fe_engine_template_tmpl.hh
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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 Dana Christen <dana.christen@gmail.com>
	* @author Mauro Corrado <mauro.corrado@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
	* @author Mohit Pundir <mohit.pundir@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: Fri May 14 2021
	*
	* @brief Template implementation of FEEngineTemplate
	*
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2021 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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