CellQuadrature.hpp

/*
  Copyright 2012 SINTEF ICT, Applied Mathematics.
 
  This file is part of the Open Porous Media project (OPM).
 
  OPM is free software: you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published by
  the Free Software Foundation, either version 3 of the License, or
  (at your option) any later version.
 
  OPM is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.
 
  You should have received a copy of the GNU General Public License
  along with OPM.  If not, see <http://www.gnu.org/licenses/>.
*/
 
#ifndef OPM_CELLQUADRATURE_HEADER_INCLUDED
#define OPM_CELLQUADRATURE_HEADER_INCLUDED
 
#include <opm/grid/UnstructuredGrid.h>
#include <opm/grid/utility/ErrorMacros.hpp>
#include <algorithm>
#include <cmath>
 
namespace Opm
{
 
 
    namespace {
        inline double determinantOf(const double* a0,
                                    const double* a1,
                                    const double* a2)
        {
            return
                a0[0] * (a1[1] * a2[2] - a2[1] * a1[2]) -
                a0[1] * (a1[0] * a2[2] - a2[0] * a1[2]) +
                a0[2] * (a1[0] * a2[1] - a2[0] * a1[1]);
        }
 
        inline double tetVolume(const double* p0,
                                const double* p1,
                                const double* p2,
                                const double* p3)
        {
            double a[3] = { p1[0] - p0[0], p1[1] - p0[1], p1[2] - p0[2] };
            double b[3] = { p2[0] - p0[0], p2[1] - p0[1], p2[2] - p0[2] };
            double c[3] = { p3[0] - p0[0], p3[1] - p0[1], p3[2] - p0[2] };
            return std::fabs(determinantOf(a, b, c) / 6.0);
        }
 
        inline double triangleArea2d(const double* p0,
                                     const double* p1,
                                     const double* p2)
        {
            double a[2] = { p1[0] - p0[0], p1[1] - p0[1] };
            double b[2] = { p2[0] - p0[0], p2[1] - p0[1] };
            double a_cross_b = a[0]*b[1] - a[1]*b[0];
            return 0.5*std::fabs(a_cross_b);
        }
    } // anonymous namespace
 
 
    class CellQuadrature
    {
    public:
        CellQuadrature(const UnstructuredGrid& grid,
                       const int cell,
                       const int degree)
            : grid_(grid), cell_(cell), degree_(degree)
        {
            if (grid.dimensions > 3) {
                OPM_THROW(std::runtime_error, "CellQuadrature only implemented for up to 3 dimensions.");
            }
            if (degree > 2) {
                OPM_THROW(std::runtime_error, "CellQuadrature exact for polynomial degrees > 1 not implemented.");
            }
        }
 
        int numQuadPts() const
        {
            if (degree_ < 2 || grid_.dimensions == 1) {
                return 1;
            }
            // Degree 2 case.
            if (grid_.dimensions == 2) {
                return 3*(grid_.cell_facepos[cell_ + 1] - grid_.cell_facepos[cell_]);
            }
            assert(grid_.dimensions == 3);
            int sumnodes = 0;
            for (int hf = grid_.cell_facepos[cell_]; hf < grid_.cell_facepos[cell_ + 1]; ++hf) {
                const int face = grid_.cell_faces[hf];
                sumnodes += grid_.face_nodepos[face + 1] - grid_.face_nodepos[face];
            }
            return 4*sumnodes;
        }
 
        void quadPtCoord(const int index, double* coord) const
        {
            const int dim = grid_.dimensions;
            const double* cc = grid_.cell_centroids + dim*cell_;
            if (degree_ < 2) {
                std::copy(cc, cc + dim, coord);
                return;
            }
            // Degree 2 case.
            if (dim == 2) {
                if (index % 3 == 0) {
                    // Boundary midpoint. This is the face centroid.
                    const int hface = grid_.cell_facepos[cell_] + index/3;
                    const int face = grid_.cell_faces[hface];
                    const double* fc = grid_.face_centroids + dim*face;
                    std::copy(fc, fc + dim, coord);
                } else {
                    // Interiour midpoint. This is the average of the
                    // cell centroid and a face node (they should
                    // always have two nodes in 2d).
                    const int hface = grid_.cell_facepos[cell_] + index/3;
                    const int face = grid_.cell_faces[hface];
                    const int nodeoff = (index % 3) - 1; // == 0 or 1
                    const int node = grid_.face_nodes[grid_.face_nodepos[face] + nodeoff];
                    const double* nc = grid_.node_coordinates + dim*node;
                    for (int dd = 0; dd < dim; ++dd) {
                        coord[dd] = 0.5*(nc[dd] + cc[dd]);
                    }
                }
                return;
            }
            assert(dim == 3);
            int tetindex = index / 4;
            const int subindex = index % 4;
            const double* nc = grid_.node_coordinates;
            for (int hf = grid_.cell_facepos[cell_]; hf < grid_.cell_facepos[cell_ + 1]; ++hf) {
                const int face = grid_.cell_faces[hf];
                const int nfn = grid_.face_nodepos[face + 1] - grid_.face_nodepos[face];
                if (nfn <= tetindex) {
                    // Our tet is not associated with this face.
                    tetindex -= nfn;
                    continue;
                }
                const double* fc = grid_.face_centroids + dim*face;
                const int* fnodes = grid_.face_nodes + grid_.face_nodepos[face];
                const int node0 = fnodes[tetindex];
                const int node1 = fnodes[(tetindex + 1) % nfn];
                const double* n0c = nc + dim*node0;
                const double* n1c = nc + dim*node1;
                const double a = 0.138196601125010515179541316563436;
                // Barycentric coordinates of our point in the tet.
                double baryc[4] = { a, a, a, a };
                baryc[subindex] = 1.0 - 3.0*a;
                for (int dd = 0; dd < dim; ++dd) {
                    coord[dd] = baryc[0]*cc[dd] + baryc[1]*fc[dd] + baryc[2]*n0c[dd] + baryc[3]*n1c[dd];
                }
                return;
            }
            OPM_THROW(std::runtime_error, "Should never reach this point.");
        }
 
        double quadPtWeight(const int index) const
        {
            if (degree_ < 2) {
                return grid_.cell_volumes[cell_];
            }
            // Degree 2 case.
            const int dim = grid_.dimensions;
            const double* cc = grid_.cell_centroids + dim*cell_;
            if (dim == 2) {
                const int hface = grid_.cell_facepos[cell_] + index/3;
                const int face = grid_.cell_faces[hface];
                const int* nptr = grid_.face_nodes + grid_.face_nodepos[face];
                const double* nc0 = grid_.node_coordinates + dim*nptr[0];
                const double* nc1 = grid_.node_coordinates + dim*nptr[1];
                return triangleArea2d(nc0, nc1, cc)/3.0;
            }
            assert(dim == 3);
            int tetindex = index / 4;
            const double* nc = grid_.node_coordinates;
            for (int hf = grid_.cell_facepos[cell_]; hf < grid_.cell_facepos[cell_ + 1]; ++hf) {
                const int face = grid_.cell_faces[hf];
                const int nfn = grid_.face_nodepos[face + 1] - grid_.face_nodepos[face];
                if (nfn <= tetindex) {
                    // Our tet is not associated with this face.
                    tetindex -= nfn;
                    continue;
                }
                const double* fc = grid_.face_centroids + dim*face;
                const int* fnodes = grid_.face_nodes + grid_.face_nodepos[face];
                const int node0 = fnodes[tetindex];
                const int node1 = fnodes[(tetindex + 1) % nfn];
                const double* n0c = nc + dim*node0;
                const double* n1c = nc + dim*node1;
                return 0.25*tetVolume(cc, fc, n0c, n1c);
            }
            OPM_THROW(std::runtime_error, "Should never reach this point.");
        }
 
    private:
        const UnstructuredGrid& grid_;
        const int cell_;
        const int degree_;
    };
 
} // namespace Opm
 
#endif // OPM_CELLQUADRATURE_HEADER_INCLUDED