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// Copyright (C) 2019-2025 Garth N. Wells and Paul T. Kühner
//
// This file is part of DOLFINx (https://www.fenicsproject.org)
//
// SPDX-License-Identifier: LGPL-3.0-or-later
#pragma once
#include "Constant.h"
#include "Form.h"
#include "FunctionSpace.h"
#include "utils.h"
#include <algorithm>
#include <basix/mdspan.hpp>
#include <dolfinx/common/IndexMap.h>
#include <dolfinx/mesh/Geometry.h>
#include <dolfinx/mesh/Mesh.h>
#include <dolfinx/mesh/Topology.h>
#include <memory>
#include <vector>
namespace dolfinx::fem::impl
{
/// Assemble functional over cells
template <dolfinx::scalar T>
T assemble_cells(mdspan2_t x_dofmap,
md::mdspan<const scalar_value_t<T>,
md::extents<std::size_t, md::dynamic_extent, 3>>
x,
std::span<const std::int32_t> cells, FEkernel<T> auto fn,
std::span<const T> constants,
md::mdspan<const T, md::dextents<std::size_t, 2>> coeffs,
std::span<scalar_value_t<T>> cdofs_b)
{
T value(0);
if (cells.empty())
return value;
assert(cdofs_b.size() >= 3 * x_dofmap.extent(1));
// Iterate over all cells
for (std::size_t index = 0; index < cells.size(); ++index)
{
std::int32_t c = cells[index];
// Get cell coordinates/geometry
auto x_dofs = md::submdspan(x_dofmap, c, md::full_extent);
for (std::size_t i = 0; i < x_dofs.size(); ++i)
std::copy_n(&x(x_dofs[i], 0), 3, std::next(cdofs_b.begin(), 3 * i));
fn(&value, &coeffs(index, 0), constants.data(), cdofs_b.data(), nullptr,
nullptr, nullptr);
}
return value;
}
/// @brief Execute kernel over entities of codimension ≥ 1 and accumulate result
/// in a scalar.
///
/// Each entity is represented by (i) a cell that the entity is attached to
/// and (ii) the local index of the entity with respect to the cell. The
/// kernel is executed for each entity. The kernel can access data
/// (e.g., coefficients, basis functions) associated with the attached cell.
/// However, entities may be attached to more than one cell. This function
/// therefore computes 'one-sided' integrals, i.e. evaluates integrals as seen
/// from cell used to define the entity.
template <dolfinx::scalar T>
T assemble_entities(
mdspan2_t x_dofmap,
md::mdspan<const scalar_value_t<T>,
md::extents<std::size_t, md::dynamic_extent, 3>>
x,
md::mdspan<const std::int32_t,
md::extents<std::size_t, md::dynamic_extent, 2>>
entities,
FEkernel<T> auto fn, std::span<const T> constants,
md::mdspan<const T, md::dextents<std::size_t, 2>> coeffs,
md::mdspan<const std::uint8_t, md::dextents<std::size_t, 2>> perms,
std::span<scalar_value_t<T>> cdofs_b)
{
T value(0);
if (entities.empty())
return value;
assert(cdofs_b.size() >= 3 * x_dofmap.extent(1));
// Iterate over all facets
for (std::size_t f = 0; f < entities.extent(0); ++f)
{
std::int32_t cell = entities(f, 0);
std::int32_t local_entity = entities(f, 1);
// Get cell coordinates/geometry
auto x_dofs = md::submdspan(x_dofmap, cell, md::full_extent);
for (std::size_t i = 0; i < x_dofs.size(); ++i)
std::copy_n(&x(x_dofs[i], 0), 3, std::next(cdofs_b.begin(), 3 * i));
// Permutations
std::uint8_t perm = perms.empty() ? 0 : perms(cell, local_entity);
fn(&value, &coeffs(f, 0), constants.data(), cdofs_b.data(), &local_entity,
&perm, nullptr);
}
return value;
}
/// Assemble functional over interior facets
template <dolfinx::scalar T>
T assemble_interior_facets(
mdspan2_t x_dofmap,
md::mdspan<const scalar_value_t<T>,
md::extents<std::size_t, md::dynamic_extent, 3>>
x,
md::mdspan<const std::int32_t,
md::extents<std::size_t, md::dynamic_extent, 2, 2>>
facets,
FEkernel<T> auto fn, std::span<const T> constants,
md::mdspan<const T, md::extents<std::size_t, md::dynamic_extent, 2,
md::dynamic_extent>>
coeffs,
md::mdspan<const std::uint8_t, md::dextents<std::size_t, 2>> perms,
std::span<scalar_value_t<T>> cdofs_b)
{
T value(0);
if (facets.empty())
return value;
// Create data structures used in assembly
assert(cdofs_b.size() >= 2 * 3 * x_dofmap.extent(1));
auto cdofs0 = cdofs_b.first(3 * x_dofmap.extent(1));
auto cdofs1 = cdofs_b.last(3 * x_dofmap.extent(1));
// Iterate over all facets
for (std::size_t f = 0; f < facets.extent(0); ++f)
{
std::array cells = {facets(f, 0, 0), facets(f, 1, 0)};
std::array local_facet = {facets(f, 0, 1), facets(f, 1, 1)};
// Get cell geometry
auto x_dofs0 = md::submdspan(x_dofmap, cells[0], md::full_extent);
for (std::size_t i = 0; i < x_dofs0.size(); ++i)
std::copy_n(&x(x_dofs0[i], 0), 3, std::next(cdofs0.begin(), 3 * i));
auto x_dofs1 = md::submdspan(x_dofmap, cells[1], md::full_extent);
for (std::size_t i = 0; i < x_dofs1.size(); ++i)
std::copy_n(&x(x_dofs1[i], 0), 3, std::next(cdofs1.begin(), 3 * i));
std::array perm = perms.empty()
? std::array<std::uint8_t, 2>{0, 0}
: std::array{perms(cells[0], local_facet[0]),
perms(cells[1], local_facet[1])};
fn(&value, &coeffs(f, 0, 0), constants.data(), cdofs_b.data(),
local_facet.data(), perm.data(), nullptr);
}
return value;
}
/// Assemble functional into an scalar with provided mesh geometry.
template <dolfinx::scalar T, std::floating_point U>
T assemble_scalar(
const fem::Form<T, U>& M, mdspan2_t x_dofmap,
md::mdspan<const scalar_value_t<T>,
md::extents<std::size_t, md::dynamic_extent, 3>>
x,
std::span<const T> constants,
const std::map<std::pair<IntegralType, int>,
std::pair<std::span<const T>, int>>& coefficients)
{
std::shared_ptr<const mesh::Mesh<U>> mesh = M.mesh();
assert(mesh);
std::vector<scalar_value_t<T>> cdofs_b(2 * 3 * x_dofmap.extent(1));
T value = 0;
for (int i = 0; i < M.num_integrals(IntegralType::cell, 0); ++i)
{
auto fn = M.kernel(IntegralType::cell, i, 0);
assert(fn);
auto& [coeffs, cstride] = coefficients.at({IntegralType::cell, i});
std::span<const std::int32_t> cells = M.domain(IntegralType::cell, i, 0);
assert(cells.size() * cstride == coeffs.size());
value += impl::assemble_cells(
x_dofmap, x, cells, fn, constants,
md::mdspan(coeffs.data(), cells.size(), cstride), cdofs_b);
}
mesh::CellType cell_type = mesh->topology()->cell_type();
int num_facets_per_cell
= mesh::cell_num_entities(cell_type, mesh->topology()->dim() - 1);
md::mdspan<const std::uint8_t, md::dextents<std::size_t, 2>> facet_perms;
if (M.needs_facet_permutations())
{
mesh->topology_mutable()->create_entity_permutations();
const std::vector<std::uint8_t>& p
= mesh->topology()->get_facet_permutations();
facet_perms = md::mdspan(p.data(), p.size() / num_facets_per_cell,
num_facets_per_cell);
}
for (int i = 0; i < M.num_integrals(IntegralType::interior_facet, 0); ++i)
{
auto fn = M.kernel(IntegralType::interior_facet, i, 0);
assert(fn);
auto& [coeffs, cstride]
= coefficients.at({IntegralType::interior_facet, i});
std::span facets = M.domain(IntegralType::interior_facet, i, 0);
constexpr std::size_t num_adjacent_cells = 2;
// Two values per each adj. cell (cell index and local facet index).
constexpr std::size_t shape1 = 2 * num_adjacent_cells;
assert((facets.size() / shape1) * 2 * cstride == coeffs.size());
value += impl::assemble_interior_facets(
x_dofmap, x,
md::mdspan<const std::int32_t,
md::extents<std::size_t, md::dynamic_extent, 2, 2>>(
facets.data(), facets.size() / shape1, 2, 2),
fn, constants,
md::mdspan<const T, md::extents<std::size_t, md::dynamic_extent, 2,
md::dynamic_extent>>(
coeffs.data(), facets.size() / shape1, 2, cstride),
facet_perms, cdofs_b);
}
for (auto itg_type : {fem::IntegralType::exterior_facet,
fem::IntegralType::vertex, fem::IntegralType::ridge})
{
md::mdspan<const std::uint8_t, md::dextents<std::size_t, 2>> perms
= (itg_type == fem::IntegralType::exterior_facet)
? facet_perms
: md::mdspan<const std::uint8_t, md::dextents<std::size_t, 2>>{};
for (int i = 0; i < M.num_integrals(itg_type, 0); ++i)
{
auto fn = M.kernel(itg_type, i, 0);
assert(fn);
auto& [coeffs, cstride] = coefficients.at({itg_type, i});
std::span entities = M.domain(itg_type, i, 0);
// Two values per each adj. cell (cell index and local entity index).
assert((entities.size() / 2) * cstride == coeffs.size());
value += impl::assemble_entities(
x_dofmap, x,
md::mdspan<const std::int32_t,
md::extents<std::size_t, md::dynamic_extent, 2>>(
entities.data(), entities.size() / 2, 2),
fn, constants,
md::mdspan(coeffs.data(), entities.size() / 2, cstride), perms,
cdofs_b);
}
}
return value;
}
} // namespace dolfinx::fem::impl
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