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// Copyright (c) 2020-2025 Chris Richardson, Matthew Scroggs
// FEniCS Project
// SPDX-License-Identifier: MIT
#include "e-crouzeix-raviart.h"
#include "cell.h"
#include "element-families.h"
#include "maps.h"
#include "math.h"
#include "mdspan.hpp"
#include "quadrature.h"
#include "sobolev-spaces.h"
#include <array>
#include <vector>
using namespace basix;
//-----------------------------------------------------------------------------
template <std::floating_point T>
FiniteElement<T> basix::element::create_cr(cell::type celltype, int degree,
bool discontinuous)
{
if (degree != 1)
throw std::runtime_error("Degree must be 1 for Crouzeix-Raviart");
const std::size_t tdim = cell::topological_dimension(celltype);
if (tdim < 2)
{
throw std::runtime_error(
"topological dim must be 2 or 3 for Crouzeix-Raviart");
}
if (celltype != cell::type::triangle and celltype != cell::type::tetrahedron
and celltype != cell::type::quadrilateral
and celltype != cell::type::hexahedron)
{
throw std::runtime_error("Crouzeix-Raviart is only defined on triangles, "
"quadrilaterals, tetrahedra and hexahedra.");
}
const std::vector<std::vector<std::vector<int>>> topology
= cell::topology(celltype);
const std::vector<std::vector<int>>& facet_topology = topology[tdim - 1];
const std::size_t ndofs = facet_topology.size();
const auto [gdata, shape] = cell::geometry<T>(celltype);
impl::mdspan_t<const T, 2> geometry(gdata.data(), shape);
std::array<std::vector<impl::mdarray_t<T, 2>>, 4> x;
std::array<std::vector<impl::mdarray_t<T, 4>>, 4> M;
for (std::size_t i = 0; i < tdim - 1; ++i)
{
const std::size_t num_ent = topology[i].size();
x[i] = std::vector(num_ent, impl::mdarray_t<T, 2>(0, tdim));
M[i] = std::vector(num_ent, impl::mdarray_t<T, 4>(0, 1, 0, 1));
}
x[tdim - 1]
= std::vector(facet_topology.size(), impl::mdarray_t<T, 2>(1, tdim));
M[tdim - 1] = std::vector(
facet_topology.size(),
impl::mdarray_t<T, 4>(std::array<std::size_t, 4>{1, 1, 1, 1}, 1));
// Compute facet midpoints
for (std::size_t f = 0; f < facet_topology.size(); ++f)
{
const std::vector<int>& ft = facet_topology[f];
auto& _x = x[tdim - 1][f];
for (std::size_t i = 0; i < ft.size(); ++i)
{
for (std::size_t j = 0; j < geometry.extent(1); ++j)
_x(0, j) += geometry(ft[i], j) / ft.size();
}
}
x[tdim] = std::vector(topology[tdim].size(), impl::mdarray_t<T, 2>(0, tdim));
M[tdim]
= std::vector(topology[tdim].size(), impl::mdarray_t<T, 4>(0, 1, 0, 1));
std::array<std::vector<mdspan_t<const T, 2>>, 4> xview = impl::to_mdspan(x);
std::array<std::vector<mdspan_t<const T, 4>>, 4> Mview = impl::to_mdspan(M);
std::array<std::vector<std::vector<T>>, 4> xbuffer;
std::array<std::vector<std::vector<T>>, 4> Mbuffer;
if (discontinuous)
{
std::array<std::vector<std::array<std::size_t, 2>>, 4> xshape;
std::array<std::vector<std::array<std::size_t, 4>>, 4> Mshape;
std::tie(xbuffer, xshape, Mbuffer, Mshape)
= element::make_discontinuous(xview, Mview, tdim, 1);
xview = impl::to_mdspan(xbuffer, xshape);
Mview = impl::to_mdspan(Mbuffer, Mshape);
}
if (celltype == cell::type::triangle or celltype == cell::type::tetrahedron)
{
return FiniteElement<T>(
element::family::CR, celltype, polyset::type::standard, 1, {},
impl::mdspan_t<T, 2>(math::eye<T>(ndofs).data(), ndofs, ndofs), xview,
Mview, 0, maps::type::identity, sobolev::space::L2, discontinuous,
degree, degree, element::lagrange_variant::unset,
element::dpc_variant::unset);
}
else if (celltype == cell::type::quadrilateral)
{
const auto [_pts, wts] = quadrature::make_quadrature<T>(
quadrature::type::Default, cell::type::quadrilateral,
polyset::type::standard, 6);
impl::mdspan_t<const T, 2> pts(_pts.data(), wts.size(),
_pts.size() / wts.size());
const auto [_phi, shape] = polyset::tabulate(
cell::type::quadrilateral, polyset::type::standard, degree + 1, 0, pts);
impl::mdspan_t<const T, 3> phi(_phi.data(), shape);
impl::mdarray_t<T, 2> wcoeffs(ndofs, 9);
wcoeffs(0, 0) = 1;
wcoeffs(1, 1) = 1;
wcoeffs(2, 3) = 1;
for (int i = 2; i < 9; ++i)
{
if (i != 3)
{
wcoeffs(3, i) = 0.0;
for (std::size_t k = 0; k < wts.size(); ++k)
wcoeffs(3, i) += wts[k] * (pts(k, 0) + pts(k, 1))
* (pts(k, 0) - pts(k, 1)) * phi(0, i, k);
}
}
math::orthogonalise<T>(wcoeffs, 3);
return FiniteElement<T>(
element::family::CR, celltype, polyset::type::standard, 1, {}, wcoeffs,
xview, Mview, 0, maps::type::identity, sobolev::space::L2,
discontinuous, 0, degree + 1, element::lagrange_variant::unset,
element::dpc_variant::unset);
}
else if (celltype == cell::type::hexahedron)
{
const auto [_pts, wts] = quadrature::make_quadrature<T>(
quadrature::type::Default, cell::type::hexahedron,
polyset::type::standard, 6);
impl::mdspan_t<const T, 2> pts(_pts.data(), wts.size(),
_pts.size() / wts.size());
const auto [_phi, shape] = polyset::tabulate(
cell::type::hexahedron, polyset::type::standard, degree + 1, 0, pts);
impl::mdspan_t<const T, 3> phi(_phi.data(), shape);
impl::mdarray_t<T, 2> wcoeffs(ndofs, 27);
wcoeffs(0, 0) = 1;
wcoeffs(1, 1) = 1;
wcoeffs(2, 3) = 1;
wcoeffs(3, 9) = 1;
for (int i = 2; i < 27; ++i)
{
if (i != 3 and i != 9)
{
wcoeffs(4, i) = 0.0;
wcoeffs(5, i) = 0.0;
for (std::size_t k = 0; k < wts.size(); ++k)
{
wcoeffs(4, i) += wts[k] * (pts(k, 0) + pts(k, 1))
* (pts(k, 0) - pts(k, 1)) * phi(0, i, k);
wcoeffs(5, i) += wts[k] * (pts(k, 0) + pts(k, 2))
* (pts(k, 0) - pts(k, 2)) * phi(0, i, k);
}
}
}
math::orthogonalise<T>(wcoeffs, 4);
return FiniteElement<T>(
element::family::CR, celltype, polyset::type::standard, 1, {}, wcoeffs,
xview, Mview, 0, maps::type::identity, sobolev::space::L2,
discontinuous, 0, degree + 1, element::lagrange_variant::unset,
element::dpc_variant::unset);
}
else
{
throw std::runtime_error("Invalid cell type");
}
}
//-----------------------------------------------------------------------------
template FiniteElement<float> element::create_cr(cell::type, int, bool);
template FiniteElement<double> element::create_cr(cell::type, int, bool);
//-----------------------------------------------------------------------------
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