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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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