_l[2], gp ) / detT_l };
    std::array< tk::real, 3> ref_gp_r{
      Jacobian( coordel_r[0], gp, coordel_r[2], coordel_r[3] ) / detT_r,
      Jacobian( coordel_r[0], coordel_r[1], gp, coordel_r[3] ) / detT_r,
      Jacobian( coordel_r[0], coordel_r[1], coordel_r[2], gp ) / detT_r };

    //Compute the basis functions
    auto B_l = eval_basis( rdof, ref_gp_l[0], ref_gp_l[1], ref_gp_l[2] );
    auto B_r = eval_basis( rdof, ref_gp_r[0], ref_gp_r[1], ref_gp_r[2] );

    std::array< std::vector< real >, 2 > state;

    state[0] = evalPolynomialSol(system, offset, intsharp, ncomp, nprim, rdof,
      nmat, el, rdof, inpoel, coord, geoElem, ref_gp_l, B_l, U, P);
    state[1] = evalPolynomialSol(system, offset, intsharp, ncomp, nprim, rdof,
      nmat, er, rdof, inpoel, coord, geoElem, ref_gp_r, B_r, U, P);

    Assert( state[0].size() == ncomp+nprim, "Incorrect size for "
            "appended boundary state vector" );
    Assert( state[1].size() == ncomp+nprim, "Incorrect size for "
            "appended boundary state vector" );

    // evaluate prescribed velocity (if any)
    auto v = vel( system, ncomp, gp[0], gp[1], gp[2], t );

    // compute flux
    auto fl = flux( fn, state, v );

    // Add the surface integration term to the rhs
    for (ncomp_t c=0; c<ncomp; ++c)
    {
      R(el, c, offset) -= geoFace(f,0,0) * fl[c];
      R(er, c, offset) += geoFace(f,0,0) * fl[c];
    }

    // Prep for non-conservative terms in multimat
    if (fl.size() > ncomp)
    {
      // Gradients of partial pressures
      for (std::size_t k=0; k<nmat; ++k)
      {
        for (std::size_t idir=0; idir<3; ++idir)
        {
          riemannDeriv[3*k+idir][el] += geoFace(f,0,0) * fl[ncomp+k] * fn[idir];
          riemannDeriv[3*k+idir][er] -= geoFace(f,0,0) * fl[ncomp+k] * fn[idir];
        }
      }

      // Divergence of velocity
      riemannDeriv[3*nmat][el] += geoFace(f,0,0) * fl[ncomp+nmat];
      riemannDeriv[3*nmat][er] -= geoFace(f,0,0) * fl[ncomp+nmat];
    }
  }
}

} // tk::