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integrator_gauss_inline_impl.cc
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			/**
			* @file integrator_gauss_inline_impl.cc
			*
			* @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
			*
			* @section LICENSE
			*
			* 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"
			#if defined(AKANTU_DEBUG_TOOLS)
			#include "aka_debug_tools.hh"
			#endif
			/* -------------------------------------------------------------------------- */

			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, const 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, const 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 {
			memset(inte, 0, nb_degree_of_freedom * sizeof(Real));

			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(
			const 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(
			const 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(
			const 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(
			const 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, const 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, const 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, 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, const 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,
			const 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,
			const 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();
			Array<Real> * 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,
			const 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, const 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, const 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,
			const 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();
			Array<Real> * 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, const 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, \
			const ElementType & type, const 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, const 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, const ElementType & type, \
			const 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, const ElementType & type,
			const 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, \
			const ElementType & type, const 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, const ElementType & type,
			const 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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