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// Copyright (C) 2018-2021 Garth N. Wells, Jørgen S. Dokken, Igor A. Baratta
//
// This file is part of DOLFINx (https://www.fenicsproject.org)
//
// SPDX-License-Identifier: LGPL-3.0-or-later
#include "CoordinateElement.h"
#include <algorithm>
#include <basix/finite-element.h>
#include <cmath>
#include <dolfinx/common/math.h>
#include <dolfinx/mesh/cell_types.h>
using namespace dolfinx;
using namespace dolfinx::fem;
//-----------------------------------------------------------------------------
template <std::floating_point T>
CoordinateElement<T>::CoordinateElement(
std::shared_ptr<const basix::FiniteElement<T>> element)
: _element(std::move(element))
{
int degree = _element->degree();
mesh::CellType cell = this->cell_shape();
_is_affine = mesh::is_simplex(cell) and degree == 1;
}
//-----------------------------------------------------------------------------
template <std::floating_point T>
CoordinateElement<T>::CoordinateElement(mesh::CellType celltype, int degree,
basix::element::lagrange_variant type)
: CoordinateElement(std::make_shared<basix::FiniteElement<T>>(
basix::create_element<T>(basix::element::family::P,
mesh::cell_type_to_basix_type(celltype),
degree, type,
basix::element::dpc_variant::unset, false)))
{
// Do nothing
}
//-----------------------------------------------------------------------------
template <std::floating_point T>
mesh::CellType CoordinateElement<T>::cell_shape() const
{
return mesh::cell_type_from_basix_type(_element->cell_type());
}
//-----------------------------------------------------------------------------
template <std::floating_point T>
std::array<std::size_t, 4>
CoordinateElement<T>::tabulate_shape(std::size_t nd,
std::size_t num_points) const
{
return _element->tabulate_shape(nd, num_points);
}
//-----------------------------------------------------------------------------
template <std::floating_point T>
void CoordinateElement<T>::tabulate(int nd, std::span<const T> X,
std::array<std::size_t, 2> shape,
std::span<T> basis) const
{
assert(_element);
_element->tabulate(nd, X, shape, basis);
}
//--------------------------------------------------------------------------------
template <std::floating_point T>
void CoordinateElement<T>::permute_subentity_closure(std::span<std::int32_t> d,
std::uint32_t cell_info,
mesh::CellType entity_type,
int entity_index) const
{
assert(_element);
_element->permute_subentity_closure_inv(
d, cell_info, mesh::cell_type_to_basix_type(entity_type), entity_index);
}
//--------------------------------------------------------------------------------
template <std::floating_point T>
ElementDofLayout CoordinateElement<T>::create_dof_layout() const
{
assert(_element);
return ElementDofLayout(1, _element->entity_dofs(),
_element->entity_closure_dofs(), {}, {});
}
//-----------------------------------------------------------------------------
template <std::floating_point T>
void CoordinateElement<T>::pull_back_nonaffine(mdspan2_t<T> X,
mdspan2_t<const T> x,
mdspan2_t<const T> cell_geometry,
double tol, int maxit) const
{
// Number of points
std::size_t num_points = x.extent(0);
if (num_points == 0)
return;
const std::size_t tdim = mesh::cell_dim(this->cell_shape());
const std::size_t gdim = x.extent(1);
const std::size_t num_xnodes = cell_geometry.extent(0);
assert(cell_geometry.extent(1) == gdim);
assert(X.extent(0) == num_points);
assert(X.extent(1) == tdim);
std::vector<T> dphi_b(tdim * num_xnodes);
mdspan2_t<T> dphi(dphi_b.data(), tdim, num_xnodes);
std::vector<T> Xk_b(tdim);
mdspan2_t<T> Xk(Xk_b.data(), 1, tdim);
std::array<T, 3> xk{0, 0, 0};
std::vector<T> dX(tdim);
std::vector<T> J_b(gdim * tdim);
mdspan2_t<T> J(J_b.data(), gdim, tdim);
std::vector<T> K_b(tdim * gdim);
mdspan2_t<T> K(K_b.data(), tdim, gdim);
using mdspan4_t = md::mdspan<T, md::dextents<std::size_t, 4>>;
const std::array<std::size_t, 4> bsize = _element->tabulate_shape(1, 1);
std::vector<T> basis_b(
std::reduce(bsize.begin(), bsize.end(), 1, std::multiplies{}));
mdspan4_t basis(basis_b.data(), bsize);
std::vector<T> phi(basis.extent(2));
for (std::size_t p = 0; p < num_points; ++p)
{
std::ranges::fill(Xk_b, 0);
int k;
for (k = 0; k < maxit; ++k)
{
_element->tabulate(1, Xk_b, {1, tdim}, basis_b);
// x = cell_geometry * phi
std::ranges::fill(xk, 0);
for (std::size_t i = 0; i < cell_geometry.extent(0); ++i)
for (std::size_t j = 0; j < cell_geometry.extent(1); ++j)
xk[j] += cell_geometry(i, j) * basis(0, 0, i, 0);
// Compute Jacobian, its inverse and determinant
std::ranges::fill(J_b, 0);
for (std::size_t i = 0; i < tdim; ++i)
for (std::size_t j = 0; j < basis.extent(2); ++j)
dphi(i, j) = basis(i + 1, 0, j, 0);
compute_jacobian(dphi, cell_geometry, J);
compute_jacobian_inverse(J, K);
// Compute dX = K * (x_p - x_k)
std::ranges::fill(dX, 0);
for (std::size_t i = 0; i < K.extent(0); ++i)
for (std::size_t j = 0; j < K.extent(1); ++j)
dX[i] += K(i, j) * (x(p, j) - xk[j]);
// Compute Xk += dX
std::ranges::transform(dX, Xk_b, Xk_b.begin(),
[](auto a, auto b) { return a + b; });
// Compute norm(dX)
if (auto dX_squared
= std::transform_reduce(dX.cbegin(), dX.cend(), 0.0, std::plus{},
[](auto v) { return v * v; });
std::sqrt(dX_squared) < tol)
{
break;
}
}
std::copy(Xk_b.cbegin(), std::next(Xk_b.cbegin(), tdim),
X.data_handle() + p * tdim);
if (k == maxit)
{
throw std::runtime_error(
"Newton method failed to converge for non-affine geometry");
}
}
}
//-----------------------------------------------------------------------------
template <std::floating_point T>
void CoordinateElement<T>::permute(std::span<std::int32_t> dofs,
std::uint32_t cell_perm) const
{
assert(_element);
_element->permute(dofs, cell_perm);
}
//-----------------------------------------------------------------------------
template <std::floating_point T>
void CoordinateElement<T>::permute_inv(std::span<std::int32_t> dofs,
std::uint32_t cell_perm) const
{
assert(_element);
_element->permute_inv(dofs, cell_perm);
}
//-----------------------------------------------------------------------------
template <std::floating_point T>
bool CoordinateElement<T>::needs_dof_permutations() const
{
assert(_element);
assert(_element->dof_transformations_are_permutations());
return !_element->dof_transformations_are_identity();
}
//-----------------------------------------------------------------------------
template <std::floating_point T>
int CoordinateElement<T>::degree() const
{
assert(_element);
return _element->degree();
}
//-----------------------------------------------------------------------------
template <std::floating_point T>
int CoordinateElement<T>::dim() const
{
assert(_element);
return _element->dim();
}
//-----------------------------------------------------------------------------
template <std::floating_point T>
basix::element::lagrange_variant CoordinateElement<T>::variant() const
{
assert(_element);
return _element->lagrange_variant();
}
//-----------------------------------------------------------------------------
template <std::floating_point T>
std::uint64_t CoordinateElement<T>::hash() const
{
assert(_element);
return _element->hash();
}
//-----------------------------------------------------------------------------
template class fem::CoordinateElement<float>;
template class fem::CoordinateElement<double>;
//-----------------------------------------------------------------------------
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