element_class.hh
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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: Tue Feb 20 2018
	*
	* @brief Declaration of the ElementClass main class and the
	* Integration and Interpolation elements
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2018 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__

	namespace 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}; \
	}

	AKANTU_DEFINE_SHAPE(_gt_hexahedron_20, _gst_square);
	AKANTU_DEFINE_SHAPE(_gt_hexahedron_8, _gst_square);
	AKANTU_DEFINE_SHAPE(_gt_pentahedron_15, _gst_prism);
	AKANTU_DEFINE_SHAPE(_gt_pentahedron_6, _gst_prism);
	AKANTU_DEFINE_SHAPE(_gt_point, _gst_point);
	AKANTU_DEFINE_SHAPE(_gt_quadrangle_4, _gst_square);
	AKANTU_DEFINE_SHAPE(_gt_quadrangle_8, _gst_square);
	AKANTU_DEFINE_SHAPE(_gt_segment_2, _gst_square);
	AKANTU_DEFINE_SHAPE(_gt_segment_3, _gst_square);
	AKANTU_DEFINE_SHAPE(_gt_tetrahedron_10, _gst_triangle);
	AKANTU_DEFINE_SHAPE(_gt_tetrahedron_4, _gst_triangle);
	AKANTU_DEFINE_SHAPE(_gt_triangle_3, _gst_triangle);
	AKANTU_DEFINE_SHAPE(_gt_triangle_6, _gst_triangle);

	/* -------------------------------------------------------------------------- */
	template <GeometricalType geometrical_type>
	struct GeometricalElementProperty {};

	template <ElementType element_type>
	struct ElementClassExtraGeometryProperties {};

	/* -------------------------------------------------------------------------- */
	/// Templated GeometricalElement with function getInradius
	template <GeometricalType geometrical_type,
	GeometricalShapeType shape =
	GeometricalShape<geometrical_type>::shape>
	class GeometricalElement {
	using geometrical_property = GeometricalElementProperty<geometrical_type>;

	public:
	/// compute the in-radius: \todo should be renamed for characteristic length
	static inline Real getInradius(__attribute__((unused))
	const Matrix<Real> & coord) {
	AKANTU_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,
	geometrical_property::spatial_dimension,
	UInt);
	static AKANTU_GET_MACRO_NOT_CONST(NbNodesPerElement,
	geometrical_property::nb_nodes_per_element,
	UInt);
	static inline constexpr auto getNbFacetTypes() {
	return geometrical_property::nb_facet_types;
	};
	static inline UInt getNbFacetsPerElement(UInt t);
	static inline UInt getNbFacetsPerElement();
	static inline constexpr auto getFacetLocalConnectivityPerElement(UInt t = 0);
	};

	/* -------------------------------------------------------------------------- */
	/* Interpolation */
	/* -------------------------------------------------------------------------- */
	/// default InterpolationProperty structure
	template <InterpolationType interpolation_type> struct InterpolationProperty {};

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

	/* -------------------------------------------------------------------------- */
	/// 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 =
	InterpolationProperty<interpolation_type>::kind>
	class InterpolationElement {
	public:
	using interpolation_property = InterpolationProperty<interpolation_type>;

	/// 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(const vector_type &, vector_type &) {
	AKANTU_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(const vector_type &, matrix_type &) {
	AKANTU_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(const Matrix<Real> &, Real &) {
	AKANTU_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,
	InterpolationProperty<interpolation_type>::nb_nodes_per_element, UInt);
	static AKANTU_GET_MACRO_NOT_CONST(
	ShapeDerivativesSize,
	(InterpolationProperty<interpolation_type>::nb_nodes_per_element *
	InterpolationProperty<interpolation_type>::natural_space_dimension),
	UInt);
	static AKANTU_GET_MACRO_NOT_CONST(
	NaturalSpaceDimension,
	InterpolationProperty<interpolation_type>::natural_space_dimension, UInt);
	static AKANTU_GET_MACRO_NOT_CONST(
	NbNodesPerInterpolationElement,
	InterpolationProperty<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:
	using geometrical_element =
	GeometricalElement<ElementClassProperty<element_type>::geometrical_type>;
	using interpolation_element = InterpolationElement<
	ElementClassProperty<element_type>::interpolation_type>;

	using element_property = ElementClassProperty<element_type>;
	using interpolation_property =
	typename interpolation_element::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-10);

	/// 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-10);

	public:
	static AKANTU_GET_MACRO_NOT_CONST(Kind, element_kind, ElementKind);
	static constexpr AKANTU_GET_MACRO_NOT_CONST(
	SpatialDimension, ElementClassProperty<element_type>::spatial_dimension,
	UInt);

	using element_class_extra_geom_property =
	ElementClassExtraGeometryProperties<element_type>;

	static constexpr auto getP1ElementType() {
	return element_class_extra_geom_property::p1_type;
	}
	static constexpr auto getFacetType(UInt t = 0) {
	return element_class_extra_geom_property::facet_type[t];
	}
	static constexpr auto getFacetTypes();
	};

	/* -------------------------------------------------------------------------- */
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	#include "geometrical_element_property.hh"
	#include "interpolation_element_tmpl.hh"
	/* -------------------------------------------------------------------------- */
	#include "element_class_tmpl.hh"
	/* -------------------------------------------------------------------------- */
	namespace akantu {
	#include "element_class_pentahedron_6_inline_impl.cc"
	/* keep order */
	#include "element_class_hexahedron_8_inline_impl.cc"
	#include "element_class_hexahedron_20_inline_impl.cc"
	#include "element_class_pentahedron_15_inline_impl.cc"
	#include "element_class_point_1_inline_impl.cc"
	#include "element_class_quadrangle_4_inline_impl.cc"
	#include "element_class_quadrangle_8_inline_impl.cc"
	#include "element_class_segment_2_inline_impl.cc"
	#include "element_class_segment_3_inline_impl.cc"
	#include "element_class_tetrahedron_10_inline_impl.cc"
	#include "element_class_tetrahedron_4_inline_impl.cc"
	#include "element_class_triangle_3_inline_impl.cc"
	#include "element_class_triangle_6_inline_impl.cc"
	} // namespace akantu

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

	#if defined(AKANTU_COHESIVE_ELEMENT)
	#include "cohesive_element.hh"
	#endif

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

	#endif /* __AKANTU_ELEMENT_CLASS_HH__ */

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