shape_igfem_inline_impl.hh
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shape_igfem_inline_impl.hh
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	/**
	* @file shape_igfem_inline_impl.hh
	*
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	*
	*
	* @brief ShapeIGFEM inline implementation
	*
	*
	* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	*/

	/* -------------------------------------------------------------------------- */
	#ifndef AKANTU_SHAPE_IGFEM_INLINE_IMPL_HH_
	#define AKANTU_SHAPE_IGFEM_INLINE_IMPL_HH_

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	inline const Array<Real> &
	ShapeLagrange<_ek_igfem>::getShapes(ElementType el_type,
	GhostType ghost_type) const {
	return shapes(FEEngine::getInterpolationType(el_type), ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	inline const Array<Real> & ShapeLagrange<_ek_igfem>::getShapesDerivatives(
	ElementType el_type, GhostType ghost_type) const {
	return shapes_derivatives(FEEngine::getInterpolationType(el_type),
	ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	#define INIT_SHAPE_FUNCTIONS(type) \
	setIntegrationPointsByType<type>(integration_points, ghost_type); \
	setIntegrationPointsByType<ElementClassProperty<type>::sub_element_type_1>( \
	integration_points_1, ghost_type); \
	setIntegrationPointsByType<ElementClassProperty<type>::sub_element_type_2>( \
	integration_points_2, ghost_type); \
	precomputeShapesOnIntegrationPoints<type>(nodes, ghost_type); \
	if (ElementClass<type>::getNaturalSpaceDimension() == \
	mesh.getSpatialDimension()) \
	precomputeShapeDerivativesOnIntegrationPoints<type>(nodes, ghost_type); \
	precomputeShapesOnEnrichedNodes<type>(nodes, ghost_type);

	inline void ShapeLagrange<_ek_igfem>::initShapeFunctions(
	const Array<Real> & nodes, const Matrix<Real> & integration_points,
	const Matrix<Real> & integration_points_1,
	const Matrix<Real> & integration_points_2, ElementType type,
	GhostType ghost_type) {

	AKANTU_BOOST_IGFEM_ELEMENT_SWITCH(INIT_SHAPE_FUNCTIONS);
	}
	#undef INIT_SHAPE_FUNCTIONS

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	inline void ShapeLagrange<_ek_igfem>::computeShapeDerivativesOnCPointsByElement(
	const Matrix<Real> & node_coords, const Matrix<Real> & natural_coords,
	Tensor3<Real> & shapesd) const {
	AKANTU_DEBUG_IN();

	// compute dnds
	Tensor3<Real> dnds(node_coords.rows(), node_coords.cols(),
	natural_coords.cols());
	ElementClass<type>::computeDNDS(natural_coords, dnds);
	// compute dxds
	Tensor3<Real> J(node_coords.rows(), natural_coords.rows(),
	natural_coords.cols());
	ElementClass<type>::computeJMat(dnds, node_coords, J);

	// compute shape derivatives
	ElementClass<type>::computeShapeDerivatives(J, dnds, shapesd);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::inverseMap(const Vector<Real> & real_coords,
	UInt elem,
	Vector<Real> & natural_coords,
	UInt sub_element,
	GhostType ghost_type) const {

	AKANTU_DEBUG_IN();
	/// typedef for the two subelement_types and the parent element type
	const ElementType sub_type_1 = ElementClassProperty<type>::sub_element_type_1;
	const ElementType sub_type_2 = ElementClassProperty<type>::sub_element_type_2;

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();

	UInt * elem_val = mesh.getConnectivity(type, ghost_type).storage();
	Matrix<Real> nodes_coord(spatial_dimension, nb_nodes_per_element);

	mesh.extractNodalValuesFromElement(mesh.getNodes(), nodes_coord.storage(),
	elem_val + elem * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);

	if (!sub_element) {
	UInt nb_nodes_sub_el =
	ElementClass<sub_type_1>::getNbNodesPerInterpolationElement();
	Matrix<Real> sub_el_coords(spatial_dimension, nb_nodes_sub_el);
	ElementClass<type>::getSubElementCoords(nodes_coord, sub_el_coords,
	sub_element);
	ElementClass<sub_type_1>::inverseMap(real_coords, sub_el_coords,
	natural_coords);
	}

	else {
	UInt nb_nodes_sub_el =
	ElementClass<sub_type_2>::getNbNodesPerInterpolationElement();
	Matrix<Real> sub_el_coords(spatial_dimension, nb_nodes_sub_el);
	ElementClass<type>::getSubElementCoords(nodes_coord, sub_el_coords,
	sub_element);
	ElementClass<sub_type_2>::inverseMap(real_coords, sub_el_coords,
	natural_coords);
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::inverseMap(const Vector<Real> & real_coords,
	UInt elem,
	Vector<Real> & natural_coords,
	GhostType ghost_type) const {

	/// map point into parent reference domain
	AKANTU_DEBUG_IN();

	const ElementType parent_type =
	ElementClassProperty<type>::parent_element_type;

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();

	UInt * elem_val = mesh.getConnectivity(type, ghost_type).storage();
	Matrix<Real> nodes_coord(spatial_dimension, nb_nodes_per_element);

	mesh.extractNodalValuesFromElement(mesh.getNodes(), nodes_coord.storage(),
	elem_val + elem * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);

	UInt nb_nodes_parent_el =
	ElementClass<parent_type>::getNbNodesPerInterpolationElement();
	Matrix<Real> parent_coords(spatial_dimension, nb_nodes_parent_el);
	ElementClass<type>::getParentCoords(nodes_coord, parent_coords);
	ElementClass<parent_type>::inverseMap(real_coords, parent_coords,
	natural_coords);
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	bool ShapeLagrange<_ek_igfem>::contains(const Vector<Real> & real_coords,
	UInt elem,
	GhostType ghost_type) const {

	UInt spatial_dimension = mesh.getSpatialDimension();
	Vector<Real> natural_coords(spatial_dimension);

	inverseMap<type>(real_coords, elem, natural_coords, ghost_type);
	return ElementClass<type>::contains(natural_coords);
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::interpolate(const Vector<Real> & real_coords,
	UInt elem,
	const Matrix<Real> & nodal_values,
	Vector<Real> & interpolated,
	GhostType ghost_type) const {
	UInt nb_shapes = ElementClass<type>::getShapeSize();
	Vector<Real> shapes(nb_shapes);
	computeShapes<type>(real_coords, elem, shapes, ghost_type);
	ElementClass<type>::interpolate(nodal_values, shapes, interpolated);
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::computeShapes(
	const Vector<Real> & real_coords, UInt elem, Vector<Real> & shapes,
	GhostType ghost_type) const {

	AKANTU_DEBUG_IN();
	/// typedef for the two subelement_types and the parent element type
	const ElementType sub_type_1 = ElementClassProperty<type>::sub_element_type_1;
	const ElementType sub_type_2 = ElementClassProperty<type>::sub_element_type_2;
	const ElementType parent_type =
	ElementClassProperty<type>::parent_element_type;

	UInt spatial_dimension = mesh.getSpatialDimension();

	/// parent contribution
	/// get the size of the parent shapes
	UInt size_of_parent_shapes = ElementClass<parent_type>::getShapeSize();
	Vector<Real> parent_shapes(size_of_parent_shapes);

	/// compute parent shapes -> map shapes in the physical domain of the parent
	Vector<Real> natural_coords(spatial_dimension);
	Real tol = Math::getTolerance();
	Math::setTolerance(1e-14);
	inverseMap<type>(real_coords, elem, natural_coords, ghost_type);
	ElementClass<parent_type>::computeShapes(natural_coords, parent_shapes);
	natural_coords.zero();

	/// sub-element contribution
	/// check which sub-element contains the physical point
	/// check if point is in sub-element 1
	inverseMap<type>(real_coords, elem, natural_coords, 0, ghost_type);
	if (ElementClass<sub_type_1>::contains(natural_coords)) {
	UInt size_of_sub_shapes = ElementClass<sub_type_1>::getShapeSize();
	Vector<Real> sub_shapes(size_of_sub_shapes);
	ElementClass<sub_type_1>::computeShapes(natural_coords, sub_shapes);
	/// assemble shape functions
	ElementClass<type>::assembleShapes(parent_shapes, sub_shapes, shapes, 0);
	} else {
	natural_coords.zero();
	inverseMap<type>(real_coords, elem, natural_coords, 1, ghost_type);

	AKANTU_DEBUG_ASSERT(ElementClass<sub_type_2>::contains(natural_coords),
	"Physical point not contained in any element");

	UInt size_of_sub_shapes = ElementClass<sub_type_2>::getShapeSize();
	Vector<Real> sub_shapes(size_of_sub_shapes);
	ElementClass<sub_type_2>::computeShapes(natural_coords, sub_shapes);
	/// assemble shape functions
	ElementClass<type>::assembleShapes(parent_shapes, sub_shapes, shapes, 1);
	}

	Math::setTolerance(tol);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::computeShapeDerivatives(
	const Matrix<Real> & real_coords, UInt elem, Tensor3<Real> & shapesd,
	GhostType ghost_type) const {

	AKANTU_DEBUG_TO_IMPLEMENT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::precomputeShapesOnIntegrationPoints(
	__attribute__((unused)) const Array<Real> & nodes, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;

	/// typedef for the two subelement_types and the parent element type
	const ElementType sub_type_1 = ElementClassProperty<type>::sub_element_type_1;
	const ElementType sub_type_2 = ElementClassProperty<type>::sub_element_type_2;
	const ElementType parent_type =
	ElementClassProperty<type>::parent_element_type;

	/// get the spatial dimension for the given element type
	UInt spatial_dimension = ElementClass<type>::getSpatialDimension();
	/// get the integration points for the subelements
	Matrix<Real> & natural_coords_sub_1 =
	integration_points(sub_type_1, ghost_type);
	Matrix<Real> & natural_coords_sub_2 =
	integration_points(sub_type_2, ghost_type);

	/// store the number of quadrature points on each subelement and the toal
	/// number
	UInt nb_points_sub_1 = natural_coords_sub_1.cols();
	UInt nb_points_sub_2 = natural_coords_sub_2.cols();
	UInt nb_total_points = nb_points_sub_1 + nb_points_sub_2;

	// get the integration points for the parent element
	UInt nb_element = mesh.getConnectivity(type, ghost_type).getSize();
	Array<Real> & natural_coords_parent = igfem_integration_points.alloc(
	nb_element * nb_total_points, spatial_dimension, type, ghost_type);
	Array<Real>::matrix_iterator natural_coords_parent_it =
	natural_coords_parent.begin_reinterpret(spatial_dimension,
	nb_total_points, nb_element);

	/// get the size of the shapes
	UInt size_of_shapes = ElementClass<type>::getShapeSize();
	UInt size_of_parent_shapes = ElementClass<parent_type>::getShapeSize();
	UInt size_of_sub_1_shapes = ElementClass<sub_type_1>::getShapeSize();
	UInt size_of_sub_2_shapes = ElementClass<sub_type_2>::getShapeSize();

	/// initialize the matrices to store the shape functions of the subelements
	/// and the parent
	Matrix<Real> sub_1_shapes(size_of_sub_1_shapes, nb_points_sub_1);
	Matrix<Real> sub_2_shapes(size_of_sub_2_shapes, nb_points_sub_2);
	Matrix<Real> parent_1_shapes(size_of_parent_shapes, nb_points_sub_1);
	Matrix<Real> parent_2_shapes(size_of_parent_shapes, nb_points_sub_2);
	/// compute the shape functions of the subelements
	ElementClass<sub_type_1>::computeShapes(natural_coords_sub_1, sub_1_shapes);
	ElementClass<sub_type_2>::computeShapes(natural_coords_sub_2, sub_2_shapes);

	/// get the nodal coordinates per element
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
	Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type);
	Array<Real>::matrix_iterator x_it =
	x_el.begin(spatial_dimension, nb_nodes_per_element);

	/// allocate the shapes for the given element type
	Array<Real> & shapes_tmp = shapes.alloc(nb_element * nb_total_points,
	size_of_shapes, itp_type, ghost_type);

	Array<Real>::matrix_iterator shapes_it = shapes_tmp.begin_reinterpret(
	ElementClass<type>::getNbNodesPerInterpolationElement(), nb_total_points,
	nb_element);

	Matrix<Real> physical_points_1(spatial_dimension, nb_points_sub_1);
	Matrix<Real> physical_points_2(spatial_dimension, nb_points_sub_2);
	Matrix<Real> parent_natural_coords_1(spatial_dimension, nb_points_sub_1);
	Matrix<Real> parent_natural_coords_2(spatial_dimension, nb_points_sub_2);

	/// intialize the matrices for the parent and subelement coordinates
	UInt nb_nodes_parent_el =
	ElementClass<parent_type>::getNbNodesPerInterpolationElement();
	UInt nb_nodes_sub_el_1 =
	ElementClass<sub_type_1>::getNbNodesPerInterpolationElement();
	UInt nb_nodes_sub_el_2 =
	ElementClass<sub_type_2>::getNbNodesPerInterpolationElement();
	Matrix<Real> parent_coords(spatial_dimension, nb_nodes_parent_el);
	Matrix<Real> sub_el_1_coords(spatial_dimension, nb_nodes_sub_el_1);
	Matrix<Real> sub_el_2_coords(spatial_dimension, nb_nodes_sub_el_2);

	/// loop over all elements of the given type and compute the shape functions
	Vector<Real> all_shapes(size_of_shapes);

	for (UInt elem = 0; elem < nb_element;
	++elem, ++shapes_it, ++x_it, ++natural_coords_parent_it) {
	Matrix<Real> & N = *shapes_it;
	const Matrix<Real> & X = *x_it;
	Matrix<Real> & nc_parent = *natural_coords_parent_it;

	/// map the sub element integration points into the parent reference domain
	ElementClass<type>::mapFromSubRefToParentRef(
	X, sub_el_1_coords, parent_coords, sub_1_shapes, physical_points_1,
	parent_natural_coords_1, 0);
	ElementClass<type>::mapFromSubRefToParentRef(
	X, sub_el_2_coords, parent_coords, sub_2_shapes, physical_points_2,
	parent_natural_coords_2, 1);

	/// compute the parent shape functions on all integration points
	ElementClass<sub_type_1>::computeShapes(parent_natural_coords_1,
	parent_1_shapes);
	ElementClass<sub_type_1>::computeShapes(parent_natural_coords_2,
	parent_2_shapes);

	/// copy the results into the shape functions iterator and natural coords
	/// iterator
	for (UInt i = 0; i < nb_points_sub_1; ++i) {
	ElementClass<type>::assembleShapes(parent_1_shapes(i), sub_1_shapes(i),
	all_shapes, 0);
	N(i) = all_shapes;
	nc_parent(i) = parent_natural_coords_1(i);
	}
	for (UInt i = 0; i < nb_points_sub_2; ++i) {
	ElementClass<type>::assembleShapes(parent_2_shapes(i), sub_2_shapes(i),
	all_shapes, 1);
	N(i + nb_points_sub_1) = all_shapes;

	/// N(i + nb_points_sub_2) = all_shapes;
	nc_parent(i + nb_points_sub_1) = parent_natural_coords_2(i);
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::precomputeShapeDerivativesOnIntegrationPoints(
	const Array<Real> & nodes, GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	/// typedef for the two subelement_types and the parent element type
	const ElementType sub_type_1 = ElementClassProperty<type>::sub_element_type_1;
	const ElementType sub_type_2 = ElementClassProperty<type>::sub_element_type_2;
	const ElementType parent_type =
	ElementClassProperty<type>::parent_element_type;

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
	UInt spatial_dimension = mesh.getSpatialDimension();

	/// get the integration points for the subelements
	Matrix<Real> & natural_coords_sub_1 =
	integration_points(sub_type_1, ghost_type);
	Matrix<Real> & natural_coords_sub_2 =
	integration_points(sub_type_2, ghost_type);
	/// store the number of quadrature points on each subelement and the toal
	/// number
	UInt nb_points_sub_1 = natural_coords_sub_1.cols();
	UInt nb_points_sub_2 = natural_coords_sub_2.cols();
	UInt nb_points_total = nb_points_sub_1 + nb_points_sub_2;

	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();
	UInt size_of_shapesd = ElementClass<type>::getShapeDerivativesSize();

	/// intialize the matrices for the parent and subelement coordinates
	UInt nb_nodes_parent_el =
	ElementClass<parent_type>::getNbNodesPerInterpolationElement();
	UInt nb_nodes_sub_el_1 =
	ElementClass<sub_type_1>::getNbNodesPerInterpolationElement();
	UInt nb_nodes_sub_el_2 =
	ElementClass<sub_type_2>::getNbNodesPerInterpolationElement();
	Matrix<Real> parent_coords(spatial_dimension, nb_nodes_parent_el);
	Matrix<Real> sub_el_1_coords(spatial_dimension, nb_nodes_sub_el_1);
	Matrix<Real> sub_el_2_coords(spatial_dimension, nb_nodes_sub_el_2);

	UInt nb_element = mesh.getConnectivity(type, ghost_type).getSize();
	Array<Real> & shapes_derivatives_tmp = shapes_derivatives.alloc(
	nb_element * nb_points_total, size_of_shapesd, itp_type, ghost_type);

	/// get an iterator to the coordiantes of the elements
	Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type);

	Real * shapesd_val = shapes_derivatives_tmp.storage();
	Array<Real>::matrix_iterator x_it =
	x_el.begin(spatial_dimension, nb_nodes_per_element);

	/// get an iterator to the integration points of the parent element
	Array<Real> & natural_coords_parent =
	igfem_integration_points(type, ghost_type);
	Array<Real>::matrix_iterator natural_coords_parent_it =
	natural_coords_parent.begin_reinterpret(spatial_dimension,
	nb_points_total, nb_element);

	Tensor3<Real> B_sub_1(spatial_dimension, nb_nodes_sub_el_1, nb_points_sub_1);
	Tensor3<Real> B_sub_2(spatial_dimension, nb_nodes_sub_el_2, nb_points_sub_2);
	Tensor3<Real> B_parent(spatial_dimension, nb_nodes_parent_el,
	nb_points_total);
	/// assemble the shape derivatives
	Matrix<Real> all_shapes(spatial_dimension, nb_nodes_per_element);
	for (UInt elem = 0; elem < nb_element;
	++elem, ++x_it, ++natural_coords_parent_it) {
	Matrix<Real> & X = *x_it;
	Matrix<Real> & nc_parent = *natural_coords_parent_it;

	Tensor3<Real> B(shapesd_val, spatial_dimension, nb_nodes_per_element,
	nb_points_total);

	/// get the coordinates of the two sub elements and the parent element
	ElementClass<type>::getSubElementCoords(X, sub_el_1_coords, 0);
	ElementClass<type>::getSubElementCoords(X, sub_el_2_coords, 1);
	ElementClass<type>::getParentCoords(X, parent_coords);

	/// compute the subelements' shape derivatives and the parent shape
	/// derivatives
	computeShapeDerivativesOnCPointsByElement<sub_type_1>(
	sub_el_1_coords, natural_coords_sub_1, B_sub_1);
	computeShapeDerivativesOnCPointsByElement<sub_type_2>(
	sub_el_2_coords, natural_coords_sub_2, B_sub_2);
	computeShapeDerivativesOnCPointsByElement<parent_type>(parent_coords,
	nc_parent, B_parent);

	for (UInt i = 0; i < nb_points_sub_1; ++i) {
	ElementClass<type>::assembleShapeDerivatives(B_parent(i), B_sub_1(i),
	all_shapes, 0);
	B(i) = all_shapes;
	}

	for (UInt i = 0; i < nb_points_sub_2; ++i) {
	ElementClass<type>::assembleShapeDerivatives(B_parent(i), B_sub_2(i),
	all_shapes, 1);
	B(i + nb_points_sub_1) = all_shapes;
	}

	shapesd_val += size_of_shapesd * nb_points_total;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::interpolateOnIntegrationPoints(
	const Array<Real> & in_u, Array<Real> & out_uq, UInt nb_degree_of_freedom,
	GhostType ghost_type, const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
	AKANTU_DEBUG_ASSERT(shapes.exists(itp_type, ghost_type),
	"No shapes for the type "
	<< shapes.printType(itp_type, ghost_type));

	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();

	Array<Real> u_el(0, nb_degree_of_freedom * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, in_u, u_el, type, ghost_type,
	filter_elements);

	this->interpolateElementalFieldOnIntegrationPoints<type>(
	u_el, out_uq, ghost_type, shapes(itp_type, ghost_type), filter_elements);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::gradientOnIntegrationPoints(
	const Array<Real> & in_u, Array<Real> & out_nablauq,
	UInt nb_degree_of_freedom, GhostType ghost_type,
	const Array<UInt> & filter_elements) const {
	AKANTU_DEBUG_IN();

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
	AKANTU_DEBUG_ASSERT(
	shapes_derivatives.exists(itp_type, ghost_type),
	"No shapes derivatives for the type "
	<< shapes_derivatives.printType(itp_type, ghost_type));

	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();

	Array<Real> u_el(0, nb_degree_of_freedom * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, in_u, u_el, type, ghost_type,
	filter_elements);

	this->gradientElementalFieldOnIntegrationPoints<type>(
	u_el, out_nablauq, ghost_type, shapes_derivatives(itp_type, ghost_type),
	filter_elements);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::fieldTimesShapes(
	const Array<Real> & field, Array<Real> & field_times_shapes,
	GhostType ghost_type) const {
	AKANTU_DEBUG_IN();

	field_times_shapes.resize(field.getSize());

	UInt size_of_shapes = ElementClass<type>::getShapeSize();
	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;
	UInt nb_degree_of_freedom = field.getNbComponent();

	const Array<Real> & shape = shapes(itp_type, ghost_type);

	Array<Real>::const_matrix_iterator field_it =
	field.begin(nb_degree_of_freedom, 1);
	Array<Real>::const_matrix_iterator shapes_it = shape.begin(1, size_of_shapes);

	Array<Real>::matrix_iterator it =
	field_times_shapes.begin(nb_degree_of_freedom, size_of_shapes);
	Array<Real>::matrix_iterator end =
	field_times_shapes.end(nb_degree_of_freedom, size_of_shapes);

	for (; it != end; ++it, ++field_it, ++shapes_it) {
	it->mul<false, false>(field_it, shapes_it);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::interpolateOnPhysicalPoint(
	const Vector<Real> & real_coords, UInt elem, const Array<Real> & field,
	Vector<Real> & interpolated, GhostType ghost_type) const {

	AKANTU_DEBUG_IN();
	Vector<Real> shapes(ElementClass<type>::getShapeSize());
	computeShapes<type>(real_coords, elem, shapes, ghost_type);

	UInt spatial_dimension = mesh.getSpatialDimension();
	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();

	UInt * elem_val = mesh.getConnectivity(type, ghost_type).storage();
	Matrix<Real> nodes_val(spatial_dimension, nb_nodes_per_element);
	mesh.extractNodalValuesFromElement(field, nodes_val.storage(),
	elem_val + elem * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);

	ElementClass<type>::interpolate(nodes_val, shapes, interpolated);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::precomputeShapesOnEnrichedNodes(
	__attribute__((unused)) const Array<Real> & nodes,
	GhostType ghost_type) {

	AKANTU_DEBUG_IN();

	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;

	const ElementType parent_type =
	ElementClassProperty<type>::parent_element_type;
	const ElementType sub_type = ElementClassProperty<type>::sub_element_type_1;

	/// get the spatial dimension for the given element type
	UInt spatial_dimension = ElementClass<type>::getSpatialDimension();

	// get the integration points for the parent element
	UInt nb_element = mesh.getConnectivity(type, ghost_type).getSize();

	/// get the size of the shapes
	UInt nb_enriched_nodes = ElementClass<type>::getNbEnrichments();
	UInt nb_parent_nodes =
	ElementClass<parent_type>::getNbNodesPerInterpolationElement();
	UInt size_of_shapes = ElementClass<type>::getShapeSize();
	UInt size_of_parent_shapes = ElementClass<parent_type>::getShapeSize();
	UInt size_of_sub_shapes = ElementClass<sub_type>::getShapeSize();

	Vector<Real> parent_shapes(size_of_parent_shapes);
	Vector<Real> sub_shapes(size_of_sub_shapes);

	Vector<Real> shapes(size_of_shapes);

	/// get the nodal coordinates per element
	UInt nb_nodes_per_element = mesh.getNbNodesPerElement(type);
	Array<Real> x_el(0, spatial_dimension * nb_nodes_per_element);
	FEEngine::extractNodalToElementField(mesh, nodes, x_el, type, ghost_type);
	Array<Real>::matrix_iterator x_it =
	x_el.begin(spatial_dimension, nb_nodes_per_element);

	/// allocate the shapes for the given element type
	Array<Real> & shapes_tmp = shapes_at_enrichments.alloc(
	nb_element * nb_enriched_nodes, size_of_shapes, itp_type, ghost_type);

	Array<Real>::matrix_iterator shapes_it = shapes_tmp.begin_reinterpret(
	ElementClass<type>::getNbNodesPerInterpolationElement(),
	nb_enriched_nodes, nb_element);

	Vector<Real> real_coords(spatial_dimension);
	Vector<Real> natural_coords(spatial_dimension);
	Matrix<Real> parent_coords(spatial_dimension, nb_parent_nodes);
	UInt * sub_element_enrichments =
	ElementClass<type>::getSubElementEnrichments();

	/// loop over all elements
	for (UInt elem = 0; elem < nb_element; ++elem, ++shapes_it, ++x_it) {
	Matrix<Real> & N = *shapes_it;
	const Matrix<Real> & X = *x_it;
	for (UInt i = 0; i < nb_enriched_nodes; ++i) {
	/// get the parent element coordinates
	ElementClass<type>::getParentCoords(X, parent_coords);
	/// get the physical coords of the enriched node
	real_coords = X(nb_parent_nodes + i);
	/// map the physical point into the parent ref domain
	ElementClass<parent_type>::inverseMap(real_coords, parent_coords,
	natural_coords);
	/// compute the parent shape functions
	ElementClass<parent_type>::computeShapes(natural_coords, parent_shapes);
	/// Sub-element contribution
	sub_shapes.zero();
	sub_shapes(sub_element_enrichments[i]) = 1.;
	ElementClass<type>::assembleShapes(parent_shapes, sub_shapes, shapes, 0);
	N(i) = shapes;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	template <ElementType type>
	void ShapeLagrange<_ek_igfem>::interpolateAtEnrichedNodes(
	const Array<Real> & src, Array<Real> & dst,
	GhostType ghost_type) const {

	AKANTU_DEBUG_IN();

	const ElementType parent_type =
	ElementClassProperty<type>::parent_element_type;

	UInt nb_element = mesh.getNbElement(type, ghost_type);
	UInt nb_nodes_per_element =
	ElementClass<type>::getNbNodesPerInterpolationElement();
	UInt nb_parent_nodes =
	ElementClass<parent_type>::getNbNodesPerInterpolationElement();
	UInt nb_enrichments = ElementClass<type>::getNbEnrichments();
	UInt * elem_val = mesh.getConnectivity(type, ghost_type).storage();
	UInt spatial_dimension = mesh.getSpatialDimension();
	Matrix<Real> nodes_val(spatial_dimension, nb_nodes_per_element);
	InterpolationType itp_type = ElementClassProperty<type>::interpolation_type;

	const Array<Real> & shapes = shapes_at_enrichments(itp_type, ghost_type);
	Array<Real>::const_matrix_iterator shapes_it = shapes.begin_reinterpret(
	nb_nodes_per_element, nb_enrichments, nb_element);
	Array<Real>::vector_iterator dst_vect = dst.begin(spatial_dimension);

	Vector<Real> interpolated(spatial_dimension);
	for (UInt e = 0; e < nb_element; ++e, ++shapes_it) {
	const Matrix<Real> & el_shapes = *shapes_it;
	mesh.extractNodalValuesFromElement(src, nodes_val.storage(),
	elem_val + e * nb_nodes_per_element,
	nb_nodes_per_element, spatial_dimension);
	;
	for (UInt i = 0; i < nb_enrichments; ++i) {
	ElementClass<type>::interpolate(nodes_val, el_shapes(i), interpolated);
	UInt enr_node_idx =
	elem_val[e * nb_nodes_per_element + nb_parent_nodes + i];
	dst_vect[enr_node_idx] = interpolated;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	#define COMPUTE_ENRICHED_VALUES(type) \
	interpolateAtEnrichedNodes<type>(src, dst, ghost_type);

	inline void ShapeLagrange<_ek_igfem>::interpolateEnrichmentsAllTypes(
	const Array<Real> & src, Array<Real> & dst, ElementType type,
	GhostType ghost_type) const {

	AKANTU_BOOST_IGFEM_ELEMENT_SWITCH(COMPUTE_ENRICHED_VALUES);
	}
	#undef COMPUTE_ENRICHED_VALUES

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

	} // namespace akantu

	#endif /* AKANTU_SHAPE_IGFEM_INLINE_IMPL_HH_ */

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