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fe_engine_template_tmpl.hh
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			/**
			* Copyright (©) 2011-2023 EPFL (Ecole Polytechnique Fédérale de Lausanne)
			* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
			*
			* This file is part of Akantu
			*
			* 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 "aka_common.hh"
			#include "dof_manager.hh"
			#include "fe_engine_template.hh"
			/* -------------------------------------------------------------------------- */

			namespace akantu {

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::FEEngineTemplate(
			Mesh & mesh, Int spatial_dimension, const ID & id, bool do_not_precompute)
			: FEEngine(mesh, spatial_dimension, id),
			integrator(mesh, spatial_dimension, id),
			shape_functions(mesh, spatial_dimension, id) {
			if (not do_not_precompute) {
			initShapeFunctions(_not_ghost);
			initShapeFunctions(_ghost);
			}
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::~FEEngineTemplate() =
			default;

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
			gradientOnIntegrationPoints(const Array<Real> & u, Array<Real> & nablauq,
			Int nb_degree_of_freedom, ElementType type,
			GhostType ghost_type,
			const Array<Int> & filter_elements) const {
			AKANTU_DEBUG_IN();

			auto nb_element = mesh.getNbElement(type, ghost_type);
			if (filter_elements != empty_filter) {
			nb_element = filter_elements.size();
			}
			auto nb_points =
			shape_functions.getIntegrationPoints(type, ghost_type).cols();

			#ifndef AKANTU_NDEBUG

			auto element_dimension = mesh.getSpatialDimension(type);

			AKANTU_DEBUG_ASSERT(u.size() == mesh.getNbNodes(),
			"The vector u(" << u.getID()
			<< ") has not the good size.");
			AKANTU_DEBUG_ASSERT(u.getNbComponent() == nb_degree_of_freedom,
			"The vector u("
			<< u.getID()
			<< ") has not the good number of component.");

			AKANTU_DEBUG_ASSERT(
			nablauq.getNbComponent() == nb_degree_of_freedom * element_dimension,
			"The vector nablauq(" << nablauq.getID()
			<< ") has not the good number of component.");
			#endif

			nablauq.resize(nb_element * nb_points);

			auto call = [&](auto type) {
			if (element_dimension == ElementClass<type.value>::getSpatialDimension())
			shape_functions.template gradientOnIntegrationPoints<type.value>(
			u, nablauq, nb_degree_of_freedom, ghost_type, filter_elements);
			};

			tuple_dispatch<ElementTypes_t<kind>>(call, type);
			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::initShapeFunctions(
			GhostType ghost_type) {
			initShapeFunctions(mesh.getNodes(), ghost_type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::initShapeFunctions(
			const Array<Real> & nodes, GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			for (const auto & type :
			mesh.elementTypes(element_dimension, ghost_type, kind)) {
			integrator.initIntegrator(nodes, type, ghost_type);
			const auto & control_points = getIntegrationPoints(type, ghost_type);
			shape_functions.initShapeFunctions(nodes, control_points, type, ghost_type);
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::integrate(
			const Array<Real> & f, Array<Real> & intf, Int nb_degree_of_freedom,
			ElementType type, GhostType ghost_type,
			const Array<Idx> & filter_elements) const {

			auto nb_element = mesh.getNbElement(type, ghost_type);
			if (filter_elements != empty_filter) {
			nb_element = filter_elements.size();
			}
			#ifndef AKANTU_NDEBUG

			auto nb_quadrature_points = getNbIntegrationPoints(type);

			AKANTU_DEBUG_ASSERT(f.size() == nb_element * nb_quadrature_points,
			"The vector f(" << f.getID() << " size " << f.size()
			<< ") has not the good size ("
			<< nb_element << ").");
			AKANTU_DEBUG_ASSERT(f.getNbComponent() == nb_degree_of_freedom,
			"The vector f("
			<< f.getID()
			<< ") has not the good number of component.");
			AKANTU_DEBUG_ASSERT(intf.getNbComponent() == nb_degree_of_freedom,
			"The vector intf("
			<< intf.getID()
			<< ") has not the good number of component.");
			#endif

			intf.resize(nb_element);

			auto && call = [&](auto type) {
			integrator.template integrate<type.value>(f, intf, nb_degree_of_freedom,
			ghost_type, filter_elements);
			};
			tuple_dispatch<ElementTypes_t<kind>>(call, type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			Real FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::integrate(
			const Array<Real> & f, ElementType type, GhostType ghost_type,
			const Array<Int> & filter_elements) const {
			AKANTU_DEBUG_IN();

			#ifndef AKANTU_NDEBUG
			auto nb_element = mesh.getNbElement(type, ghost_type);
			if (filter_elements != empty_filter) {
			nb_element = filter_elements.size();
			}

			auto nb_quadrature_points = getNbIntegrationPoints(type, ghost_type);

			AKANTU_DEBUG_ASSERT(
			f.size() == nb_element * nb_quadrature_points,
			"The vector f(" << f.getID() << ") has not the good size. (" << f.size()
			<< "!=" << nb_quadrature_points * nb_element << ")");
			AKANTU_DEBUG_ASSERT(f.getNbComponent() == 1,
			"The vector f("
			<< f.getID()
			<< ") has not the good number of component.");
			#endif

			auto && call = [&](auto type) {
			return integrator.template integrate<type.value>(f, ghost_type,
			filter_elements);
			};
			return tuple_dispatch<ElementTypes_t<kind>>(call, type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			Real FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::integrate(
			const Ref<const VectorXr> f, ElementType type, Int index,
			GhostType ghost_type) const {
			auto && call = [&](auto type) {
			return integrator.template integrate<type.value>(f, index, ghost_type);
			};
			return tuple_dispatch<ElementTypes_t<kind>>(call, type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
			interpolateOnIntegrationPoints(const Array<Real> & u, Array<Real> & uq,
			Int nb_degree_of_freedom, ElementType type,
			GhostType ghost_type,
			const Array<Int> & filter_elements) const {
			AKANTU_DEBUG_IN();

			auto nb_points =
			shape_functions.getIntegrationPoints(type, ghost_type).cols();
			auto nb_element = mesh.getNbElement(type, ghost_type);
			if (filter_elements != empty_filter) {
			nb_element = filter_elements.size();
			}

			AKANTU_DEBUG_ASSERT(u.size() == mesh.getNbNodes(),
			"The vector u(" << u.getID()
			<< ") has not the good size.");
			AKANTU_DEBUG_ASSERT(u.getNbComponent() == nb_degree_of_freedom,
			"The vector u("
			<< u.getID()
			<< ") has not the good number of component.");
			AKANTU_DEBUG_ASSERT(uq.getNbComponent() == nb_degree_of_freedom,
			"The vector uq("
			<< uq.getID()
			<< ") has not the good number of component.");

			uq.resize(nb_element * nb_points);

			auto && call = [&](auto type) {
			shape_functions.template interpolateOnIntegrationPoints<type.value>(
			u, uq, nb_degree_of_freedom, ghost_type, filter_elements);
			};
			tuple_dispatch<ElementTypes_t<kind>>(call, type);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
			interpolateOnIntegrationPoints(
			const Array<Real> & u, ElementTypeMapArray<Real> & uq,
			const ElementTypeMapArray<Idx> * filter_elements) const {
			AKANTU_DEBUG_IN();

			const Array<Idx> * filter = nullptr;

			for (auto ghost_type : ghost_types) {
			auto && types = uq.elementTypes(_all_dimensions, ghost_type, kind);
			for (const auto & type : types) {
			auto nb_quad_per_element = getNbIntegrationPoints(type, ghost_type);

			Int nb_element = 0;

			if (filter_elements != nullptr) {
			filter = &((*filter_elements)(type, ghost_type));
			nb_element = filter->size();
			} else {
			filter = &empty_filter;
			nb_element = mesh.getNbElement(type, ghost_type);
			}

			auto nb_tot_quad = nb_quad_per_element * nb_element;

			Array<Real> & quad = uq(type, ghost_type);
			quad.resize(nb_tot_quad);

			interpolateOnIntegrationPoints(u, quad, quad.getNbComponent(), type,
			ghost_type, *filter);
			}
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::computeBtD(
			const Array<Real> & Ds, Array<Real> & BtDs, ElementType type,
			GhostType ghost_type, const Array<Idx> & filter_elements) const {

			auto && call = [&](auto type) {
			shape_functions.template computeBtD<type.value>(Ds, BtDs, ghost_type,
			filter_elements);
			};
			tuple_dispatch<ElementTypes_t<kind>>(call, type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::computeBtDB(
			const Array<Real> & Ds, Array<Real> & BtDBs, Int order_d, ElementType type,
			GhostType ghost_type, const Array<Idx> & filter_elements) const {
			auto && call = [&](auto type) {
			shape_functions.template computeBtDB<type.value>(
			Ds, BtDBs, order_d, ghost_type, filter_elements);
			};
			tuple_dispatch<ElementTypes_t<kind>>(call, type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::computeNtbN(
			const Array<Real> & bs, Array<Real> & NtbNs, ElementType type,
			GhostType ghost_type, const Array<Idx> & filter_elements) const {
			auto && call = [&](auto type) {
			shape_functions.template computeNtbN<type.value>(bs, NtbNs, ghost_type,
			filter_elements);
			};
			tuple_dispatch<ElementTypes_t<kind>>(call, type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::computeNtb(
			const Array<Real> & bs, Array<Real> & Ntbs, ElementType type,
			GhostType ghost_type, const Array<Idx> & filter_elements) const {
			auto && call = [&](auto type) {
			shape_functions.template computeNtb<type.value>(bs, Ntbs, ghost_type,
			filter_elements);
			};
			tuple_dispatch<ElementTypes_t<kind>>(call, type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
			computeIntegrationPointsCoordinates(
			ElementTypeMapArray<Real> & quadrature_points_coordinates,
			const ElementTypeMapArray<Idx> * filter_elements) const {

			const Array<Real> & nodes_coordinates = mesh.getNodes();

			interpolateOnIntegrationPoints(
			nodes_coordinates, quadrature_points_coordinates, filter_elements);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
			computeIntegrationPointsCoordinates(
			Array<Real> & quadrature_points_coordinates, ElementType type,
			GhostType ghost_type, const Array<Idx> & filter_elements) const {
			const Array<Real> & nodes_coordinates = mesh.getNodes();

			auto spatial_dimension = mesh.getSpatialDimension();

			interpolateOnIntegrationPoints(
			nodes_coordinates, quadrature_points_coordinates, spatial_dimension, type,
			ghost_type, filter_elements);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
			initElementalFieldInterpolationFromIntegrationPoints(
			const ElementTypeMapArray<Real> & interpolation_points_coordinates,
			ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
			ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
			const ElementTypeMapArray<Idx> * element_filter) const {
			AKANTU_DEBUG_IN();

			auto spatial_dimension = this->mesh.getSpatialDimension();

			ElementTypeMapArray<Real> quadrature_points_coordinates(
			"quadrature_points_coordinates_for_interpolation", getID());

			quadrature_points_coordinates.initialize(*this,
			_nb_component = spatial_dimension);

			computeIntegrationPointsCoordinates(quadrature_points_coordinates,
			element_filter);
			shape_functions.initElementalFieldInterpolationFromIntegrationPoints(
			interpolation_points_coordinates,
			interpolation_points_coordinates_matrices,
			quad_points_coordinates_inv_matrices, quadrature_points_coordinates,
			element_filter);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
			interpolateElementalFieldFromIntegrationPoints(
			const ElementTypeMapArray<Real> & field,
			const ElementTypeMapArray<Real> & interpolation_points_coordinates,
			ElementTypeMapArray<Real> & result, const GhostType ghost_type,
			const ElementTypeMapArray<Idx> * element_filter) const {

			ElementTypeMapArray<Real> interpolation_points_coordinates_matrices(
			"interpolation_points_coordinates_matrices", id);
			ElementTypeMapArray<Real> quad_points_coordinates_inv_matrices(
			"quad_points_coordinates_inv_matrices", id);

			initElementalFieldInterpolationFromIntegrationPoints(
			interpolation_points_coordinates,
			interpolation_points_coordinates_matrices,
			quad_points_coordinates_inv_matrices, element_filter);

			interpolateElementalFieldFromIntegrationPoints(
			field, interpolation_points_coordinates_matrices,
			quad_points_coordinates_inv_matrices, result, ghost_type, element_filter);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
			interpolateElementalFieldFromIntegrationPoints(
			const ElementTypeMapArray<Real> & field,
			const ElementTypeMapArray<Real> &
			interpolation_points_coordinates_matrices,
			const ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
			ElementTypeMapArray<Real> & result, const GhostType ghost_type,
			const ElementTypeMapArray<Idx> * element_filter) const {
			shape_functions.interpolateElementalFieldFromIntegrationPoints(
			field, interpolation_points_coordinates_matrices,
			quad_points_coordinates_inv_matrices, result, ghost_type, element_filter);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			template <ElementKind kind_, typename D1, typename D2, typename D3,
			std::enable_if_t<aka::are_vectors<D1, D3>::value and
			kind_ == _ek_regular> *>
			inline void
			FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::interpolateImpl(
			const Eigen::MatrixBase<D1> & real_coords,
			const Eigen::MatrixBase<D2> & nodal_values,
			Eigen::MatrixBase<D3> & interpolated, const Element & element) const {
			auto && call = [&](auto type) {
			shape_functions.template interpolate<type.value>(
			real_coords, element.element, nodal_values, interpolated,
			element.ghost_type);
			};
			tuple_dispatch<ElementTypes_t<kind>>(call, element.type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::interpolate(
			const Ref<const VectorXr> real_coords,
			const Ref<const MatrixXr> nodal_values, Ref<VectorXr> interpolated,
			const Element & element) const {
			interpolateImpl(real_coords, nodal_values, interpolated, element);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
			computeNormalsOnIntegrationPoints(GhostType ghost_type) {
			computeNormalsOnIntegrationPoints(mesh.getNodes(), ghost_type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
			computeNormalsOnIntegrationPoints(const Array<Real> & field,
			GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			// Real * coord = mesh.getNodes().data();
			auto spatial_dimension = mesh.getSpatialDimension();

			// allocate the normal arrays
			normals_on_integration_points.initialize(
			*this, _nb_component = spatial_dimension,
			_spatial_dimension = element_dimension, _ghost_type = ghost_type,
			_element_kind = kind);

			// loop over the type to build the normals
			for (const auto & type :
			mesh.elementTypes(element_dimension, ghost_type, kind)) {
			auto & normals_on_quad = normals_on_integration_points(type, ghost_type);
			computeNormalsOnIntegrationPoints(field, normals_on_quad, type, ghost_type);
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			template <ElementType type, ElementKind kind_,
			std::enable_if_t<kind_ == _ek_regular and type != _point_1> *>
			void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
			computeNormalsOnIntegrationPoints(const Array<Real> & field,
			Array<Real> & normal,
			GhostType ghost_type) const {
			AKANTU_DEBUG_IN();

			auto spatial_dimension = mesh.getSpatialDimension();
			constexpr auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			auto nb_points = getNbIntegrationPoints(type, ghost_type);

			auto nb_element = mesh.getConnectivity(type, ghost_type).size();
			normal.resize(nb_element * nb_points);

			Array<Real> f_el(0, spatial_dimension * nb_nodes_per_element);
			FEEngine::extractNodalToElementField(mesh, field, f_el, type, ghost_type);

			const auto & quads =
			integrator.template getIntegrationPoints<type>(ghost_type);

			for (auto && data : zip(make_view(normal, spatial_dimension, nb_points),
			make_view<Eigen::Dynamic, nb_nodes_per_element>(
			f_el, spatial_dimension, nb_nodes_per_element))) {
			ElementClass<type>::computeNormalsOnNaturalCoordinates(
			quads, std::get<1>(data), std::get<0>(data));
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			template <ElementType type, ElementKind kind_,
			std::enable_if_t<kind_ == _ek_regular and type == _point_1> *>
			inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
			computeNormalsOnIntegrationPoints(const Array<Real> & /field/,
			Array<Real> & normal,
			GhostType ghost_type) const {
			AKANTU_DEBUG_IN();

			AKANTU_DEBUG_ASSERT(mesh.getSpatialDimension() == 1,
			"Mesh dimension must be 1 to compute normals on points!");

			auto spatial_dimension = mesh.getSpatialDimension();
			// Int nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			auto nb_points = getNbIntegrationPoints(type, ghost_type);
			const auto & connectivity = mesh.getConnectivity(type, ghost_type);
			auto nb_element = connectivity.size();

			normal.resize(nb_element * nb_points);
			auto normals_on_quad =
			make_view(normal, spatial_dimension, nb_points).begin();
			const auto & segments = mesh.getElementToSubelement(type, ghost_type);
			const auto & coords = mesh.getNodes();

			const Mesh * mesh_segment;
			if (mesh.isMeshFacets()) {
			mesh_segment = &(mesh.getMeshParent());
			} else {
			mesh_segment = &mesh;
			}

			for (Idx elem = 0; elem < nb_element; ++elem) {
			auto nb_segment = segments(elem).size();
			AKANTU_DEBUG_ASSERT(
			nb_segment > 0,
			"Impossible to compute a normal on a point connected to 0 segments");

			Real normal_value = 1;
			if (nb_segment == 1) {
			auto point = connectivity(elem);
			const auto segment = segments(elem)[0];
			const auto & segment_connectivity =
			mesh_segment->getConnectivity(segment.type, segment.ghost_type);
			Vector<Idx> segment_points = segment_connectivity.begin(
			Mesh::getNbNodesPerElement(segment.type))[segment.element];
			Real difference;
			if (segment_points(0) == point) {
			difference = coords(elem) - coords(segment_points(1));
			} else {
			difference = coords(elem) - coords(segment_points(0));
			}

			normal_value = difference / std::abs(difference);
			}

			for (Idx n(0); n < nb_points; ++n) {
			(*normals_on_quad)(0, n) = normal_value;
			}
			++normals_on_quad;
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
			computeNormalsOnIntegrationPoints(const Array<Real> & field,
			Array<Real> & normal, ElementType type,
			GhostType ghost_type) const {
			auto && call = [&](auto type) {
			this->computeNormalsOnIntegrationPoints<type.value>(field, normal,
			ghost_type);
			};
			tuple_dispatch<ElementTypes_t<kind>>(call, type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::inverseMap(
			const Ref<const VectorXr> real_coords, Int element, ElementType type,
			Ref<VectorXr> natural_coords, GhostType ghost_type) const {
			/// need sfinea to avoid structural
			auto && call = [&](auto type) {
			shape_functions.template inverseMap<type.value>(real_coords, element,
			natural_coords, ghost_type);
			};
			tuple_dispatch<ElementTypes_t<kind>>(call, type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline bool FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::contains(
			const Ref<const VectorXr> real_coords, Int element, ElementType type,
			GhostType ghost_type) const {
			auto && call = [&](auto type) {
			return shape_functions.template contains<type.value>(real_coords, element,
			ghost_type);
			};
			return tuple_dispatch<ElementTypes_t<kind>>(call, type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			template <ElementKind kind_, typename D1, typename D2,
			std::enable_if_t<aka::are_vectors<D1, D2>::value and
			kind_ != _ek_cohesive> *>
			inline void
			FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::computeShapesImpl(
			const Eigen::MatrixBase<D1> & real_coords, Idx element, ElementType type,
			Eigen::MatrixBase<D2> & shapes, GhostType ghost_type) const {

			auto && call = [&](auto type) {
			this->shape_functions.template computeShapes<type.value>(
			real_coords, element, shapes, ghost_type);
			};
			tuple_dispatch<ElementTypes_t<kind>>(call, type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			template <ElementKind kind_, typename D1, typename D2,
			std::enable_if_t<aka::is_vector_v<D1> and kind_ != _ek_cohesive> *>
			inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
			computeShapeDerivativesImpl(const Eigen::MatrixBase<D1> & real_coords,
			Int element, ElementType type,
			Eigen::MatrixBase<D2> & shape_derivatives,
			GhostType ghost_type) const {
			MatrixProxy<const Real> coords_mat(real_coords.derived().data(),
			shape_derivatives.rows(), 1);
			Tensor3Proxy<Real> shapesd_tensor(shape_derivatives.derived().data(),
			shape_derivatives.rows(),
			shape_derivatives.cols(), 1);
			auto && call = [&](auto type) {
			shape_functions.template computeShapeDerivatives<type.value>(
			coords_mat, element, shapesd_tensor, ghost_type);
			};
			tuple_dispatch<ElementTypes_t<kind>>(call, type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline Int
			FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::getNbIntegrationPoints(
			ElementType type, GhostType ghost_type) const {
			return tuple_dispatch<ElementTypes_t<kind>>(
			[&](auto type) {
			return integrator.template getNbIntegrationPoints<type.value>(
			ghost_type);
			},
			type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline const Array<Real> &
			FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::getShapes(
			ElementType type, GhostType ghost_type, Int /id/) const {
			return shape_functions.getShapes(type, ghost_type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline const Array<Real> &
			FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::getShapesDerivatives(
			ElementType type, GhostType ghost_type, Int /id/) const {
			return shape_functions.getShapesDerivatives(type, ghost_type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline const Matrix<Real> &
			FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::getIntegrationPoints(
			ElementType type, GhostType ghost_type) const {

			return tuple_dispatch<ElementTypes_t<kind>>(
			[&](auto type) -> const Matrix<Real> & {
			return (
			integrator.template getIntegrationPoints<type.value>(ghost_type));
			},
			type);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::printself(
			std::ostream & stream, int indent) const {
			std::string space(indent, AKANTU_INDENT);

			stream << space << "FEEngineTemplate [" << std::endl;
			stream << space << " + parent [" << std::endl;
			FEEngine::printself(stream, indent + 3);
			stream << space << " ]" << std::endl;
			stream << space << " + shape functions [" << std::endl;
			shape_functions.printself(stream, indent + 3);
			stream << space << " ]" << std::endl;
			stream << space << " + integrator [" << std::endl;
			integrator.printself(stream, indent + 3);
			stream << space << " ]" << std::endl;
			stream << space << "]" << std::endl;
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::onElementsAdded(
			const Array<Element> & new_elements, const NewElementsEvent & /unused/) {
			integrator.onElementsAdded(new_elements);

			const auto & points = integrator.getIntegrationPoints();
			// for each distinct type add missing integration points to shape_functions
			for (auto ghost_type : ghost_types) {
			for (const auto & type : points.elementTypes(_ghost_type = ghost_type)) {
			tuple_dispatch<ElementTypes_t<kind>>(
			[&](auto type) {
			shape_functions.template setIntegrationPointsByType<type.value>(
			points(type, ghost_type), ghost_type);
			},
			type);
			}
			}

			shape_functions.onElementsAdded(new_elements);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::onElementsRemoved(
			const Array<Element> & removed_elements,
			const ElementTypeMapArray<Idx> & new_numbering,
			const RemovedElementsEvent & /event/) {
			integrator.onElementsRemoved(removed_elements, new_numbering);
			shape_functions.onElementsRemoved(removed_elements, new_numbering);
			}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::onElementsChanged(
			const Array<Element> & /unused/, const Array<Element> & /unused/,
			const ElementTypeMapArray<Idx> & /unused/,
			const ChangedElementsEvent & /unused/) {}

			} // namespace akantu

rAKA/src/fe_engine/fe_engine_template_tmpl.hh676bfba8c50ffeatures/friction_examp…

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rAKA/src/fe_engine/fe_engine_template_tmpl.hh
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