ElementAssemblyValues.cpp

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#include "ElementAssemblyValues.hpp"
 
namespace polyfem
{
    using namespace basis;
    using namespace quadrature;
 
    namespace assembler
    {
        void ElementAssemblyValues::finalize_global_element(const Eigen::MatrixXd &v)
        {
            val = v;
 
            has_parameterization = false;
            det.resize(v.rows(), 1);
 
            jac_it.resize(v.rows());
            for (long i = 0; i < v.rows(); ++i)
                jac_it[i] = Eigen::MatrixXd::Identity(v.cols(), v.cols());
 
            det.setConstant(1); // volume (det of the geometric mapping)
            for (std::size_t j = 0; j < basis_values.size(); ++j)
                basis_values[j].grad_t_m = basis_values[j].grad; // / scaling
        }
 
        bool ElementAssemblyValues::is_geom_mapping_positive(const Eigen::MatrixXd &dx, const Eigen::MatrixXd &dy, const Eigen::MatrixXd &dz) const
        {
            Eigen::Matrix3d tmp;
            for (long i = 0; i < dx.rows(); ++i)
            {
                tmp.row(0) = dx.row(i);
                tmp.row(1) = dy.row(i);
                tmp.row(2) = dz.row(i);
 
                if (tmp.determinant() <= 0)
                {
                    // std::cout<<tmp.determinant()<<std::endl;
                    return false;
                }
            }
 
            return true;
        }
 
        bool ElementAssemblyValues::is_geom_mapping_positive(const Eigen::MatrixXd &dx, const Eigen::MatrixXd &dy) const
        {
            Eigen::Matrix2d tmp;
            for (long i = 0; i < dx.rows(); ++i)
            {
                tmp.row(0) = dx.row(i);
                tmp.row(1) = dy.row(i);
 
                if (tmp.determinant() <= 0)
                {
                    // std::cout<<tmp.determinant()<<std::endl;
                    return false;
                }
            }
 
            return true;
        }
 
        void ElementAssemblyValues::finalize3d(const ElementBases &gbasis, const std::vector<AssemblyValues> &gbasis_values)
        {
            // if(det.size() != val.rows())
            //  logger().trace("Reallocating memory");
            det.resize(val.rows(), 1);
 
            for (std::size_t j = 0; j < basis_values.size(); ++j)
                basis_values[j].finalize();
 
            Eigen::Matrix3d tmp;
            jac_it.resize(val.rows());
 
            // loop over points
            for (long k = 0; k < val.rows(); ++k)
            {
                tmp.setZero();
                for (int j = 0; j < gbasis_values.size(); ++j)
                {
                    const Basis &b = gbasis.bases[j];
                    assert(gbasis.has_parameterization);
                    assert(gbasis_values[j].grad.rows() == val.rows());
                    assert(gbasis_values[j].grad.cols() == 3);
 
                    for (std::size_t ii = 0; ii < b.global().size(); ++ii)
                    {
                        tmp.row(0) += gbasis_values[j].grad(k, 0) * b.global()[ii].node * b.global()[ii].val;
                        tmp.row(1) += gbasis_values[j].grad(k, 1) * b.global()[ii].node * b.global()[ii].val;
                        tmp.row(2) += gbasis_values[j].grad(k, 2) * b.global()[ii].node * b.global()[ii].val;
                    }
                }
 
                det(k) = tmp.determinant();
                // assert(det(k)>0);
                // std::cout<<det(k)<<std::endl;
 
                jac_it[k] = tmp.inverse().transpose();
                for (std::size_t j = 0; j < basis_values.size(); ++j)
                    basis_values[j].grad_t_m.row(k) = basis_values[j].grad.row(k) * jac_it[k];
            }
        }
 
        void ElementAssemblyValues::finalize2d(const ElementBases &gbasis, const std::vector<AssemblyValues> &gbasis_values)
        {
            det.resize(val.rows(), 1);
 
            for (std::size_t j = 0; j < basis_values.size(); ++j)
                basis_values[j].finalize();
 
            Eigen::Matrix2d tmp;
            jac_it.resize(val.rows());
 
            // loop over points
            for (long k = 0; k < val.rows(); ++k)
            {
                tmp.setZero();
                for (int j = 0; j < gbasis_values.size(); ++j)
                {
                    const Basis &b = gbasis.bases[j];
                    assert(gbasis.has_parameterization);
                    assert(gbasis_values[j].grad.rows() == val.rows());
                    assert(gbasis_values[j].grad.cols() == 2);
 
                    for (std::size_t ii = 0; ii < b.global().size(); ++ii)
                    {
                        // add given geometric basis function + node's contribution to the Jacobian
                        tmp.row(0) += gbasis_values[j].grad(k, 0) * b.global()[ii].node * b.global()[ii].val;
                        tmp.row(1) += gbasis_values[j].grad(k, 1) * b.global()[ii].node * b.global()[ii].val;
                    }
                }
 
                // save Jacobian's determinant
                det(k) = tmp.determinant();
                // assert(det(k)>0);
                // std::cout<<det(k)<<std::endl;
 
                // save Jacobian's inverse transpose
                jac_it[k] = tmp.inverse().transpose();
                for (std::size_t j = 0; j < basis_values.size(); ++j)
                    basis_values[j].grad_t_m.row(k) = basis_values[j].grad.row(k) * jac_it[k];
            }
        }
 
        void ElementAssemblyValues::compute(const int el_index, const bool is_volume, const ElementBases &basis, const ElementBases &gbasis)
        {
            basis.compute_quadrature(quadrature);
            compute(el_index, is_volume, quadrature.points, basis, gbasis);
        }
 
        void ElementAssemblyValues::compute(const int el_index, const bool is_volume, const Eigen::MatrixXd &pts, const ElementBases &basis, const ElementBases &gbasis)
        {
            element_id = el_index;
            // const bool poly = !gbasis.has_parameterization;
 
            basis_values.resize(basis.bases.size());
 
            if (&basis != &gbasis)
                g_basis_values_cache_.resize(gbasis.bases.size());
 
            const int n_local_bases = int(basis.bases.size());
            const int n_local_g_bases = int(gbasis.bases.size());
 
            // evaluate on reference element
            basis.evaluate_bases(pts, basis_values);
            basis.evaluate_grads(pts, basis_values);
 
            if (&basis != &gbasis)
            {
                gbasis.evaluate_bases(pts, g_basis_values_cache_);
                gbasis.evaluate_grads(pts, g_basis_values_cache_);
            }
 
            for (int j = 0; j < n_local_bases; ++j)
            {
                AssemblyValues &ass_val = basis_values[j];
                ass_val.global = basis.bases[j].global();
                assert(ass_val.val.cols() == 1);
                assert(ass_val.grad.cols() == pts.cols());
            }
 
            if (!gbasis.has_parameterization)
            {
                // v = G(pts)
                finalize_global_element(pts);
                return;
            }
            
            // compute geometric mapping as linear combination of geometric basis functions
            const auto &gbasis_values = (&basis == &gbasis) ? basis_values : g_basis_values_cache_;
            assert(gbasis_values.size() == n_local_g_bases);
            val.resize(pts.rows(), pts.cols());
            val.setZero();
 
            // loop over geometric basis functions
            for (int j = 0; j < n_local_g_bases; ++j)
            {
                const Basis &b = gbasis.bases[j];
                const auto &tmp = gbasis_values[j].val;
 
                assert(gbasis.has_parameterization);
                assert(tmp.size() == val.rows());
 
                // loop over relevant global nodes
                for (std::size_t ii = 0; ii < b.global().size(); ++ii)
                {
                    for (long k = 0; k < val.rows(); ++k)
                    {
                        // add contribution from geometric basis function + node
                        val.row(k) += tmp(k) * b.global()[ii].node * b.global()[ii].val;
                    }
                }
            }
 
            // compute Jacobian
            if (is_volume)
                finalize3d(gbasis, gbasis_values);
            else
                finalize2d(gbasis, gbasis_values);
        }
 
        bool ElementAssemblyValues::is_geom_mapping_positive(const bool is_volume, const ElementBases &gbasis) const
        {
            if (!gbasis.has_parameterization)
                return true;
 
            const int n_local_bases = int(gbasis.bases.size());
 
            if (n_local_bases <= 0)
                return true;
 
            Quadrature quad;
            gbasis.compute_quadrature(quad);
 
            std::vector<AssemblyValues> tmp;
 
            Eigen::MatrixXd dxmv = Eigen::MatrixXd::Zero(quad.points.rows(), quad.points.cols());
            Eigen::MatrixXd dymv = Eigen::MatrixXd::Zero(quad.points.rows(), quad.points.cols());
            Eigen::MatrixXd dzmv;
            if (is_volume)
                dzmv = Eigen::MatrixXd::Zero(quad.points.rows(), quad.points.cols());
 
            gbasis.evaluate_grads(quad.points, tmp);
 
            for (int j = 0; j < n_local_bases; ++j)
            {
                const Basis &b = gbasis.bases[j];
 
                // b.grad(quad.points, grad);
                // assert(grad.cols() == quad.points.cols());
 
                for (std::size_t ii = 0; ii < b.global().size(); ++ii)
                {
                    for (long k = 0; k < quad.points.rows(); ++k)
                    {
                        dxmv.row(k) += tmp[j].grad(k, 0) * b.global()[ii].node * b.global()[ii].val;
                        dymv.row(k) += tmp[j].grad(k, 1) * b.global()[ii].node * b.global()[ii].val;
                        if (is_volume)
                            dzmv.row(k) += tmp[j].grad(k, 2) * b.global()[ii].node * b.global()[ii].val;
                    }
                }
            }
 
            return is_volume ? is_geom_mapping_positive(dxmv, dymv, dzmv) : is_geom_mapping_positive(dxmv, dymv);
        }
    } // namespace assembler
} // namespace polyfem