integrator_gauss_inline_impl.hh
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Created: Tue, Nov 19, 21:56

integrator_gauss_inline_impl.hh
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	/**
	* @file integrator_gauss_inline_impl.hh
	*
	* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Feb 15 2011
	* @date last modification: Tue Feb 20 2018
	*
	* @brief inline function of gauss integrator
	*
	*
	* Copyright (©) 2010-2018 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	*
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	*
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "fe_engine.hh"
	#include "mesh_iterators.hh"
	/* -------------------------------------------------------------------------- */

	namespace akantu {
	namespace debug {
	struct IntegratorGaussException : public Exception {};
	} // namespace debug
	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	inline void IntegratorGauss<kind, IntegrationOrderFunctor>::integrateOnElement(
	const Array<Real> & f, Real * intf, UInt nb_degree_of_freedom,
	const UInt elem, GhostType ghost_type) const {
	Array<Real> & jac_loc = jacobians(type, ghost_type);

	UInt nb_quadrature_points = ElementClass<type>::getNbQuadraturePoints();
	AKANTU_DEBUG_ASSERT(f.getNbComponent() == nb_degree_of_freedom,
	"The vector f do not have the good number of component.");

	Real * f_val = f.storage() + elem * f.getNbComponent();
	Real * jac_val = jac_loc.storage() + elem * nb_quadrature_points;

	integrate(f_val, jac_val, intf, nb_degree_of_freedom, nb_quadrature_points);
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	inline Real IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
	const Vector<Real> & in_f, UInt index, GhostType ghost_type) const {
	const Array<Real> & jac_loc = jacobians(type, ghost_type);

	UInt nb_quadrature_points =
	GaussIntegrationElement<type>::getNbQuadraturePoints();
	AKANTU_DEBUG_ASSERT(in_f.size() == nb_quadrature_points,
	"The vector f do not have nb_quadrature_points entries.");

	Real * jac_val = jac_loc.storage() + index * nb_quadrature_points;
	Real intf;

	integrate(in_f.storage(), jac_val, &intf, 1, nb_quadrature_points);

	return intf;
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	inline void IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
	Real * f, Real * jac, Real * inte, UInt nb_degree_of_freedom,
	UInt nb_quadrature_points) const {
	std::fill_n(inte, nb_degree_of_freedom, 0.);

	Real * cjac = jac;
	for (UInt q = 0; q < nb_quadrature_points; ++q) {
	for (UInt dof = 0; dof < nb_degree_of_freedom; ++dof) {
	inte[dof] += f *cjac;
	++f;
	}
	++cjac;
	}
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	inline const Matrix<Real> &
	IntegratorGauss<kind, IntegrationOrderFunctor>::getIntegrationPoints(
	GhostType ghost_type) const {
	AKANTU_DEBUG_ASSERT(
	quadrature_points.exists(type, ghost_type),
	"Quadrature points for type "
	<< quadrature_points.printType(type, ghost_type)
	<< " have not been initialized."
	<< " Did you use 'computeQuadraturePoints' function ?");
	return quadrature_points(type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	inline UInt
	IntegratorGauss<kind, IntegrationOrderFunctor>::getNbIntegrationPoints(
	GhostType ghost_type) const {
	AKANTU_DEBUG_ASSERT(
	quadrature_points.exists(type, ghost_type),
	"Quadrature points for type "
	<< quadrature_points.printType(type, ghost_type)
	<< " have not been initialized."
	<< " Did you use 'computeQuadraturePoints' function ?");
	return quadrature_points(type, ghost_type).cols();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type, UInt polynomial_degree>
	inline Matrix<Real>
	IntegratorGauss<kind, IntegrationOrderFunctor>::getIntegrationPoints() const {
	return GaussIntegrationElement<type,
	polynomial_degree>::getQuadraturePoints();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type, UInt polynomial_degree>
	inline Vector<Real>
	IntegratorGauss<kind, IntegrationOrderFunctor>::getIntegrationWeights() const {
	return GaussIntegrationElement<type, polynomial_degree>::getWeights();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	inline void
	IntegratorGauss<kind, IntegrationOrderFunctor>::computeQuadraturePoints(
	GhostType ghost_type) {
	Matrix<Real> & quads = quadrature_points(type, ghost_type);
	const UInt polynomial_degree =
	IntegrationOrderFunctor::template getOrder<type>();
	quads =
	GaussIntegrationElement<type, polynomial_degree>::getQuadraturePoints();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	inline void IntegratorGauss<kind, IntegrationOrderFunctor>::
	computeJacobianOnQuadPointsByElement(const Matrix<Real> & node_coords,
	const Matrix<Real> & quad,
	Vector<Real> & jacobians) const {
	// jacobian
	ElementClass<type>::computeJacobian(quad, node_coords, jacobians);
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	IntegratorGauss<kind, IntegrationOrderFunctor>::IntegratorGauss(
	const Mesh & mesh, UInt spatial_dimension, const ID & id,
	const MemoryID & memory_id)
	: Integrator(mesh, spatial_dimension, id, memory_id) {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::checkJacobians(
	GhostType ghost_type) const {
	AKANTU_DEBUG_IN();

	UInt nb_quadrature_points = this->quadrature_points(type, ghost_type).cols();

	UInt nb_element = mesh.getConnectivity(type, ghost_type).size();

	Real * jacobians_val = jacobians(type, ghost_type).storage();

	for (UInt i = 0; i < nb_element * nb_quadrature_points;
	++i, ++jacobians_val) {
	if (*jacobians_val < 0) {
	AKANTU_CUSTOM_EXCEPTION_INFO(debug::IntegratorGaussException{},
	"Negative jacobian computed,"
	<< " possible problem in the element "
	"node ordering (Quadrature Point "
	<< i % nb_quadrature_points << ":"
	<< i / nb_quadrature_points << ":"
	<< type << ":" << ghost_type << ")");
	}
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::
	computeJacobiansOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & quad_points,
	Array<Real> & jacobians, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	UInt nb_quadrature_points = quad_points.cols();

	UInt nb_element = mesh.getNbElement(type, ghost_type);
	jacobians.resize(nb_element * nb_quadrature_points);

	auto jacobians_it =
	jacobians.begin_reinterpret(nb_quadrature_points, nb_element);
	auto jacobians_begin = jacobians_it;

	Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type,
	filter_elements);

	auto x_it = x_el.begin(spatial_dimension, nb_nodes_per_element);

	nb_element = x_el.size();

	// Matrix<Real> local_coord(spatial_dimension, nb_nodes_per_element);
	for (UInt elem = 0; elem < nb_element; ++elem, ++x_it) {
	const Matrix<Real> & x = *x_it;
	if (filter_elements != empty_filter) {
	jacobians_it = jacobians_begin + filter_elements(elem);
	}

	Vector<Real> & J = *jacobians_it;
	computeJacobianOnQuadPointsByElement<type>(x, quad_points, J);

	if (filter_elements == empty_filter) {
	++jacobians_it;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	#if defined(AKANTU_STRUCTURAL_MECHANICS)
	template <>
	template <ElementType type>
	void IntegratorGauss<_ek_structural, DefaultIntegrationOrderFunctor>::
	computeJacobiansOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & quad_points,
	Array<Real> & jacobians, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	const UInt spatial_dimension = mesh.getSpatialDimension();
	const UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	const UInt nb_quadrature_points = quad_points.cols();
	const UInt nb_dofs = ElementClass<type>::getNbDegreeOfFreedom();

	UInt nb_element = mesh.getNbElement(type, ghost_type);
	jacobians.resize(nb_element * nb_quadrature_points);

	auto jacobians_it =
	jacobians.begin_reinterpret(nb_quadrature_points, nb_element);
	auto jacobians_begin = jacobians_it;

	Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type,
	filter_elements);

	auto x_it = x_el.begin(spatial_dimension, nb_nodes_per_element);

	nb_element = x_el.size();

	const bool has_extra_normal =
	mesh.hasData<Real>("extra_normal", type, ghost_type);
	Array<Real>::const_vector_iterator extra_normal;
	Array<Real>::const_vector_iterator extra_normal_begin;
	if (has_extra_normal) {
	extra_normal = mesh.getData<Real>("extra_normal", type, ghost_type)
	.begin(spatial_dimension);
	extra_normal_begin = extra_normal;
	}

	// Matrix<Real> local_coord(spatial_dimension, nb_nodes_per_element);
	for (UInt elem = 0; elem < nb_element; ++elem, ++x_it) {
	if (filter_elements != empty_filter) {
	jacobians_it = jacobians_begin + filter_elements(elem);
	extra_normal = extra_normal_begin + filter_elements(elem);
	}

	const Matrix<Real> & X = *x_it;
	Vector<Real> & J = *jacobians_it;
	Matrix<Real> R(nb_dofs, nb_dofs);

	if (has_extra_normal) {
	ElementClass<type>::computeRotationMatrix(R, X, *extra_normal);
	} else {
	ElementClass<type>::computeRotationMatrix(R, X, Vector<Real>(X.rows()));
	}
	// Extracting relevant lines
	auto x = (R.block(0, 0, spatial_dimension, spatial_dimension) * X)
	.block(0, 0, ElementClass<type>::getNaturalSpaceDimension(),
	ElementClass<type>::getNbNodesPerElement());

	computeJacobianOnQuadPointsByElement<type>(x, quad_points, J);

	if (filter_elements == empty_filter) {
	++jacobians_it;
	++extra_normal;
	}
	}

	AKANTU_DEBUG_OUT();
	}
	#endif

	/* -------------------------------------------------------------------------- */
	#if defined(AKANTU_COHESIVE_ELEMENT)
	template <>
	template <ElementType type>
	void IntegratorGauss<_ek_cohesive, DefaultIntegrationOrderFunctor>::
	computeJacobiansOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & quad_points,
	Array<Real> & jacobians, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	UInt nb_quadrature_points = quad_points.cols();

	UInt nb_element = mesh.getNbElement(type, ghost_type);
	jacobians.resize(nb_element * nb_quadrature_points);

	auto jacobians_begin =
	jacobians.begin_reinterpret(nb_quadrature_points, nb_element);

	Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type,
	filter_elements);

	auto x_it = x_el.begin(spatial_dimension, nb_nodes_per_element);

	UInt nb_nodes_per_subelement = nb_nodes_per_element / 2;
	Matrix<Real> x(spatial_dimension, nb_nodes_per_subelement);

	nb_element = x_el.size();
	UInt l_el = 0;
	auto compute = [&](const auto & el) {
	Vector<Real> J(jacobians_begin[el]);
	Matrix<Real> X(x_it[l_el]);
	++l_el;

	for (UInt n = 0; n < nb_nodes_per_subelement; ++n) {
	Vector<Real>(x(n)) =
	(Vector<Real>(X(n)) + Vector<Real>(X(n + nb_nodes_per_subelement))) /
	2.;
	}

	if (type == _cohesive_1d_2) {
	J(0) = 1;
	} else {
	this->computeJacobianOnQuadPointsByElement<type>(x, quad_points, J);
	}
	};

	for_each_element(nb_element, filter_elements, compute);

	AKANTU_DEBUG_OUT();
	}
	#endif
	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::
	precomputeJacobiansOnQuadraturePoints(const Array<Real> & nodes,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	Array<Real> & jacobians_tmp = jacobians.alloc(0, 1, type, ghost_type);

	this->computeJacobiansOnIntegrationPoints<type>(
	nodes, quadrature_points(type, ghost_type), jacobians_tmp, ghost_type);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type, UInt polynomial_degree>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::multiplyJacobiansByWeights(
	Array<Real> & jacobians, const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	UInt nb_quadrature_points =
	GaussIntegrationElement<type, polynomial_degree>::getNbQuadraturePoints();

	Vector<Real> weights =
	GaussIntegrationElement<type, polynomial_degree>::getWeights();

	auto && view = make_view(jacobians, nb_quadrature_points);

	if (filter_elements != empty_filter) {
	auto J_it = view.begin();
	for (auto el : filter_elements) {
	Vector<Real> J(J_it[el]);
	J *= weights;
	}
	} else {
	for (auto & J : make_view(jacobians, nb_quadrature_points)) {
	J *= weights;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
	const Array<Real> & in_f, Array<Real> & intf, UInt nb_degree_of_freedom,
	const Array<Real> & jacobians, UInt nb_element) const {
	AKANTU_DEBUG_IN();

	intf.resize(nb_element);
	if (nb_element == 0) {
	return;
	}

	UInt nb_points = jacobians.size() / nb_element;

	Array<Real>::const_matrix_iterator J_it;
	Array<Real>::matrix_iterator inte_it;
	Array<Real>::const_matrix_iterator f_it;

	f_it = in_f.begin_reinterpret(nb_degree_of_freedom, nb_points, nb_element);
	inte_it = intf.begin_reinterpret(nb_degree_of_freedom, 1, nb_element);
	J_it = jacobians.begin_reinterpret(nb_points, 1, nb_element);

	for (UInt el = 0; el < nb_element; ++el, ++J_it, ++f_it, ++inte_it) {
	const Matrix<Real> & f = *f_it;
	const Matrix<Real> & J = *J_it;
	Matrix<Real> & inte_f = *inte_it;

	inte_f.mul<false, false>(f, J);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
	const Array<Real> & in_f, Array<Real> & intf, UInt nb_degree_of_freedom,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(jacobians.exists(type, ghost_type),
	"No jacobians for the type "
	<< jacobians.printType(type, ghost_type));

	const Array<Real> & jac_loc = jacobians(type, ghost_type);
	if (filter_elements != empty_filter) {
	UInt nb_element = filter_elements.size();
	auto * filtered_J = new Array<Real>(0, jac_loc.getNbComponent());
	FEEngine::filterElementalData(mesh, jac_loc, *filtered_J, type, ghost_type,
	filter_elements);
	this->integrate(in_f, intf, nb_degree_of_freedom, *filtered_J, nb_element);
	delete filtered_J;
	} else {
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	this->integrate(in_f, intf, nb_degree_of_freedom, jac_loc, nb_element);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type, UInt polynomial_degree>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
	const Array<Real> & in_f, Array<Real> & intf, UInt nb_degree_of_freedom,
	GhostType ghost_type) const {
	AKANTU_DEBUG_IN();

	Matrix<Real> quads = this->getIntegrationPoints<type, polynomial_degree>();

	Array<Real> jacobians;
	this->computeJacobiansOnIntegrationPoints<type>(mesh.getNodes(), quads,
	jacobians, ghost_type);
	this->multiplyJacobiansByWeights<type, polynomial_degree>(jacobians);

	this->integrate(in_f, intf, nb_degree_of_freedom, jacobians,
	mesh.getNbElement(type, ghost_type));

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type, UInt polynomial_degree>
	Real IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
	const Array<Real> & in_f, GhostType ghost_type) const {
	AKANTU_DEBUG_IN();

	Array<Real> intfv(0, 1);
	integrate<type, polynomial_degree>(in_f, intfv, 1, ghost_type);

	Real res = Math::reduce(intfv);

	AKANTU_DEBUG_OUT();
	return res;
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	Real IntegratorGauss<kind, IntegrationOrderFunctor>::integrate(
	const Array<Real> & in_f, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(jacobians.exists(type, ghost_type),
	"No jacobians for the type "
	<< jacobians.printType(type, ghost_type));

	Array<Real> intfv(0, 1);
	integrate<type>(in_f, intfv, 1, ghost_type, filter_elements);

	Real res = Math::reduce(intfv);

	AKANTU_DEBUG_OUT();
	return res;
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::
	integrateOnIntegrationPoints(const Array<Real> & in_f, Array<Real> & intf,
	UInt nb_degree_of_freedom,
	const Array<Real> & jacobians,
	UInt nb_element) const {
	AKANTU_DEBUG_IN();

	UInt nb_points = jacobians.size() / nb_element;

	intf.resize(nb_element * nb_points);

	auto J_it = jacobians.begin();
	auto f_it = in_f.begin(nb_degree_of_freedom);
	auto inte_it = intf.begin(nb_degree_of_freedom);

	for (UInt el = 0; el < nb_element; ++el, ++J_it, ++f_it, ++inte_it) {
	const Real & J = *J_it;
	const Vector<Real> & f = *f_it;
	Vector<Real> & inte_f = *inte_it;

	inte_f = f;
	inte_f *= J;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::
	integrateOnIntegrationPoints(const Array<Real> & in_f, Array<Real> & intf,
	UInt nb_degree_of_freedom,
	GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(jacobians.exists(type, ghost_type),
	"No jacobians for the type "
	<< jacobians.printType(type, ghost_type));

	const Array<Real> & jac_loc = this->jacobians(type, ghost_type);

	if (filter_elements != empty_filter) {

	UInt nb_element = filter_elements.size();
	auto * filtered_J = new Array<Real>(0, jac_loc.getNbComponent());
	FEEngine::filterElementalData(mesh, jac_loc, *filtered_J, type, ghost_type,
	filter_elements);

	this->integrateOnIntegrationPoints(in_f, intf, nb_degree_of_freedom,
	*filtered_J, nb_element);
	} else {
	UInt nb_element = mesh.getNbElement(type, ghost_type);
	this->integrateOnIntegrationPoints(in_f, intf, nb_degree_of_freedom,
	jac_loc, nb_element);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	inline void
	IntegratorGauss<kind, IntegrationOrderFunctor>::onElementsAddedByType(
	const Array<UInt> & elements, GhostType ghost_type) {
	const auto & nodes = mesh.getNodes();

	if (not quadrature_points.exists(type, ghost_type)) {
	computeQuadraturePoints<type>(ghost_type);
	}

	if (not jacobians.exists(type, ghost_type)) {
	jacobians.alloc(0, 1, type, ghost_type);
	}

	this->computeJacobiansOnIntegrationPoints(
	nodes, quadrature_points(type, ghost_type), jacobians(type, ghost_type),
	type, ghost_type, elements);

	constexpr UInt polynomial_degree =
	IntegrationOrderFunctor::template getOrder<type>();

	multiplyJacobiansByWeights<type, polynomial_degree>(
	this->jacobians(type, ghost_type), elements);
	}

	/* -------------------------------------------------------------------------- */
	namespace integrator {
	namespace details {
	template <ElementKind kind> struct IntegratorOnElementsAddedHelper {};

	#define ON_ELEMENT_ADDED(type) \
	integrator.template onElementsAddedByType<type>(elements, ghost_type);

	#define AKANTU_SPECIALIZE_ON_ELEMENT_ADDED_HELPER(kind) \
	template <> struct IntegratorOnElementsAddedHelper<kind> { \
	template <class I> \
	static void call(I & integrator, const Array<UInt> & elements, \
	ElementType type, GhostType ghost_type) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(ON_ELEMENT_ADDED, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_ON_ELEMENT_ADDED_HELPER)

	#undef AKANTU_SPECIALIZE_ON_ELEMENT_ADDED_HELPER
	#undef ON_ELEMENT_ADDED
	} // namespace details
	} // namespace integrator

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::onElementsAdded(
	const Array<Element> & new_elements) {
	for (auto elements_range : MeshElementsByTypes(new_elements)) {
	auto type = elements_range.getType();
	auto ghost_type = elements_range.getGhostType();

	if (mesh.getSpatialDimension(type) != _spatial_dimension) {
	continue;
	}

	if (mesh.getKind(type) != kind) {
	continue;
	}

	integrator::details::IntegratorOnElementsAddedHelper<kind>::call(
	*this, elements_range.getElements(), type, ghost_type);
	}
	}

	/* -------------------------------------------------------------------------- */
	template <ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	inline void IntegratorGauss<kind, IntegrationOrderFunctor>::initIntegrator(
	const Array<Real> & nodes, GhostType ghost_type) {
	computeQuadraturePoints<type>(ghost_type);
	precomputeJacobiansOnQuadraturePoints<type>(nodes, ghost_type);
	checkJacobians<type>(ghost_type);
	constexpr UInt polynomial_degree =
	IntegrationOrderFunctor::template getOrder<type>();
	multiplyJacobiansByWeights<type, polynomial_degree>(
	this->jacobians(type, ghost_type));
	}

	namespace integrator {
	namespace details {
	template <ElementKind kind> struct GaussIntegratorInitHelper {};

	#define INIT_INTEGRATOR(type) \
	_int.template initIntegrator<type>(nodes, ghost_type)

	#define AKANTU_GAUSS_INTERGRATOR_INIT_HELPER(kind) \
	template <> struct GaussIntegratorInitHelper<kind> { \
	template <ElementKind k, class IOF> \
	static void call(IntegratorGauss<k, IOF> & _int, \
	const Array<Real> & nodes, ElementType type, \
	GhostType ghost_type) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(INIT_INTEGRATOR, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND(AKANTU_GAUSS_INTERGRATOR_INIT_HELPER)

	#undef AKANTU_GAUSS_INTERGRATOR_INIT_HELPER
	#undef INIT_INTEGRATOR
	} // namespace details
	} // namespace integrator

	template <ElementKind kind, class IntegrationOrderFunctor>
	inline void IntegratorGauss<kind, IntegrationOrderFunctor>::initIntegrator(
	const Array<Real> & nodes, ElementType type, GhostType ghost_type) {
	integrator::details::GaussIntegratorInitHelper<kind>::call(*this, nodes, type,
	ghost_type);
	}

	namespace integrator {
	namespace details {
	template <ElementKind kind> struct GaussIntegratorComputeJacobiansHelper {};

	#define AKANTU_COMPUTE_JACOBIANS(type) \
	_int.template computeJacobiansOnIntegrationPoints<type>( \
	nodes, quad_points, jacobians, ghost_type, filter_elements);

	#define AKANTU_GAUSS_INTERGRATOR_COMPUTE_JACOBIANS(kind) \
	template <> struct GaussIntegratorComputeJacobiansHelper<kind> { \
	template <ElementKind k, class IOF> \
	static void \
	call(const IntegratorGauss<k, IOF> & _int, const Array<Real> & nodes, \
	const Matrix<Real> & quad_points, Array<Real> & jacobians, \
	ElementType type, GhostType ghost_type, \
	const Array<UInt> & filter_elements) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(AKANTU_COMPUTE_JACOBIANS, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND(AKANTU_GAUSS_INTERGRATOR_COMPUTE_JACOBIANS)

	#undef AKANTU_GAUSS_INTERGRATOR_COMPUTE_JACOBIANS
	#undef AKANTU_COMPUTE_JACOBIANS
	} // namespace details
	} // namespace integrator

	template <ElementKind kind, class IntegrationOrderFunctor>
	void IntegratorGauss<kind, IntegrationOrderFunctor>::
	computeJacobiansOnIntegrationPoints(
	const Array<Real> & nodes, const Matrix<Real> & quad_points,
	Array<Real> & jacobians, ElementType type, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	integrator::details::GaussIntegratorComputeJacobiansHelper<kind>::call(
	*this, nodes, quad_points, jacobians, type, ghost_type, filter_elements);
	}

	} // namespace akantu

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