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// Copyright (c) 2020 Chris Richardson & Matthew Scroggs
// FEniCS Project
// SPDX-License-Identifier: MIT
#include "lagrange.h"
#include "dof-permutations.h"
#include "lattice.h"
#include "polyset.h"
#include <Eigen/Dense>
#include <iostream>
#include <numeric>
using namespace basix;
//----------------------------------------------------------------------------
FiniteElement basix::create_lagrange(cell::type celltype, int degree,
const std::string& name)
{
if (celltype == cell::type::point)
throw std::runtime_error("Invalid celltype");
const int ndofs = polyset::dim(celltype, degree);
const std::vector<std::vector<std::vector<int>>> topology
= cell::topology(celltype);
std::vector<std::vector<int>> entity_dofs(topology.size());
// Create points at nodes, ordered by topology (vertices first)
Eigen::ArrayXXd pt(ndofs, topology.size() - 1);
if (degree == 0)
{
pt = lattice::create(celltype, 0, lattice::type::equispaced, true);
for (std::size_t i = 0; i < entity_dofs.size(); ++i)
entity_dofs[i].resize(topology[i].size(), 0);
entity_dofs[topology.size() - 1][0] = 1;
}
else
{
int c = 0;
for (std::size_t dim = 0; dim < topology.size(); ++dim)
{
for (std::size_t i = 0; i < topology[dim].size(); ++i)
{
const Eigen::ArrayXXd entity_geom
= cell::sub_entity_geometry(celltype, dim, i);
if (dim == 0)
{
pt.row(c++) = entity_geom.row(0);
entity_dofs[0].push_back(1);
}
else if (dim == topology.size() - 1)
{
const Eigen::ArrayXXd lattice = lattice::create(
celltype, degree, lattice::type::equispaced, false);
for (int j = 0; j < lattice.rows(); ++j)
pt.row(c++) = lattice.row(j);
entity_dofs[dim].push_back(lattice.rows());
}
else
{
cell::type ct = cell::sub_entity_type(celltype, dim, i);
const Eigen::ArrayXXd lattice
= lattice::create(ct, degree, lattice::type::equispaced, false);
entity_dofs[dim].push_back(lattice.rows());
for (int j = 0; j < lattice.rows(); ++j)
{
pt.row(c) = entity_geom.row(0);
for (int k = 0; k < lattice.cols(); ++k)
{
pt.row(c) += (entity_geom.row(k + 1) - entity_geom.row(0))
* lattice(j, k);
}
++c;
}
}
}
}
}
int perm_count = 0;
for (std::size_t i = 1; i < topology.size() - 1; ++i)
perm_count += topology[i].size() * i;
std::vector<Eigen::MatrixXd> base_permutations(
perm_count, Eigen::MatrixXd::Identity(ndofs, ndofs));
if (celltype == cell::type::interval)
{
assert(perm_count == 0);
}
else if (celltype == cell::type::triangle)
{
Eigen::ArrayXi edge_ref = dofperms::interval_reflection(degree - 1);
for (int edge = 0; edge < 3; ++edge)
{
const int start = 3 + edge_ref.size() * edge;
for (int i = 0; i < edge_ref.size(); ++i)
{
base_permutations[edge](start + i, start + i) = 0;
base_permutations[edge](start + i, start + edge_ref[i]) = 1;
}
}
}
else if (celltype == cell::type::quadrilateral)
{
Eigen::ArrayXi edge_ref = dofperms::interval_reflection(degree - 1);
for (int edge = 0; edge < 4; ++edge)
{
const int start = 4 + edge_ref.size() * edge;
for (int i = 0; i < edge_ref.size(); ++i)
{
base_permutations[edge](start + i, start + i) = 0;
base_permutations[edge](start + i, start + edge_ref[i]) = 1;
}
}
}
else if (celltype == cell::type::tetrahedron)
{
Eigen::ArrayXi edge_ref = dofperms::interval_reflection(degree - 1);
for (int edge = 0; edge < 6; ++edge)
{
const int start = 4 + edge_ref.size() * edge;
for (int i = 0; i < edge_ref.size(); ++i)
{
base_permutations[edge](start + i, start + i) = 0;
base_permutations[edge](start + i, start + edge_ref[i]) = 1;
}
}
Eigen::ArrayXi face_ref = dofperms::triangle_reflection(degree - 2);
Eigen::ArrayXi face_rot = dofperms::triangle_rotation(degree - 2);
for (int face = 0; face < 4; ++face)
{
const int start = 4 + edge_ref.size() * 6 + face_ref.size() * face;
for (int i = 0; i < face_rot.size(); ++i)
{
base_permutations[6 + 2 * face](start + i, start + i) = 0;
base_permutations[6 + 2 * face](start + i, start + face_rot[i]) = 1;
base_permutations[6 + 2 * face + 1](start + i, start + i) = 0;
base_permutations[6 + 2 * face + 1](start + i, start + face_ref[i]) = 1;
}
}
}
else if (celltype == cell::type::hexahedron)
{
Eigen::ArrayXi edge_ref = dofperms::interval_reflection(degree - 1);
for (int edge = 0; edge < 12; ++edge)
{
const int start = 8 + edge_ref.size() * edge;
for (int i = 0; i < edge_ref.size(); ++i)
{
base_permutations[edge](start + i, start + i) = 0;
base_permutations[edge](start + i, start + edge_ref[i]) = 1;
}
}
Eigen::ArrayXi face_ref = dofperms::quadrilateral_reflection(degree - 1);
Eigen::ArrayXi face_rot = dofperms::quadrilateral_rotation(degree - 1);
for (int face = 0; face < 6; ++face)
{
const int start = 8 + edge_ref.size() * 12 + face_ref.size() * face;
for (int i = 0; i < face_rot.size(); ++i)
{
base_permutations[12 + 2 * face](start + i, start + i) = 0;
base_permutations[12 + 2 * face](start + i, start + face_rot[i]) = 1;
base_permutations[12 + 2 * face + 1](start + i, start + i) = 0;
base_permutations[12 + 2 * face + 1](start + i, start + face_ref[i])
= 1;
}
}
}
else
{
std::cout << "Base permutations not implemented for this cell type."
<< std::endl;
}
// Point evaluation of basis
Eigen::MatrixXd dualmat = polyset::tabulate(celltype, degree, 0, pt)[0];
Eigen::MatrixXd coeffs = compute_expansion_coefficients(
Eigen::MatrixXd::Identity(ndofs, ndofs), dualmat);
return FiniteElement(name, celltype, degree, {1}, coeffs, entity_dofs,
base_permutations, pt,
Eigen::MatrixXd::Identity(ndofs, ndofs));
}
//-----------------------------------------------------------------------------
FiniteElement basix::create_dlagrange(cell::type celltype, int degree,
const std::string& name)
{
// Only tabulate for scalar. Vector spaces can easily be built from
// the scalar space.
const int ndofs = polyset::dim(celltype, degree);
std::vector<std::vector<std::vector<int>>> topology
= cell::topology(celltype);
std::vector<std::vector<int>> entity_dofs(topology.size());
for (std::size_t i = 0; i < topology.size(); ++i)
entity_dofs[i].resize(topology[i].size(), 0);
entity_dofs[topology.size() - 1][0] = ndofs;
Eigen::ArrayXXd geometry = cell::geometry(celltype);
const Eigen::ArrayXXd pt
= lattice::create(celltype, degree, lattice::type::equispaced, true);
// Point evaluation of basis
Eigen::MatrixXd dualmat = polyset::tabulate(celltype, degree, 0, pt)[0];
Eigen::MatrixXd coeffs = compute_expansion_coefficients(
Eigen::MatrixXd::Identity(ndofs, ndofs), dualmat);
int perm_count = 0;
for (std::size_t i = 1; i < topology.size() - 1; ++i)
perm_count += topology[i].size() * i;
std::vector<Eigen::MatrixXd> base_permutations(
perm_count, Eigen::MatrixXd::Identity(ndofs, ndofs));
return FiniteElement(name, celltype, degree, {1}, coeffs, entity_dofs,
base_permutations, pt,
Eigen::MatrixXd::Identity(ndofs, ndofs));
}
//-----------------------------------------------------------------------------
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