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element_class.hh
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			/**
			* @file element_class.hh
			*
			* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
			* @author Nicolas Richart <nicolas.richart@epfl.ch>
			*
			* @date creation: Fri Jun 18 2010
			* @date last modification: Thu Jan 21 2016
			*
			* @brief Declaration of the ElementClass main class and the
			* Integration and Interpolation elements
			*
			* @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"
			#include "aka_types.hh"
			/* -------------------------------------------------------------------------- */

			#ifndef __AKANTU_ELEMENT_CLASS_HH__
			#define __AKANTU_ELEMENT_CLASS_HH__

			__BEGIN_AKANTU__

			/* -------------------------------------------------------------------------- */
			/// default element class structure
			template <ElementType element_type> struct ElementClassProperty {
			static const GeometricalType geometrical_type = _gt_not_defined;
			static const InterpolationType interpolation_type = _itp_not_defined;
			static const ElementKind element_kind = _ek_regular;
			static const UInt spatial_dimension = 0;
			static const GaussIntegrationType gauss_integration_type = _git_not_defined;
			static const UInt polynomial_degree = 0;
			};

			/// Macro to generate the element class structures for different element types
			#define AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(elem_type, geom_type, \
			interp_type, elem_kind, sp, \
			gauss_int_type, min_int_order) \
			template <> struct ElementClassProperty<elem_type> { \
			static const GeometricalType geometrical_type = geom_type; \
			static const InterpolationType interpolation_type = interp_type; \
			static const ElementKind element_kind = elem_kind; \
			static const UInt spatial_dimension = sp; \
			static const GaussIntegrationType gauss_integration_type = \
			gauss_int_type; \
			static const UInt polynomial_degree = min_int_order; \
			}

			/* -------------------------------------------------------------------------- */
			/* Geometry */
			/* -------------------------------------------------------------------------- */
			/// Default GeometricalShape structure
			template <GeometricalType geometrical_type> struct GeometricalShape {
			static const GeometricalShapeType shape = _gst_point;
			};

			/// Templated GeometricalShape with function contains
			template <GeometricalShapeType shape> struct GeometricalShapeContains {
			/// Check if the point (vector in 2 and 3D) at natural coordinate coor
			template <class vector_type>
			static inline bool contains(const vector_type & coord);
			};

			/// Macro to generate the GeometricalShape structures for different geometrical
			/// types
			#define AKANTU_DEFINE_SHAPE(geom_type, geom_shape) \
			template <> struct GeometricalShape<geom_type> { \
			static const GeometricalShapeType shape = geom_shape; \
			}

			/* -------------------------------------------------------------------------- */
			/// Templated GeometricalElement with function getInradius
			template <GeometricalType geometrical_type,
			GeometricalShapeType shape =
			GeometricalShape<geometrical_type>::shape>
			class GeometricalElement {
			public:
			/// compute the in-radius
			static inline Real getInradius(__attribute__((unused))
			const Matrix<Real> & coord) {
			AKANTU_DEBUG_TO_IMPLEMENT();
			}

			/// true if the natural coordinates are in the element
			template <class vector_type>
			static inline bool contains(const vector_type & coord);

			public:
			static AKANTU_GET_MACRO_NOT_CONST(SpatialDimension, spatial_dimension, UInt);
			static AKANTU_GET_MACRO_NOT_CONST(NbNodesPerElement, nb_nodes_per_element, UInt);
			static AKANTU_GET_MACRO_NOT_CONST(NbFacetTypes, nb_facet_types, UInt);
			static inline UInt getNbFacetsPerElement(UInt t);
			static inline UInt getNbFacetsPerElement();
			static inline const MatrixProxy<UInt>
			getFacetLocalConnectivityPerElement(UInt t = 0);

			protected:
			/// Number of nodes per element
			static UInt nb_nodes_per_element;
			/// spatial dimension of the element
			static UInt spatial_dimension;
			/// number of different facet types
			static UInt nb_facet_types;
			/// number of facets for element
			static UInt nb_facets[];
			/// storage of the facet local connectivity
			static UInt facet_connectivity_vect[];
			/// local connectivity of facets
			static UInt * facet_connectivity[];

			private:
			/// Type of the facet elements
			static UInt nb_nodes_per_facet[];
			};

			/* -------------------------------------------------------------------------- */
			/* Interpolation */
			/* -------------------------------------------------------------------------- */
			/// default InterpolationPorperty structure
			template <InterpolationType interpolation_type> struct InterpolationPorperty {
			static const InterpolationKind kind = _itk_not_defined;
			static const UInt nb_nodes_per_element = 0;
			static const UInt natural_space_dimension = 0;
			};

			/// Macro to generate the InterpolationPorperty structures for different
			/// interpolation types
			#define AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(itp_type, itp_kind, \
			nb_nodes, ndim) \
			template <> struct InterpolationPorperty<itp_type> { \
			static const InterpolationKind kind = itp_kind; \
			static const UInt nb_nodes_per_element = nb_nodes; \
			static const UInt natural_space_dimension = ndim; \
			}

			#include "interpolation_element_tmpl.hh"

			/* -------------------------------------------------------------------------- */
			/// Generic (templated by the enum InterpolationType which specifies the order
			/// and the dimension of the interpolation) class handling the elemental
			/// interpolation
			template <InterpolationType interpolation_type,
			InterpolationKind kind =
			InterpolationPorperty<interpolation_type>::kind>
			class InterpolationElement {
			public:
			typedef InterpolationPorperty<interpolation_type> interpolation_property;

			/// compute the shape values for a given set of points in natural coordinates
			static inline void computeShapes(const Matrix<Real> & natural_coord,
			Matrix<Real> & N);

			/// compute the shape values for a given point in natural coordinates
			template <class vector_type>
			static inline void computeShapes(__attribute__((unused))
			const vector_type & natural_coord,
			__attribute__((unused)) vector_type & N) {
			AKANTU_DEBUG_TO_IMPLEMENT();
			}

			/**
			* compute @f$ B_{ij} = \frac{\partial N_j}{\partial S_i} @f$ the variation of
			* shape functions along with variation of natural coordinates on a given set
			* of points in natural coordinates
			*/
			static inline void computeDNDS(const Matrix<Real> & natural_coord,
			Tensor3<Real> & dnds);
			/**
			* compute @f$ B_{ij} = \frac{\partial N_j}{\partial S_i} @f$ the variation of
			* shape functions along with
			* variation of natural coordinates on a given point in natural
			* coordinates
			*/
			template <class vector_type, class matrix_type>
			static inline void computeDNDS(__attribute__((unused))
			const vector_type & natural_coord,
			__attribute__((unused)) matrix_type & dnds) {
			AKANTU_DEBUG_TO_IMPLEMENT();
			}

			/// compute jacobian (or integration variable change factor) for a given point
			/// in the case of spatial_dimension != natural_space_dimension
			static inline void computeSpecialJacobian(__attribute__((unused))
			const Matrix<Real> & J,
			__attribute__((unused))
			Real & jacobians) {
			AKANTU_DEBUG_TO_IMPLEMENT();
			}

			/// interpolate a field given (arbitrary) natural coordinates
			static inline void
			interpolateOnNaturalCoordinates(const Vector<Real> & natural_coords,
			const Matrix<Real> & nodal_values,
			Vector<Real> & interpolated);

			/// interpolate a field given the shape functions on the interpolation point
			static inline void interpolate(const Matrix<Real> & nodal_values,
			const Vector<Real> & shapes,
			Vector<Real> & interpolated);

			/// interpolate a field given the shape functions on the interpolations points
			static inline void interpolate(const Matrix<Real> & nodal_values,
			const Matrix<Real> & shapes,
			Matrix<Real> & interpolated);

			/// compute the gradient of a given field on the given natural coordinates
			static inline void
			gradientOnNaturalCoordinates(const Vector<Real> & natural_coords,
			const Matrix<Real> & f, Matrix<Real> & gradient);

			public:
			static AKANTU_GET_MACRO_NOT_CONST(
			ShapeSize,
			InterpolationPorperty<interpolation_type>::nb_nodes_per_element, UInt);
			static AKANTU_GET_MACRO_NOT_CONST(
			ShapeDerivativesSize,
			(InterpolationPorperty<interpolation_type>::nb_nodes_per_element *
			InterpolationPorperty<interpolation_type>::natural_space_dimension),
			UInt);
			static AKANTU_GET_MACRO_NOT_CONST(
			NaturalSpaceDimension,
			InterpolationPorperty<interpolation_type>::natural_space_dimension, UInt);
			static AKANTU_GET_MACRO_NOT_CONST(
			NbNodesPerInterpolationElement,
			InterpolationPorperty<interpolation_type>::nb_nodes_per_element, UInt);
			};

			/* -------------------------------------------------------------------------- */
			/* Integration */
			/* -------------------------------------------------------------------------- */
			template <GaussIntegrationType git_class, UInt nb_points>
			struct GaussIntegrationTypeData {
			/// quadrature points in natural coordinates
			static Real quad_positions[];
			/// weights for the Gauss integration
			static Real quad_weights[];
			};

			template <ElementType type,
			UInt n = ElementClassProperty<type>::polynomial_degree>
			class GaussIntegrationElement {
			public:
			static UInt getNbQuadraturePoints();
			static const Matrix<Real> getQuadraturePoints();
			static const Vector<Real> getWeights();
			};

			/* -------------------------------------------------------------------------- */
			/* ElementClass */
			/* -------------------------------------------------------------------------- */
			template <ElementType element_type,
			ElementKind element_kind =
			ElementClassProperty<element_type>::element_kind>
			class ElementClass
			: public GeometricalElement<
			ElementClassProperty<element_type>::geometrical_type>,
			public InterpolationElement<
			ElementClassProperty<element_type>::interpolation_type> {
			protected:
			typedef GeometricalElement<
			ElementClassProperty<element_type>::geometrical_type> geometrical_element;
			typedef InterpolationElement<ElementClassProperty<
			element_type>::interpolation_type> interpolation_element;

			typedef ElementClassProperty<element_type> element_property;
			typedef typename interpolation_element::interpolation_property
			interpolation_property;

			public:
			/**
			* compute @f$ J = \frac{\partial x_j}{\partial s_i} @f$ the variation of real
			* coordinates along with variation of natural coordinates on a given point in
			* natural coordinates
			*/
			static inline void computeJMat(const Matrix<Real> & dnds,
			const Matrix<Real> & node_coords,
			Matrix<Real> & J);

			/**
			* compute the Jacobian matrix by computing the variation of real coordinates
			* along with variation of natural coordinates on a given set of points in
			* natural coordinates
			*/
			static inline void computeJMat(const Tensor3<Real> & dnds,
			const Matrix<Real> & node_coords,
			Tensor3<Real> & J);

			/// compute the jacobians of a serie of natural coordinates
			static inline void computeJacobian(const Matrix<Real> & natural_coords,
			const Matrix<Real> & node_coords,
			Vector<Real> & jacobians);

			/// compute jacobian (or integration variable change factor) for a set of
			/// points
			static inline void computeJacobian(const Tensor3<Real> & J,
			Vector<Real> & jacobians);

			/// compute jacobian (or integration variable change factor) for a given point
			static inline void computeJacobian(const Matrix<Real> & J, Real & jacobians);

			/// compute shape derivatives (input is dxds) for a set of points
			static inline void computeShapeDerivatives(const Tensor3<Real> & J,
			const Tensor3<Real> & dnds,
			Tensor3<Real> & shape_deriv);

			/// compute shape derivatives (input is dxds) for a given point
			static inline void computeShapeDerivatives(const Matrix<Real> & J,
			const Matrix<Real> & dnds,
			Matrix<Real> & shape_deriv);

			/// compute the normal of a surface defined by the function f
			static inline void
			computeNormalsOnNaturalCoordinates(const Matrix<Real> & coord,
			Matrix<Real> & f, Matrix<Real> & normals);

			/// get natural coordinates from real coordinates
			static inline void inverseMap(const Vector<Real> & real_coords,
			const Matrix<Real> & node_coords,
			Vector<Real> & natural_coords,
			Real tolerance = 1e-8);

			/// get natural coordinates from real coordinates
			static inline void inverseMap(const Matrix<Real> & real_coords,
			const Matrix<Real> & node_coords,
			Matrix<Real> & natural_coords,
			Real tolerance = 1e-8);

			public:
			static AKANTU_GET_MACRO_NOT_CONST(Kind, element_kind, ElementKind);
			static AKANTU_GET_MACRO_NOT_CONST(
			SpatialDimension, ElementClassProperty<element_type>::spatial_dimension,
			UInt);
			static AKANTU_GET_MACRO_NOT_CONST(P1ElementType, p1_type,
			const ElementType &);
			static const ElementType & getFacetType(UInt t = 0) { return facet_type[t]; }
			static ElementType * getFacetTypeInternal() { return facet_type; }

			protected:
			/// Type of the facet elements
			static ElementType facet_type[];
			/// type of element P1 associated
			static ElementType p1_type;
			};

			/* -------------------------------------------------------------------------- */
			__END_AKANTU__

			#include "element_class_tmpl.hh"


			/* -------------------------------------------------------------------------- */
			__BEGIN_AKANTU__
			#include "element_class_point_1_inline_impl.cc"
			#include "element_class_segment_2_inline_impl.cc"
			#include "element_class_segment_3_inline_impl.cc"
			#include "element_class_triangle_3_inline_impl.cc"
			#include "element_class_triangle_6_inline_impl.cc"
			#include "element_class_tetrahedron_4_inline_impl.cc"
			#include "element_class_tetrahedron_10_inline_impl.cc"
			#include "element_class_quadrangle_4_inline_impl.cc"
			#include "element_class_quadrangle_8_inline_impl.cc"
			#include "element_class_hexahedron_8_inline_impl.cc"
			#include "element_class_hexahedron_20_inline_impl.cc"
			#include "element_class_pentahedron_6_inline_impl.cc"
			#include "element_class_pentahedron_15_inline_impl.cc"
			__END_AKANTU__

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

			#if defined(AKANTU_STRUCTURAL_MECHANICS)
			#include "element_class_structural.hh"
			#endif

			#if defined(AKANTU_IGFEM)
			#include "element_class_igfem.hh"
			#endif

			#endif /* __AKANTU_ELEMENT_CLASS_HH__ */

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element_class.hhView Options

rAKA/src/fe_engine/element_class.hh
cee9f8c9b21ffeatures/28-getelementi…

element_class.hh
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