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 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: Thu Nov 19 2015
	*
	* @brief Template implementation of FEEngineTemplate
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2012, 2014, 2015 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"

	__BEGIN_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, ID id, MemoryID memory_id)
	: FEEngine(mesh, spatial_dimension, id, memory_id),
	integrator(mesh, id, memory_id), shape_functions(mesh, id, memory_id) {}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::~FEEngineTemplate() {}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	template <ElementKind kind> struct GradientOnIntegrationPointsHelper {
	template <class S>
	static void call(__attribute__((unused)) const S & shape_functions,
	__attribute__((unused)) Mesh & mesh,
	__attribute__((unused)) const Array<Real> & u,
	__attribute__((unused)) Array<Real> & nablauq,
	__attribute__((unused)) const UInt nb_degree_of_freedom,
	__attribute__((unused)) const ElementType & type,
	__attribute__((unused)) const GhostType & ghost_type,
	__attribute__((unused))
	const Array<UInt> & filter_elements) {
	AKANTU_DEBUG_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, \
	const ElementType & type, const 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

	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,
	const ElementType & type,
	const 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.getSize();
	UInt nb_points =
	shape_functions.getIntegrationPoints(type, ghost_type).cols();

	#ifndef AKANTU_NDEBUG

	UInt element_dimension = mesh.getSpatialDimension(type);

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

	nablauq.resize(nb_element * nb_points);

	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(
	const 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, const GhostType & ghost_type) {
	AKANTU_DEBUG_IN();

	Mesh::type_iterator it = mesh.firstType(element_dimension, ghost_type, kind);
	Mesh::type_iterator end = mesh.lastType(element_dimension, ghost_type, kind);
	for (; it != end; ++it) {
	ElementType type = *it;
	integrator.initIntegrator(nodes, type, ghost_type);
	const Matrix<Real> & 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
	*/
	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, \
	const ElementType & type, const 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

	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,
	const ElementType & type, const 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.getSize();
	#ifndef AKANTU_NDEBUG

	UInt nb_quadrature_points = getNbIntegrationPoints(type);

	AKANTU_DEBUG_ASSERT(f.getSize() == nb_element * nb_quadrature_points,
	"The vector f(" << f.getID() << " size " << f.getSize()
	<< ") 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);

	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
	*/
	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, \
	const ElementType & type, const 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

	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, const ElementType & type,
	const 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.getSize();

	UInt nb_quadrature_points = getNbIntegrationPoints(type, ghost_type);

	AKANTU_DEBUG_ASSERT(f.getSize() == nb_element * nb_quadrature_points,
	"The vector f("
	<< f.getID() << ") has not the good size. ("
	<< f.getSize()
	<< "!=" << 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 = 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
	*/
	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, \
	const ElementType & type, UInt index, \
	const 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

	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, const ElementType & type, UInt index,
	const GhostType & ghost_type) const {

	Real res = 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
	*/
	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, \
	const ElementType & type, const 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

	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,
	const ElementType & type,
	const 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.getSize();
	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.getSize() == nb_element * nb_quadrature_points,
	"The vector f(" << f.getID() << " size " << f.getSize()
	<< ") 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);
	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
	*/
	template <ElementKind kind> struct InterpolateOnIntegrationPointsHelper {
	template <class S>
	static void call(__attribute__((unused)) const S & shape_functions,
	__attribute__((unused)) const Array<Real> & u,
	__attribute__((unused)) Array<Real> & uq,
	__attribute__((unused)) const UInt nb_degree_of_freedom,
	__attribute__((unused)) const ElementType & type,
	__attribute__((unused)) const GhostType & ghost_type,
	__attribute__((unused))
	const Array<UInt> & filter_elements) {
	AKANTU_DEBUG_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, \
	const ElementType & type, const 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

	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,
	const ElementType & type,
	const 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.getSize();
	#ifndef AKANTU_NDEBUG

	AKANTU_DEBUG_ASSERT(u.getSize() == 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);

	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 = NULL;

	for (ghost_type_t::iterator gt = ghost_type_t::begin();
	gt != ghost_type_t::end(); ++gt) {

	GhostType ghost_type = *gt;
	ElementTypeMapArray<Real>::type_iterator it =
	uq.firstType(_all_dimensions, ghost_type, kind);
	ElementTypeMapArray<Real>::type_iterator last =
	uq.lastType(_all_dimensions, ghost_type, kind);

	for (; it != last; ++it) {
	ElementType type = *it;

	UInt nb_quad_per_element = getNbIntegrationPoints(type, ghost_type);

	UInt nb_element = 0;

	if (filter_elements) {
	filter = &((*filter_elements)(type, ghost_type));
	nb_element = filter->getSize();
	} 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();
	}

	/* -------------------------------------------------------------------------- */
	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, const ElementType & type,
	const 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(),
	getMemoryID());
	mesh.initElementTypeMapArray(quadrature_points_coordinates, spatial_dimension,
	spatial_dimension);
	computeIntegrationPointsCoordinates(quadrature_points_coordinates,
	element_filter);
	shape_functions.initElementalFieldInterpolationFromIntegrationPoints(
	interpolation_points_coordinates,
	interpolation_points_coordinates_matrices,
	quad_points_coordinates_inv_matrices, quadrature_points_coordinates,
	element_filter);
	}

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

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

	initElementalFieldInterpolationFromIntegrationPoints(
	interpolation_points_coordinates,
	interpolation_points_coordinates_matrices,
	quad_points_coordinates_inv_matrices, element_filter);

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

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	interpolateElementalFieldFromIntegrationPoints(
	const ElementTypeMapArray<Real> & field,
	const ElementTypeMapArray<Real> &
	interpolation_points_coordinates_matrices,
	const ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
	ElementTypeMapArray<Real> & result, const GhostType ghost_type,
	const ElementTypeMapArray<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
	*/
	template <ElementKind kind> struct InterpolateHelper {
	template <class S>
	static void call(__attribute__((unused)) const S & shape_functions,
	__attribute__((unused)) const Vector<Real> & real_coords,
	__attribute__((unused)) UInt elem,
	__attribute__((unused)) const Matrix<Real> & nodal_values,
	__attribute__((unused)) Vector<Real> & interpolated,
	__attribute__((unused)) const ElementType & type,
	__attribute__((unused)) const GhostType & ghost_type) {
	AKANTU_DEBUG_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, const ElementType & type, \
	const 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

	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();

	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(const 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,
	const GhostType & ghost_type) {
	AKANTU_DEBUG_IN();

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

	// allocate the normal arrays
	Mesh::type_iterator it = mesh.firstType(element_dimension, ghost_type, kind);
	Mesh::type_iterator end = mesh.lastType(element_dimension, ghost_type, kind);
	for (; it != end; ++it) {
	ElementType type = *it;
	UInt size = mesh.getNbElement(type, ghost_type);
	if (normals_on_integration_points.exists(type, ghost_type)) {
	normals_on_integration_points(type, ghost_type).resize(size);
	} else {
	normals_on_integration_points.alloc(size, spatial_dimension, type,
	ghost_type);
	}
	}

	// loop over the type to build the normals
	it = mesh.firstType(element_dimension, ghost_type, kind);
	for (; it != end; ++it) {
	Array<Real> & normals_on_quad =
	normals_on_integration_points(*it, ghost_type);
	computeNormalsOnIntegrationPoints(field, normals_on_quad, *it, ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	template <ElementKind kind> struct ComputeNormalsOnIntegrationPoints {
	template <template <ElementKind, class> class I,
	template <ElementKind> class S, ElementKind k, class IOF>
	static void call(__attribute__((unused))
	const FEEngineTemplate<I, S, k, IOF> & fem,
	__attribute__((unused)) const Array<Real> & field,
	__attribute__((unused)) Array<Real> & normal,
	__attribute__((unused)) const ElementType & type,
	__attribute__((unused)) const GhostType & ghost_type) {
	AKANTU_DEBUG_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, \
	const ElementType & type, const 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

	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,
	const ElementType & type,
	const GhostType & ghost_type) const {
	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,
	const GhostType & ghost_type) const {
	AKANTU_DEBUG_IN();

	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).getSize();
	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();
	}

	/* -------------------------------------------------------------------------- */
	/* Matrix lumping functions */
	/* -------------------------------------------------------------------------- */

	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	template <ElementKind kind> struct AssembleLumpedTemplateHelper {};

	#define ASSEMBLE_LUMPED(type) \
	fem.template assembleLumpedTemplate<type>( \
	field_1, nb_degree_of_freedom, lumped, equation_number, ghost_type)

	#define AKANTU_SPECIALIZE_ASSEMBLE_HELPER(kind) \
	template <> struct AssembleLumpedTemplateHelper<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_1, UInt nb_degree_of_freedom, \
	Array<Real> & lumped, const Array<Int> & equation_number, \
	ElementType type, const GhostType & ghost_type) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(ASSEMBLE_LUMPED, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_ASSEMBLE_HELPER)

	#undef AKANTU_SPECIALIZE_ASSEMBLE_HELPER
	#undef ASSEMBLE_LUMPED

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::assembleFieldLumped(
	const Array<Real> & field_1, UInt nb_degree_of_freedom,
	Array<Real> & lumped, const Array<Int> & equation_number, ElementType type,
	const GhostType & ghost_type) const {
	AKANTU_DEBUG_IN();

	AssembleLumpedTemplateHelper<kind>::call(*this, field_1, nb_degree_of_freedom,
	lumped, equation_number, type,
	ghost_type);

	AKANTU_DEBUG_OUT();
	}

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

	#define ASSEMBLE_MATRIX(type) \
	fem.template assembleFieldMatrix<Functor, type>( \
	field_funct, nb_degree_of_freedom, matrix, ghost_type)

	#define AKANTU_SPECIALIZE_ASSEMBLE_FIELD_MATRIX_HELPER(kind) \
	template <> struct AssembleFieldMatrixHelper<kind> { \
	template <template <ElementKind, class> class I, \
	template <ElementKind> class S, ElementKind k, class IOF, \
	class Functor> \
	static void call(const FEEngineTemplate<I, S, k, IOF> & fem, \
	Functor field_funct, UInt nb_degree_of_freedom, \
	SparseMatrix & matrix, ElementType type, \
	const GhostType & ghost_type) { \
	AKANTU_BOOST_KIND_ELEMENT_SWITCH(ASSEMBLE_MATRIX, kind); \
	} \
	};

	AKANTU_BOOST_ALL_KIND(AKANTU_SPECIALIZE_ASSEMBLE_FIELD_MATRIX_HELPER)

	#undef AKANTU_SPECIALIZE_ASSEMBLE_FIELD_MATRIX_HELPER
	#undef ASSEMBLE_MATRIX

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	template <class Functor>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::assembleFieldMatrix(
	Functor field_funct, UInt nb_degree_of_freedom, SparseMatrix & matrix,
	ElementType type, const GhostType & ghost_type) const {
	AKANTU_DEBUG_IN();
	AssembleFieldMatrixHelper<kind>::template call(
	*this, field_funct, nb_degree_of_freedom, matrix, type, ghost_type);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	assembleLumpedTemplate(const Array<Real> & field_1,
	UInt nb_degree_of_freedom, Array<Real> & lumped,
	const Array<Int> & equation_number,
	const GhostType & ghost_type) const {
	this->template assembleLumpedRowSum<type>(
	field_1, nb_degree_of_freedom, lumped, equation_number, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	/**
	* @f$ \tilde{M}_{i} = \sum_j M_{ij} = \sum_j \int \rho \varphi_i \varphi_j dV =
	* \int \rho \varphi_i dV @f$
	*/
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	assembleLumpedRowSum(const Array<Real> & field_1, UInt nb_degree_of_freedom,
	Array<Real> & lumped,
	const Array<Int> & equation_number,
	const GhostType & ghost_type) const {
	AKANTU_DEBUG_IN();

	UInt shapes_size = ElementClass<type>::getShapeSize();

	Array<Real> * field_times_shapes =
	new Array<Real>(0, shapes_size * nb_degree_of_freedom);
	Array<Real> * field =
	new Array<Real>(field_1.getSize(), nb_degree_of_freedom);

	Array<Real>::const_scalar_iterator f1_it = field_1.begin();
	Array<Real>::const_scalar_iterator f1_end = field_1.end();
	Array<Real>::vector_iterator f_it = field->begin(nb_degree_of_freedom);

	for (; f1_it != f1_end; ++f1_it, ++f_it) {
	f_it->set(*f1_it);
	}

	shape_functions.template fieldTimesShapes<type>(field, field_times_shapes,
	ghost_type);
	delete field;

	UInt nb_element = mesh.getNbElement(type, ghost_type);
	Array<Real> * int_field_times_shapes = new Array<Real>(
	nb_element, shapes_size * nb_degree_of_freedom, "inte_rho_x_shapes");
	integrator.template integrate<type>(
	field_times_shapes, int_field_times_shapes,
	nb_degree_of_freedom * shapes_size, ghost_type, empty_filter);
	delete field_times_shapes;

	assembleArray(*int_field_times_shapes, lumped, equation_number,
	nb_degree_of_freedom, type, ghost_type);
	delete int_field_times_shapes;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* @f$ \tilde{M}_{i} = c * M_{ii} = \int_{V_e} \rho dV @f$
	*/
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	template <ElementType type>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::
	assembleLumpedDiagonalScaling(const Array<Real> & field_1,
	UInt nb_degree_of_freedom,
	Array<Real> & lumped,
	const Array<Int> & equation_number,
	const GhostType & ghost_type) const {
	AKANTU_DEBUG_IN();

	const ElementType & type_p1 = ElementClass<type>::getP1ElementType();
	UInt nb_nodes_per_element_p1 = Mesh::getNbNodesPerElement(type_p1);
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	UInt nb_quadrature_points =
	integrator.template getIntegrationPoints<type>(ghost_type).cols();

	UInt nb_element = field_1.getSize() / nb_quadrature_points;
	Vector<Real> nodal_factor(nb_nodes_per_element);

	#define ASSIGN_WEIGHT_TO_NODES(corner, mid) \
	{ \
	for (UInt n = 0; n < nb_nodes_per_element_p1; n++) \
	nodal_factor(n) = corner; \
	for (UInt n = nb_nodes_per_element_p1; n < nb_nodes_per_element; n++) \
	nodal_factor(n) = mid; \
	}

	if (type == _triangle_6)
	ASSIGN_WEIGHT_TO_NODES(1. / 12., 1. / 4.);
	if (type == _tetrahedron_10)
	ASSIGN_WEIGHT_TO_NODES(1. / 32., 7. / 48.);
	if (type == _quadrangle_8)
	ASSIGN_WEIGHT_TO_NODES(3. / 76., 16. / 76.); /** coeff. derived by scaling
	* the diagonal terms of the corresponding
	* consistent mass computed with 3x3 gauss points;
	* coeff. are (1./36., 8./36.) for 2x2 gauss points */
	if (type == _hexahedron_20)
	ASSIGN_WEIGHT_TO_NODES(7. / 248., 16. / 248.); /** coeff. derived by scaling
	* the diagonal terms of the corresponding
	* consistent mass computed with 3x3x3 gauss points;
	* coeff. are (1./40.,
	* 1./15.) for 2x2x2 gauss points */
	if (type == _pentahedron_15) {
	// coefficients derived by scaling the diagonal terms of the corresponding
	// consistent mass computed with 8 gauss points;
	for (UInt n = 0; n < nb_nodes_per_element_p1; n++)
	nodal_factor(n) = 51. / 2358.;

	Real mid_triangle = 192. / 2358.;
	Real mid_quadrangle = 300. / 2358.;

	nodal_factor(6) = mid_triangle;
	nodal_factor(7) = mid_triangle;
	nodal_factor(8) = mid_triangle;
	nodal_factor(9) = mid_quadrangle;
	nodal_factor(10) = mid_quadrangle;
	nodal_factor(11) = mid_quadrangle;
	nodal_factor(12) = mid_triangle;
	nodal_factor(13) = mid_triangle;
	nodal_factor(14) = mid_triangle;
	}

	if (nb_element == 0) {
	AKANTU_DEBUG_OUT();
	return;
	}

	#undef ASSIGN_WEIGHT_TO_NODES

	/// compute @f$ \int \rho dV = \rho V @f$ for each element
	Array<Real> * int_field_1 =
	new Array<Real>(field_1.getSize(), 1, "inte_rho_x_1");
	integrator.template integrate<type>(field_1, *int_field_1, 1, ghost_type,
	empty_filter);

	/// distribute the mass of the element to the nodes
	Array<Real> * lumped_per_node = new Array<Real>(
	nb_element, nb_degree_of_freedom * nb_nodes_per_element, "mass_per_node");
	Array<Real>::const_scalar_iterator int_field_1_it = int_field_1->begin();
	Array<Real>::matrix_iterator lumped_per_node_it =
	lumped_per_node->begin(nb_degree_of_freedom, nb_nodes_per_element);

	for (UInt e = 0; e < nb_element; ++e) {
	for (UInt n = 0; n < nb_nodes_per_element; ++n) {
	Real lmass = int_field_1_it nodal_factor(n);
	Vector<Real> l = (*lumped_per_node_it)(n);
	l.set(lmass);
	}
	++int_field_1_it;
	++lumped_per_node_it;
	}
	delete int_field_1;

	// lumped_per_node->extendComponentsInterlaced(nb_degree_of_freedom,1);
	assembleArray(*lumped_per_node, lumped, equation_number, nb_degree_of_freedom,
	type, ghost_type);
	delete lumped_per_node;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	/**
	* @f$ \tilde{M}_{i} = \sum_j M_{ij} = \sum_j \int \rho \varphi_i \varphi_j dV =
	* \int \rho \varphi_i dV @f$
	*/
	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	template <class Functor, ElementType type>
	void FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::assembleFieldMatrix(
	Functor & field_funct, UInt nb_degree_of_freedom, SparseMatrix & matrix,
	const GhostType & ghost_type) const {
	AKANTU_DEBUG_IN();

	UInt shapes_size = ElementClass<type>::getShapeSize();
	UInt lmat_size = nb_degree_of_freedom * shapes_size;
	UInt nb_element = mesh.getNbElement(type, ghost_type);

	const UInt polynomial_degree =
	2 * ElementClassProperty<type>::polynomial_degree;

	Matrix<Real> integration_points =
	integrator.template getIntegrationPoints<type, polynomial_degree>();

	UInt nb_integration_points = integration_points.cols();
	UInt vect_size = nb_integration_points * nb_element;

	Array<Real> shapes(0, shapes_size);
	shape_functions.template computeShapesOnIntegrationPoints<type>(
	mesh.getNodes(), integration_points, shapes, ghost_type);

	Array<Real> integration_points_pos(vect_size, mesh.getSpatialDimension());
	shape_functions.template interpolateElementalFieldOnIntegrationPoints<type>(
	mesh.getNodes(), integration_points_pos, ghost_type, shapes,
	empty_filter);

	Array<Real> * modified_shapes =
	new Array<Real>(vect_size, lmat_size * nb_degree_of_freedom);
	modified_shapes->clear();
	Array<Real> * local_mat = new Array<Real>(vect_size, lmat_size * lmat_size);

	Array<Real>::matrix_iterator mshapes_it =
	modified_shapes->begin(lmat_size, nb_degree_of_freedom);
	Array<Real>::const_vector_iterator shapes_it = shapes.begin(shapes_size);

	for (UInt q = 0; q < vect_size; ++q, ++mshapes_it, ++shapes_it) {
	for (UInt d = 0; d < nb_degree_of_freedom; ++d) {
	for (UInt s = 0; s < shapes_size; ++s) {
	(mshapes_it)(s nb_degree_of_freedom + d, d) = (*shapes_it)(s);
	}
	}
	}

	Array<Real> field(vect_size, nb_degree_of_freedom);
	Array<Real>::matrix_iterator field_c_it = field.begin_reinterpret(
	nb_degree_of_freedom, nb_integration_points, nb_element);
	Array<Real>::const_matrix_iterator pos_it =
	integration_points_pos.begin_reinterpret(
	mesh.getSpatialDimension(), nb_integration_points, nb_element);
	Element el;
	el.type = type, el.ghost_type = ghost_type;

	for (el.element = 0; el.element < nb_element;
	++el.element, ++field_c_it, ++pos_it) {
	field_funct(field_c_it, el, pos_it);
	}

	mshapes_it = modified_shapes->begin(lmat_size, nb_degree_of_freedom);
	Array<Real>::matrix_iterator lmat = local_mat->begin(lmat_size, lmat_size);
	Array<Real>::const_scalar_iterator field_val = field.begin();

	for (UInt q = 0; q < vect_size; ++q, ++lmat, ++mshapes_it, ++field_val) {
	(lmat).mul<false, true>(mshapes_it, mshapes_it, field_val);
	}

	delete modified_shapes;

	Array<Real> * int_field_times_shapes =
	new Array<Real>(nb_element, lmat_size * lmat_size, "inte_rho_x_shapes");
	this->integrator.template integrate<type, polynomial_degree>(
	local_mat, int_field_times_shapes, lmat_size * lmat_size, ghost_type);
	delete local_mat;

	assembleMatrix(*int_field_times_shapes, matrix, nb_degree_of_freedom, type,
	ghost_type);
	delete int_field_times_shapes;

	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(__attribute__((unused)) const S & shape_functions,
	__attribute__((unused)) const Vector<Real> & real_coords,
	__attribute__((unused)) UInt element,
	__attribute__((unused)) const ElementType & type,
	__attribute__((unused)) Vector<Real> & natural_coords,
	__attribute__((unused)) const GhostType & ghost_type) {
	AKANTU_DEBUG_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, \
	const ElementType & type, Vector<Real> & natural_coords, \
	const 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, const ElementType & type,
	Vector<Real> & natural_coords, const 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
	*/
	template <ElementKind kind> struct ContainsHelper {
	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)) const GhostType & ghost_type) {
	AKANTU_DEBUG_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, \
	const ElementType & type, const 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

	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, const ElementType & type,
	const GhostType & ghost_type) const {
	return 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
	*/
	template <ElementKind kind> struct ComputeShapesHelper {
	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)) Vector<Real> & shapes,
	__attribute__((unused)) const GhostType & ghost_type) {
	AKANTU_DEBUG_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, \
	const 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

	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, const ElementType & type,
	Vector<Real> & shapes, const GhostType & ghost_type) const {

	AKANTU_DEBUG_IN();

	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
	*/
	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)) const GhostType & ghost_type) {
	AKANTU_DEBUG_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, \
	const 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

	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, const ElementType & type,
	Matrix<Real> & shape_derivatives, const GhostType & ghost_type) const {
	AKANTU_DEBUG_IN();

	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
	*/
	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, \
	const 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

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

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	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, \
	const 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

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline const Array<Real> &
	FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::getShapes(
	const ElementType & type, const GhostType & ghost_type,
	__attribute__((unused)) UInt id) const {
	return GetShapesHelper<kind>::call(shape_functions, type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	template <ElementKind kind> struct GetShapesDerivativesHelper {
	template <template <ElementKind> class S, ElementKind k>
	static const Array<Real> &
	call(__attribute__((unused)) const S<k> & shape_functions,
	__attribute__((unused)) const ElementType & type,
	__attribute__((unused)) const GhostType & ghost_type, UInt id) {
	AKANTU_DEBUG_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, \
	const 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

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline const Array<Real> &
	FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::getShapesDerivatives(
	const ElementType & type, const GhostType & ghost_type,
	__attribute__((unused)) UInt id) const {
	return GetShapesDerivativesHelper<kind>::call(shape_functions, type,
	ghost_type, id);
	}

	/* -------------------------------------------------------------------------- */
	/**
	* Helper class to be able to write a partial specialization on the element kind
	*/
	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, \
	const 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

	template <template <ElementKind, class> class I, template <ElementKind> class S,
	ElementKind kind, class IntegrationOrderFunctor>
	inline const Matrix<Real> &
	FEEngineTemplate<I, S, kind, IntegrationOrderFunctor>::getIntegrationPoints(
	const ElementType & type, const GhostType & ghost_type) const {
	return 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;
	for (Int i = 0; i < indent; i++, space += 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;
	}

	/* -------------------------------------------------------------------------- */

	__END_AKANTU__

	#include "integrator_gauss.hh"
	#include "shape_lagrange.hh"

	__BEGIN_AKANTU__

	/* -------------------------------------------------------------------------- */
	template <>
	template <>
	inline void FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_regular,
	DefaultIntegrationOrderFunctor>::
	assembleLumpedTemplate<_triangle_6>(const Array<Real> & field_1,
	UInt nb_degree_of_freedom,
	Array<Real> & lumped,
	const Array<Int> & equation_number,
	const GhostType & ghost_type) const {
	assembleLumpedDiagonalScaling<_triangle_6>(
	field_1, nb_degree_of_freedom, lumped, equation_number, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	template <>
	inline void FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_regular,
	DefaultIntegrationOrderFunctor>::
	assembleLumpedTemplate<_tetrahedron_10>(
	const Array<Real> & field_1, UInt nb_degree_of_freedom,
	Array<Real> & lumped, const Array<Int> & equation_number,
	const GhostType & ghost_type) const {
	assembleLumpedDiagonalScaling<_tetrahedron_10>(
	field_1, nb_degree_of_freedom, lumped, equation_number, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	template <>
	inline void FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_regular,
	DefaultIntegrationOrderFunctor>::
	assembleLumpedTemplate<_quadrangle_8>(const Array<Real> & field_1,
	UInt nb_degree_of_freedom,
	Array<Real> & lumped,
	const Array<Int> & equation_number,
	const GhostType & ghost_type) const {
	assembleLumpedDiagonalScaling<_quadrangle_8>(
	field_1, nb_degree_of_freedom, lumped, equation_number, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	template <>
	inline void FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_regular,
	DefaultIntegrationOrderFunctor>::
	assembleLumpedTemplate<_hexahedron_20>(const Array<Real> & field_1,
	UInt nb_degree_of_freedom,
	Array<Real> & lumped,
	const Array<Int> & equation_number,
	const GhostType & ghost_type) const {
	assembleLumpedDiagonalScaling<_hexahedron_20>(
	field_1, nb_degree_of_freedom, lumped, equation_number, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	template <>
	inline void FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_regular,
	DefaultIntegrationOrderFunctor>::
	assembleLumpedTemplate<_pentahedron_15>(
	const Array<Real> & field_1, UInt nb_degree_of_freedom,
	Array<Real> & lumped, const Array<Int> & equation_number,
	const GhostType & ghost_type) const {
	assembleLumpedDiagonalScaling<_pentahedron_15>(
	field_1, nb_degree_of_freedom, lumped, equation_number, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	template <>
	template <>
	inline void FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_regular,
	DefaultIntegrationOrderFunctor>::
	computeNormalsOnIntegrationPoints<_point_1>(
	const Array<Real> &, Array<Real> & normal,
	const GhostType & ghost_type) const {
	AKANTU_DEBUG_IN();

	AKANTU_DEBUG_ASSERT(mesh.getSpatialDimension() == 1,
	"Mesh dimension must be 1 to compute normals on points!");
	const ElementType type = _point_1;
	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).getSize();
	normal.resize(nb_element * nb_points);
	Array<Real>::matrix_iterator normals_on_quad =
	normal.begin_reinterpret(spatial_dimension, nb_points, nb_element);
	Array<std::vector<Element> > segments =
	mesh.getElementToSubelement(type, ghost_type);
	Array<Real> 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) {
	Element segment = segments(elem)[0];
	const Array<UInt> & segment_connectivity =
	mesh_segment->getConnectivity(segment.type, segment.ghost_type);
	// const Vector<UInt> & segment_points =
	// segment_connectivity.begin(Mesh::getNbNodesPerElement(segment.type))[segment.element];
	Real difference;
	if (segment_connectivity(0) == elem) {
	difference = coords(elem) - coords(segment_connectivity(1));
	} else {
	difference = coords(elem) - coords(segment_connectivity(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();
	}

	__END_AKANTU__

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