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fe_engine_template_tmpl.hh
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			/**
			* @file fe_engine_template_tmpl.hh
			*
			* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
			* @author Mauro Corrado <mauro.corrado@epfl.ch>
			* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
			* @author Nicolas Richart <nicolas.richart@epfl.ch>
			* @author Marco Vocialta <marco.vocialta@epfl.ch>
			*
			* @date creation: Tue Feb 15 2011
			* @date last modification: Tue Feb 20 2018
			*
			* @brief Template implementation of FEEngineTemplate
			*
			*
			* 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 "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, UInt spatial_dimension, const ID & id)
			: FEEngine(mesh, spatial_dimension, id),
			integrator(mesh, spatial_dimension, id),
			shape_functions(mesh, spatial_dimension, id) {}

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

			/* -------------------------------------------------------------------------- */
			/**
			* Helper class to be able to write a partial specialization on the element kind
			*/
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct GradientOnIntegrationPointsHelper {
			template <class S>
			static void call(const S & /unused/, Mesh & /unused/,
			const Array<Real> & /unused/, Array<Real> & /unused/,
			const UInt /unused/, ElementType /unused/,
			GhostType /unused/, const Array<UInt> & /unused/) {
			AKANTU_TO_IMPLEMENT();
			}
			};

			#define COMPUTE_GRADIENT(type) \
			if (element_dimension == ElementClass<type>::getSpatialDimension()) \
			shape_functions.template gradientOnIntegrationPoints<type>( \
			u, nablauq, nb_degree_of_freedom, ghost_type, filter_elements);

			#define AKANTU_SPECIALIZE_GRADIENT_ON_INTEGRATION_POINTS_HELPER(kind) \
			template <> struct GradientOnIntegrationPointsHelper<kind> { \
			template <class S> \
			static void call(const S & shape_functions, Mesh & mesh, \
			const Array<Real> & u, Array<Real> & nablauq, \
			const UInt nb_degree_of_freedom, ElementType type, \
			GhostType ghost_type, \
			const Array<UInt> & filter_elements) { \
			UInt element_dimension = mesh.getSpatialDimension(type); \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(COMPUTE_GRADIENT, kind); \
			} \
			};

			AKANTU_BOOST_ALL_KIND_LIST(
			AKANTU_SPECIALIZE_GRADIENT_ON_INTEGRATION_POINTS_HELPER,
			AKANTU_FE_ENGINE_LIST_GRADIENT_ON_INTEGRATION_POINTS)

			#undef AKANTU_SPECIALIZE_GRADIENT_ON_INTEGRATION_POINTS_HELPER
			#undef COMPUTE_GRADIENT
			} // namespace details
			} // namespace fe_engine

			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,
			const UInt nb_degree_of_freedom,
			ElementType type, GhostType ghost_type,
			const Array<UInt> & filter_elements) const {
			AKANTU_DEBUG_IN();

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

			#ifndef AKANTU_NDEBUG

			UInt 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.");

			// AKANTU_DEBUG_ASSERT(nablauq.size() == nb_element * nb_points,
			// "The vector nablauq(" << nablauq.getID()
			// << ") has not the good size.");
			#endif

			nablauq.resize(nb_element * nb_points);

			fe_engine::details::GradientOnIntegrationPointsHelper<kind>::call(
			shape_functions, mesh, u, nablauq, nb_degree_of_freedom, type, ghost_type,
			filter_elements);
			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 (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();
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Helper class to be able to write a partial specialization on the element kind
			*/
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct IntegrateHelper {};

			#define INTEGRATE(type) \
			integrator.template integrate<type>(f, intf, nb_degree_of_freedom, \
			ghost_type, filter_elements);

			#define AKANTU_SPECIALIZE_INTEGRATE_HELPER(kind) \
			template <> struct IntegrateHelper<kind> { \
			template <class I> \
			static void call(const I & integrator, const Array<Real> & f, \
			Array<Real> & intf, UInt nb_degree_of_freedom, \
			ElementType type, GhostType ghost_type, \
			const Array<UInt> & filter_elements) { \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(INTEGRATE, kind); \
			} \
			};

			AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_INTEGRATE_HELPER)

			#undef AKANTU_SPECIALIZE_INTEGRATE_HELPER
			#undef INTEGRATE
			} // namespace details
			} // namespace fe_engine

			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, UInt nb_degree_of_freedom,
			ElementType type, GhostType ghost_type,
			const Array<UInt> & filter_elements) const {

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

			UInt 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);

			fe_engine::details::IntegrateHelper<kind>::call(integrator, f, intf,
			nb_degree_of_freedom, type,
			ghost_type, filter_elements);
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Helper class to be able to write a partial specialization on the element kind
			*/
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct IntegrateScalarHelper {};

			#define INTEGRATE(type) \
			integral = \
			integrator.template integrate<type>(f, ghost_type, filter_elements);

			#define AKANTU_SPECIALIZE_INTEGRATE_SCALAR_HELPER(kind) \
			template <> struct IntegrateScalarHelper<kind> { \
			template <class I> \
			static Real call(const I & integrator, const Array<Real> & f, \
			ElementType type, GhostType ghost_type, \
			const Array<UInt> & filter_elements) { \
			Real integral = 0.; \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(INTEGRATE, kind); \
			return integral; \
			} \
			};

			AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_INTEGRATE_SCALAR_HELPER)

			#undef AKANTU_SPECIALIZE_INTEGRATE_SCALAR_HELPER
			#undef INTEGRATE
			} // namespace details
			} // namespace fe_engine

			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<UInt> & filter_elements) const {
			AKANTU_DEBUG_IN();

			#ifndef AKANTU_NDEBUG
			// std::stringstream sstr; sstr << ghost_type;
			// AKANTU_DEBUG_ASSERT(sstr.str() == nablauq.getTag(),
			// "The vector " << nablauq.getID() << " is not taged " <<
			// ghost_type);
			UInt nb_element = mesh.getNbElement(type, ghost_type);
			if (filter_elements != empty_filter) {
			nb_element = filter_elements.size();
			}

			UInt 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

			Real integral = fe_engine::details::IntegrateScalarHelper<kind>::call(
			integrator, f, type, ghost_type, filter_elements);
			AKANTU_DEBUG_OUT();
			return integral;
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Helper class to be able to write a partial specialization on the element kind
			*/
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct IntegrateScalarOnOneElementHelper {};

			#define INTEGRATE(type) \
			res = integrator.template integrate<type>(f, index, ghost_type);

			#define AKANTU_SPECIALIZE_INTEGRATE_SCALAR_ON_ONE_ELEMENT_HELPER(kind) \
			template <> struct IntegrateScalarOnOneElementHelper<kind> { \
			template <class I> \
			static Real call(const I & integrator, const Vector<Real> & f, \
			ElementType type, UInt index, GhostType ghost_type) { \
			Real res = 0.; \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(INTEGRATE, kind); \
			return res; \
			} \
			};

			AKANTU_BOOST_ALL_KIND(
			AKANTU_SPECIALIZE_INTEGRATE_SCALAR_ON_ONE_ELEMENT_HELPER)

			#undef AKANTU_SPECIALIZE_INTEGRATE_SCALAR_ON_ONE_ELEMENT_HELPER
			#undef INTEGRATE
			} // namespace details
			} // namespace fe_engine

			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			Real FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::integrate(
			const Vector<Real> & f, ElementType type, UInt index,
			GhostType ghost_type) const {

			Real res = fe_engine::details::IntegrateScalarOnOneElementHelper<kind>::call(
			integrator, f, type, index, ghost_type);
			return res;
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Helper class to be able to write a partial specialization on the element kind
			*/
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct IntegrateOnIntegrationPointsHelper {};

			#define INTEGRATE(type) \
			integrator.template integrateOnIntegrationPoints<type>( \
			f, intf, nb_degree_of_freedom, ghost_type, filter_elements);

			#define AKANTU_SPECIALIZE_INTEGRATE_ON_INTEGRATION_POINTS_HELPER(kind) \
			template <> struct IntegrateOnIntegrationPointsHelper<kind> { \
			template <class I> \
			static void call(const I & integrator, const Array<Real> & f, \
			Array<Real> & intf, UInt nb_degree_of_freedom, \
			ElementType type, GhostType ghost_type, \
			const Array<UInt> & filter_elements) { \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(INTEGRATE, kind); \
			} \
			};

			AKANTU_BOOST_ALL_KIND(
			AKANTU_SPECIALIZE_INTEGRATE_ON_INTEGRATION_POINTS_HELPER)

			#undef AKANTU_SPECIALIZE_INTEGRATE_ON_INTEGRATION_POINTS_HELPER
			#undef INTEGRATE
			} // namespace details
			} // namespace fe_engine

			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
			integrateOnIntegrationPoints(const Array<Real> & f, Array<Real> & intf,
			UInt nb_degree_of_freedom, ElementType type,
			GhostType ghost_type,
			const Array<UInt> & filter_elements) const {

			UInt nb_element = mesh.getNbElement(type, ghost_type);
			if (filter_elements != empty_filter) {
			nb_element = filter_elements.size();
			}
			UInt nb_quadrature_points = getNbIntegrationPoints(type);
			#ifndef AKANTU_NDEBUG
			// std::stringstream sstr; sstr << ghost_type;
			// AKANTU_DEBUG_ASSERT(sstr.str() == nablauq.getTag(),
			// "The vector " << nablauq.getID() << " is not taged " <<
			// ghost_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 * nb_quadrature_points);
			fe_engine::details::IntegrateOnIntegrationPointsHelper<kind>::call(
			integrator, f, intf, nb_degree_of_freedom, type, ghost_type,
			filter_elements);
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Helper class to be able to write a partial specialization on the element kind
			*/
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct InterpolateOnIntegrationPointsHelper {
			template <class S>
			static void call(const S & /unused/, const Array<Real> & /unused/,
			Array<Real> & /unused/, const UInt /unused/,
			ElementType /unused/, GhostType /unused/,
			const Array<UInt> & /unused/) {
			AKANTU_TO_IMPLEMENT();
			}
			};

			#define INTERPOLATE(type) \
			shape_functions.template interpolateOnIntegrationPoints<type>( \
			u, uq, nb_degree_of_freedom, ghost_type, filter_elements);

			#define AKANTU_SPECIALIZE_INTERPOLATE_ON_INTEGRATION_POINTS_HELPER(kind) \
			template <> struct InterpolateOnIntegrationPointsHelper<kind> { \
			template <class S> \
			static void call(const S & shape_functions, const Array<Real> & u, \
			Array<Real> & uq, const UInt nb_degree_of_freedom, \
			ElementType type, GhostType ghost_type, \
			const Array<UInt> & filter_elements) { \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(INTERPOLATE, kind); \
			} \
			};
			AKANTU_BOOST_ALL_KIND_LIST(
			AKANTU_SPECIALIZE_INTERPOLATE_ON_INTEGRATION_POINTS_HELPER,
			AKANTU_FE_ENGINE_LIST_INTERPOLATE_ON_INTEGRATION_POINTS)

			#undef AKANTU_SPECIALIZE_INTERPOLATE_ON_INTEGRATION_POINTS_HELPER
			#undef INTERPOLATE
			} // namespace details
			} // namespace fe_engine

			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,
			const UInt nb_degree_of_freedom,
			ElementType type, GhostType ghost_type,
			const Array<UInt> & filter_elements) const {
			AKANTU_DEBUG_IN();

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

			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.");
			#endif

			uq.resize(nb_element * nb_points);

			fe_engine::details::InterpolateOnIntegrationPointsHelper<kind>::call(
			shape_functions, u, uq, nb_degree_of_freedom, type, ghost_type,
			filter_elements);

			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<UInt> * filter_elements) const {
			AKANTU_DEBUG_IN();

			const Array<UInt> * filter = nullptr;

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

			UInt 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);
			}

			UInt 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();
			}

			/* -------------------------------------------------------------------------- */
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct ComputeBtDHelper {};

			#define COMPUTE_BTD(type) \
			shape_functions.template computeBtD<type>(Ds, BtDs, ghost_type, \
			filter_elements);

			#define AKANTU_SPECIALIZE_COMPUTE_BtD_HELPER(kind) \
			template <> struct ComputeBtDHelper<kind> { \
			template <class S> \
			static void call(const S & shape_functions, const Array<Real> & Ds, \
			Array<Real> & BtDs, ElementType type, \
			GhostType ghost_type, \
			const Array<UInt> & filter_elements) { \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(COMPUTE_BTD, kind); \
			} \
			};

			AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_COMPUTE_BtD_HELPER)

			#undef AKANTU_SPECIALIZE_COMPUTE_BtD_HELPER
			#undef COMPUTE_BTD
			} // namespace details
			} // namespace fe_engine

			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<UInt> & filter_elements) const {
			fe_engine::details::ComputeBtDHelper<kind>::call(
			shape_functions, Ds, BtDs, type, ghost_type, filter_elements);
			}

			/* -------------------------------------------------------------------------- */
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct ComputeBtDBHelper {};

			#define COMPUTE_BTDB(type) \
			shape_functions.template computeBtDB<type>(Ds, BtDBs, order_d, ghost_type, \
			filter_elements);

			#define AKANTU_SPECIALIZE_COMPUTE_BtDB_HELPER(kind) \
			template <> struct ComputeBtDBHelper<kind> { \
			template <class S> \
			static void call(const S & shape_functions, const Array<Real> & Ds, \
			Array<Real> & BtDBs, UInt order_d, ElementType type, \
			GhostType ghost_type, \
			const Array<UInt> & filter_elements) { \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(COMPUTE_BTDB, kind); \
			} \
			};

			AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_COMPUTE_BtDB_HELPER)

			#undef AKANTU_SPECIALIZE_COMPUTE_BtDB_HELPER
			#undef COMPUTE_BTDB
			} // namespace details
			} // namespace fe_engine

			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, UInt order_d, ElementType type,
			GhostType ghost_type, const Array<UInt> & filter_elements) const {
			fe_engine::details::ComputeBtDBHelper<kind>::call(
			shape_functions, Ds, BtDBs, order_d, type, ghost_type, filter_elements);
			}

			/* -------------------------------------------------------------------------- */
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct ComputeNtbNHelper {};

			#define COMPUTE_NtbN(type) \
			shape_functions.template computeNtbN<type>(bs, NtbNs, ghost_type, \
			filter_elements);

			#define AKANTU_SPECIALIZE_COMPUTE_NtbN_HELPER(kind) \
			template <> struct ComputeNtbNHelper<kind> { \
			template <class S> \
			static void call(const S & shape_functions, const Array<Real> & bs, \
			Array<Real> & NtbNs, ElementType type, \
			GhostType ghost_type, \
			const Array<UInt> & filter_elements) { \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(COMPUTE_NtbN, kind); \
			} \
			};

			AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_COMPUTE_NtbN_HELPER)

			#undef AKANTU_SPECIALIZE_COMPUTE_NtbN_HELPER
			#undef COMPUTE_NtbN
			} // namespace details
			} // namespace fe_engine

			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<UInt> & filter_elements) const {
			fe_engine::details::ComputeNtbNHelper<kind>::call(
			shape_functions, bs, NtbNs, type, ghost_type, filter_elements);
			}

			/* -------------------------------------------------------------------------- */
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct ComputeNtbHelper {};

			#define COMPUTE_Ntb(type) \
			shape_functions.template computeNtb<type>(bs, Ntbs, ghost_type, \
			filter_elements);

			#define AKANTU_SPECIALIZE_COMPUTE_Ntb_HELPER(kind) \
			template <> struct ComputeNtbHelper<kind> { \
			template <class S> \
			static void call(const S & shape_functions, const Array<Real> & bs, \
			Array<Real> & Ntbs, ElementType type, \
			GhostType ghost_type, \
			const Array<UInt> & filter_elements) { \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(COMPUTE_Ntb, kind); \
			} \
			};

			AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_COMPUTE_Ntb_HELPER)

			#undef AKANTU_SPECIALIZE_COMPUTE_Ntb_HELPER
			#undef COMPUTE_Ntb
			} // namespace details
			} // namespace fe_engine

			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<UInt> & filter_elements) const {
			fe_engine::details::ComputeNtbHelper<kind>::call(
			shape_functions, bs, Ntbs, 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>::
			computeIntegrationPointsCoordinates(
			ElementTypeMapArray<Real> & quadrature_points_coordinates,
			const ElementTypeMapArray<UInt> * 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<UInt> & filter_elements) const {

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

			UInt 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<UInt> * element_filter) const {

			AKANTU_DEBUG_IN();

			UInt 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, GhostType ghost_type,
			const ElementTypeMapArray<UInt> * 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, GhostType ghost_type,
			const ElementTypeMapArray<UInt> * element_filter) const {

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

			/* -------------------------------------------------------------------------- */
			/**
			* Helper class to be able to write a partial specialization on the element kind
			*/
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct InterpolateHelper {
			template <class S>
			static void call(const S & /unused/, const Vector<Real> & /unused/,
			UInt /unused/, const Matrix<Real> & /unused/,
			Vector<Real> & /unused/, ElementType /unused/,
			GhostType /unused/) {
			AKANTU_TO_IMPLEMENT();
			}
			};

			#define INTERPOLATE(type) \
			shape_functions.template interpolate<type>( \
			real_coords, element, nodal_values, interpolated, ghost_type);

			#define AKANTU_SPECIALIZE_INTERPOLATE_HELPER(kind) \
			template <> struct InterpolateHelper<kind> { \
			template <class S> \
			static void call(const S & shape_functions, \
			const Vector<Real> & real_coords, UInt element, \
			const Matrix<Real> & nodal_values, \
			Vector<Real> & interpolated, ElementType type, \
			GhostType ghost_type) { \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(INTERPOLATE, kind); \
			} \
			};

			AKANTU_BOOST_ALL_KIND_LIST(AKANTU_SPECIALIZE_INTERPOLATE_HELPER,
			AKANTU_FE_ENGINE_LIST_INTERPOLATE)

			#undef AKANTU_SPECIALIZE_INTERPOLATE_HELPER
			#undef INTERPOLATE
			} // namespace details
			} // namespace fe_engine

			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::interpolate(
			const Vector<Real> & real_coords, const Matrix<Real> & nodal_values,
			Vector<Real> & interpolated, const Element & element) const {

			AKANTU_DEBUG_IN();

			fe_engine::details::InterpolateHelper<kind>::call(
			shape_functions, real_coords, element.element, nodal_values, interpolated,
			element.type, element.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>::
			computeNormalsOnIntegrationPoints(GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			computeNormalsOnIntegrationPoints(mesh.getNodes(), 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>::
			computeNormalsOnIntegrationPoints(const Array<Real> & field,
			GhostType ghost_type) {
			AKANTU_DEBUG_IN();

			// Real * coord = mesh.getNodes().storage();
			UInt 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 (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();
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Helper class to be able to write a partial specialization on the element kind
			*/
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct ComputeNormalsOnIntegrationPoints {
			template <template <ElementKind, class> class I,
			template <ElementKind> class S, ElementKind k, class IOF>
			static void call(const FEEngineTemplate<I, S, k, IOF> & /unused/,
			const Array<Real> & /unused/, Array<Real> & /unused/,
			ElementType /unused/, GhostType /unused/) {
			AKANTU_TO_IMPLEMENT();
			}
			};

			#define COMPUTE_NORMALS_ON_INTEGRATION_POINTS(type) \
			fem.template computeNormalsOnIntegrationPoints<type>(field, normal, \
			ghost_type);

			#define AKANTU_SPECIALIZE_COMPUTE_NORMALS_ON_INTEGRATION_POINTS(kind) \
			template <> struct ComputeNormalsOnIntegrationPoints<kind> { \
			template <template <ElementKind, class> class I, \
			template <ElementKind> class S, ElementKind k, class IOF> \
			static void call(const FEEngineTemplate<I, S, k, IOF> & fem, \
			const Array<Real> & field, Array<Real> & normal, \
			ElementType type, GhostType ghost_type) { \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(COMPUTE_NORMALS_ON_INTEGRATION_POINTS, \
			kind); \
			} \
			};

			AKANTU_BOOST_ALL_KIND_LIST(
			AKANTU_SPECIALIZE_COMPUTE_NORMALS_ON_INTEGRATION_POINTS,
			AKANTU_FE_ENGINE_LIST_COMPUTE_NORMALS_ON_INTEGRATION_POINTS)

			#undef AKANTU_SPECIALIZE_COMPUTE_NORMALS_ON_INTEGRATION_POINTS
			#undef COMPUTE_NORMALS_ON_INTEGRATION_POINTS
			} // namespace details
			} // namespace fe_engine

			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 {
			fe_engine::details::ComputeNormalsOnIntegrationPoints<kind>::call(
			*this, field, normal, type, ghost_type);
			}

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

			if (type == _point_1) {
			computeNormalsOnIntegrationPointsPoint1(field, normal, ghost_type);
			return;
			}

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

			UInt nb_element = mesh.getConnectivity(type, ghost_type).size();
			normal.resize(nb_element * nb_points);
			Array<Real>::matrix_iterator normals_on_quad =
			normal.begin_reinterpret(spatial_dimension, nb_points, nb_element);
			Array<Real> f_el(0, spatial_dimension * nb_nodes_per_element);
			FEEngine::extractNodalToElementField(mesh, field, f_el, type, ghost_type);

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

			Array<Real>::matrix_iterator f_it =
			f_el.begin(spatial_dimension, nb_nodes_per_element);

			for (UInt elem = 0; elem < nb_element; ++elem) {
			ElementClass<type>::computeNormalsOnNaturalCoordinates(quads, *f_it,
			*normals_on_quad);
			++normals_on_quad;
			++f_it;
			}

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Helper class to be able to write a partial specialization on the element kind
			*/
			template <ElementKind kind> struct InverseMapHelper {
			template <class S>
			static void call(const S & /shape_functions/,
			const Vector<Real> & /real_coords/, UInt /element/,
			ElementType /type/, Vector<Real> & /natural_coords/,
			GhostType /ghost_type/) {
			AKANTU_TO_IMPLEMENT();
			}
			};

			#define INVERSE_MAP(type) \
			shape_functions.template inverseMap<type>(real_coords, element, \
			natural_coords, ghost_type);

			#define AKANTU_SPECIALIZE_INVERSE_MAP_HELPER(kind) \
			template <> struct InverseMapHelper<kind> { \
			template <class S> \
			static void call(const S & shape_functions, \
			const Vector<Real> & real_coords, UInt element, \
			ElementType type, Vector<Real> & natural_coords, \
			GhostType ghost_type) { \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(INVERSE_MAP, kind); \
			} \
			};

			AKANTU_BOOST_ALL_KIND_LIST(AKANTU_SPECIALIZE_INVERSE_MAP_HELPER,
			AKANTU_FE_ENGINE_LIST_INVERSE_MAP)

			#undef AKANTU_SPECIALIZE_INVERSE_MAP_HELPER
			#undef INVERSE_MAP

			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::inverseMap(
			const Vector<Real> & real_coords, UInt element, ElementType type,
			Vector<Real> & natural_coords, GhostType ghost_type) const {

			AKANTU_DEBUG_IN();

			InverseMapHelper<kind>::call(shape_functions, real_coords, element, type,
			natural_coords, ghost_type);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Helper class to be able to write a partial specialization on the element kind
			*/
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct ContainsHelper {
			template <class S>
			static void call(const S & /unused/, const Vector<Real> & /unused/,
			UInt /unused/, ElementType /unused/,
			GhostType /unused/) {
			AKANTU_TO_IMPLEMENT();
			}
			};

			#define CONTAINS(type) \
			contain = shape_functions.template contains<type>(real_coords, element, \
			ghost_type);

			#define AKANTU_SPECIALIZE_CONTAINS_HELPER(kind) \
			template <> struct ContainsHelper<kind> { \
			template <template <ElementKind> class S, ElementKind k> \
			static bool call(const S<k> & shape_functions, \
			const Vector<Real> & real_coords, UInt element, \
			ElementType type, GhostType ghost_type) { \
			bool contain = false; \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(CONTAINS, kind); \
			return contain; \
			} \
			};

			AKANTU_BOOST_ALL_KIND_LIST(AKANTU_SPECIALIZE_CONTAINS_HELPER,
			AKANTU_FE_ENGINE_LIST_CONTAINS)

			#undef AKANTU_SPECIALIZE_CONTAINS_HELPER
			#undef CONTAINS
			} // namespace details
			} // namespace fe_engine

			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline bool FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::contains(
			const Vector<Real> & real_coords, UInt element, ElementType type,
			GhostType ghost_type) const {
			return fe_engine::details::ContainsHelper<kind>::call(
			shape_functions, real_coords, element, type, ghost_type);
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Helper class to be able to write a partial specialization on the element kind
			*/
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct ComputeShapesHelper {
			template <class S>
			static void call(const S & /unused/, const Vector<Real> & /unused/,
			UInt /unused/, const ElementType /unused/,
			Vector<Real> & /unused/, GhostType /unused/) {
			AKANTU_TO_IMPLEMENT();
			}
			};

			#define COMPUTE_SHAPES(type) \
			shape_functions.template computeShapes<type>(real_coords, element, shapes, \
			ghost_type);

			#define AKANTU_SPECIALIZE_COMPUTE_SHAPES_HELPER(kind) \
			template <> struct ComputeShapesHelper<kind> { \
			template <class S> \
			static void call(const S & shape_functions, \
			const Vector<Real> & real_coords, UInt element, \
			const ElementType type, Vector<Real> & shapes, \
			GhostType ghost_type) { \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(COMPUTE_SHAPES, kind); \
			} \
			};

			AKANTU_BOOST_ALL_KIND_LIST(AKANTU_SPECIALIZE_COMPUTE_SHAPES_HELPER,
			AKANTU_FE_ENGINE_LIST_COMPUTE_SHAPES)

			#undef AKANTU_SPECIALIZE_COMPUTE_SHAPES_HELPER
			#undef COMPUTE_SHAPES
			} // namespace details
			} // namespace fe_engine
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline void
			FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::computeShapes(
			const Vector<Real> & real_coords, UInt element, ElementType type,
			Vector<Real> & shapes, GhostType ghost_type) const {

			AKANTU_DEBUG_IN();

			fe_engine::details::ComputeShapesHelper<kind>::call(
			shape_functions, real_coords, element, type, shapes, ghost_type);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Helper class to be able to write a partial specialization on the element kind
			*/
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct ComputeShapeDerivativesHelper {
			template <class S>
			static void call(__attribute__((unused)) const S & shape_functions,
			__attribute__((unused)) const Vector<Real> & real_coords,
			__attribute__((unused)) UInt element,
			__attribute__((unused)) const ElementType type,
			__attribute__((unused)) Matrix<Real> & shape_derivatives,
			__attribute__((unused)) GhostType ghost_type) {
			AKANTU_TO_IMPLEMENT();
			}
			};

			#define COMPUTE_SHAPE_DERIVATIVES(type) \
			Matrix<Real> coords_mat(real_coords.storage(), shape_derivatives.rows(), 1); \
			Tensor3<Real> shapesd_tensor(shape_derivatives.storage(), \
			shape_derivatives.rows(), \
			shape_derivatives.cols(), 1); \
			shape_functions.template computeShapeDerivatives<type>( \
			coords_mat, element, shapesd_tensor, ghost_type);

			#define AKANTU_SPECIALIZE_COMPUTE_SHAPE_DERIVATIVES_HELPER(kind) \
			template <> struct ComputeShapeDerivativesHelper<kind> { \
			template <class S> \
			static void call(const S & shape_functions, \
			const Vector<Real> & real_coords, UInt element, \
			const ElementType type, Matrix<Real> & shape_derivatives, \
			GhostType ghost_type) { \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(COMPUTE_SHAPE_DERIVATIVES, kind); \
			} \
			};

			AKANTU_BOOST_ALL_KIND_LIST(
			AKANTU_SPECIALIZE_COMPUTE_SHAPE_DERIVATIVES_HELPER,
			AKANTU_FE_ENGINE_LIST_COMPUTE_SHAPES_DERIVATIVES)

			#undef AKANTU_SPECIALIZE_COMPUTE_SHAPE_DERIVATIVES_HELPER
			#undef COMPUTE_SHAPE_DERIVATIVES
			} // namespace details
			} // namespace fe_engine

			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline void
			FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::computeShapeDerivatives(
			const Vector<Real> & real_coords, UInt element, ElementType type,
			Matrix<Real> & shape_derivatives, GhostType ghost_type) const {
			AKANTU_DEBUG_IN();

			fe_engine::details::ComputeShapeDerivativesHelper<kind>::call(
			shape_functions, real_coords, element, type, shape_derivatives,
			ghost_type);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Helper class to be able to write a partial specialization on the element kind
			*/
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct GetNbIntegrationPointsHelper {};

			#define GET_NB_INTEGRATION_POINTS(type) \
			nb_quad_points = integrator.template getNbIntegrationPoints<type>(ghost_type);

			#define AKANTU_SPECIALIZE_GET_NB_INTEGRATION_POINTS_HELPER(kind) \
			template <> struct GetNbIntegrationPointsHelper<kind> { \
			template <template <ElementKind, class> class I, ElementKind k, class IOF> \
			static UInt call(const I<k, IOF> & integrator, const ElementType type, \
			GhostType ghost_type) { \
			UInt nb_quad_points = 0; \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(GET_NB_INTEGRATION_POINTS, kind); \
			return nb_quad_points; \
			} \
			};

			AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_GET_NB_INTEGRATION_POINTS_HELPER)

			#undef AKANTU_SPECIALIZE_GET_NB_INTEGRATION_POINTS_HELPER
			#undef GET_NB_INTEGRATION
			} // namespace details
			} // namespace fe_engine

			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline UInt
			FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::getNbIntegrationPoints(
			ElementType type, GhostType ghost_type) const {
			return fe_engine::details::GetNbIntegrationPointsHelper<kind>::call(
			integrator, type, ghost_type);
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Helper class to be able to write a partial specialization on the element kind
			*/
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct GetShapesHelper {};

			#define GET_SHAPES(type) ret = &(shape_functions.getShapes(type, ghost_type));

			#define AKANTU_SPECIALIZE_GET_SHAPES_HELPER(kind) \
			template <> struct GetShapesHelper<kind> { \
			template <class S> \
			static const Array<Real> & call(const S & shape_functions, \
			const ElementType type, \
			GhostType ghost_type) { \
			const Array<Real> * ret = NULL; \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(GET_SHAPES, kind); \
			return *ret; \
			} \
			};

			AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_GET_SHAPES_HELPER)

			#undef AKANTU_SPECIALIZE_GET_SHAPES_HELPER
			#undef GET_SHAPES
			} // namespace details
			} // namespace fe_engine

			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,
			__attribute__((unused)) UInt id) const {
			return fe_engine::details::GetShapesHelper<kind>::call(shape_functions, type,
			ghost_type);
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Helper class to be able to write a partial specialization on the element kind
			*/
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct GetShapesDerivativesHelper {
			template <template <ElementKind> class S, ElementKind k>
			static const Array<Real> & call(const S<k> & /unused/,
			ElementType /unused/,
			GhostType /unused/, UInt /unused/) {
			AKANTU_TO_IMPLEMENT();
			}
			};

			#define GET_SHAPES_DERIVATIVES(type) \
			ret = &(shape_functions.getShapesDerivatives(type, ghost_type));

			#define AKANTU_SPECIALIZE_GET_SHAPES_DERIVATIVES_HELPER(kind) \
			template <> struct GetShapesDerivativesHelper<kind> { \
			template <template <ElementKind> class S, ElementKind k> \
			static const Array<Real> & \
			call(const S<k> & shape_functions, const ElementType type, \
			GhostType ghost_type, __attribute__((unused)) UInt id) { \
			const Array<Real> * ret = NULL; \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(GET_SHAPES_DERIVATIVES, kind); \
			return *ret; \
			} \
			};

			AKANTU_BOOST_ALL_KIND_LIST(AKANTU_SPECIALIZE_GET_SHAPES_DERIVATIVES_HELPER,
			AKANTU_FE_ENGINE_LIST_GET_SHAPES_DERIVATIVES)

			#undef AKANTU_SPECIALIZE_GET_SHAPE_DERIVATIVES_HELPER
			#undef GET_SHAPES_DERIVATIVES
			} // namespace details
			} // namespace fe_engine

			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,
			__attribute__((unused)) UInt id) const {
			return fe_engine::details::GetShapesDerivativesHelper<kind>::call(
			shape_functions, type, ghost_type, id);
			}

			/* -------------------------------------------------------------------------- */
			/**
			* Helper class to be able to write a partial specialization on the element kind
			*/
			namespace fe_engine {
			namespace details {
			template <ElementKind kind> struct GetIntegrationPointsHelper {};

			#define GET_INTEGRATION_POINTS(type) \
			ret = &(integrator.template getIntegrationPoints<type>(ghost_type));

			#define AKANTU_SPECIALIZE_GET_INTEGRATION_POINTS_HELPER(kind) \
			template <> struct GetIntegrationPointsHelper<kind> { \
			template <template <ElementKind, class> class I, ElementKind k, class IOF> \
			static const Matrix<Real> & call(const I<k, IOF> & integrator, \
			const ElementType type, \
			GhostType ghost_type) { \
			const Matrix<Real> * ret = NULL; \
			AKANTU_BOOST_KIND_ELEMENT_SWITCH(GET_INTEGRATION_POINTS, kind); \
			return *ret; \
			} \
			};

			AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_GET_INTEGRATION_POINTS_HELPER)

			#undef AKANTU_SPECIALIZE_GET_INTEGRATION_POINTS_HELPER
			#undef GET_INTEGRATION_POINTS
			} // namespace details
			} // namespace fe_engine

			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 fe_engine::details::GetIntegrationPointsHelper<kind>::call(
			integrator, type, ghost_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);
			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> & /unused/,
			const ElementTypeMapArray<UInt> & /unused/,
			const RemovedElementsEvent & /unused/) {}

			/* -------------------------------------------------------------------------- */
			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<UInt> & /unused/,
			const ChangedElementsEvent & /unused/) {}

			/* -------------------------------------------------------------------------- */
			template <template <ElementKind, class> class I, template <ElementKind> class S,
			ElementKind kind, class IntegrationOrderFunctor>
			inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
			computeNormalsOnIntegrationPointsPoint1(const Array<Real> & /unused/,
			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!");
			const auto type = _point_1;
			auto spatial_dimension = mesh.getSpatialDimension();
			// UInt 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 =
			normal.begin_reinterpret(spatial_dimension, nb_points, nb_element);
			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 (UInt elem = 0; elem < nb_element; ++elem) {
			UInt 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<UInt> 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 (UInt n(0); n < nb_points; ++n) {
			(*normals_on_quad)(0, n) = normal_value;
			}
			++normals_on_quad;
			}

			AKANTU_DEBUG_OUT();
			}

			} // namespace akantu

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rAKA/src/fe_engine/fe_engine_template_tmpl.hh
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