element_class.hh
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element_class.hh
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	/**
	* Copyright (©) 2010-2023 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* This file is part of Akantu
	*
	* 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 constexpr GeometricalType geometrical_type{_gt_not_defined};
	static constexpr InterpolationType interpolation_type{_itp_not_defined};
	static constexpr ElementKind element_kind{_ek_regular};
	static constexpr Int spatial_dimension{0};
	static constexpr GaussIntegrationType gauss_itegration_type{_git_not_defined};
	static constexpr Int polynomial_degree{0};
	};

	#if !defined(DOXYGEN)
	/// 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 constexpr GeometricalType geometrical_type{geom_type}; \
	static constexpr InterpolationType interpolation_type{interp_type}; \
	static constexpr ElementKind element_kind{elem_kind}; \
	static constexpr Int spatial_dimension{sp}; \
	static constexpr GaussIntegrationType gauss_integration_type{ \
	gauss_int_type}; \
	static constexpr Int polynomial_degree{min_int_order}; \
	}
	#else
	#define AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(elem_type, geom_type, \
	interp_type, elem_kind, sp, \
	gauss_int_type, min_int_order)
	#endif

	/* -------------------------------------------------------------------------- */
	/* Geometry */
	/* -------------------------------------------------------------------------- */
	/// Default GeometricalShape structure
	template <GeometricalType geometrical_type> struct GeometricalShape {
	static constexpr 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 coord
	template <class D>
	static inline bool contains(const Eigen::MatrixBase<D> & coord);
	};

	#if !defined(DOXYGEN)
	/// Macro to generate the GeometricalShape structures for different geometrical
	/// types
	#define AKANTU_DEFINE_SHAPE(geom_type, geom_shape) \
	template <> struct GeometricalShape<geom_type> { \
	static constexpr 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);
	#endif
	/* -------------------------------------------------------------------------- */
	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
	template <class D>
	static inline Real getInradius(const Eigen::MatrixBase<D> & /X/) {
	return 0.;
	}

	/// compute the normal to the element
	template <class D1, class D2>
	static inline void getNormal(const Eigen::MatrixBase<D1> & /X/,
	Eigen::MatrixBase<D2> & n) {
	n.zero();
	}

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

	public:
	static constexpr auto getSpatialDimension() {
	return geometrical_property::spatial_dimension;
	}
	static constexpr auto getNbNodesPerElement() {
	return geometrical_property::nb_nodes_per_element;
	}
	static inline constexpr auto getNbFacetTypes() {
	return geometrical_property::nb_facet_types;
	};
	static inline constexpr Int getNbFacetsPerElement(Idx t);
	static inline constexpr Int getNbFacetsPerElement();

	static inline constexpr decltype(auto)
	getFacetLocalConnectivityPerElement(Idx t = 0);

	template <Idx t,
	std::size_t size = std::tuple_size<
	decltype(geometrical_property::nb_facets)>::value,
	std::enable_if_t<(t < size)> * = nullptr>
	static inline constexpr decltype(auto) getFacetLocalConnectivityPerElement();

	template <Idx t,
	std::size_t size = std::tuple_size<
	decltype(geometrical_property::nb_facets)>::value,
	std::enable_if_t<not(t < size)> * = nullptr>
	static inline constexpr decltype(auto) getFacetLocalConnectivityPerElement();
	};

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

	#if !defined(DOXYGEN)
	/// 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 Int nb_nodes_per_element{nb_nodes}; \
	static constexpr Int natural_space_dimension{ndim}; \
	}
	#else
	#define AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(itp_type, itp_kind, \
	nb_nodes, ndim)
	#endif
	/* -------------------------------------------------------------------------- */
	/// 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
	template <class D1, class D2,
	aka::enable_if_t<aka::are_matrices<D1, D2>::value> * = nullptr>
	static inline void computeShapes(const Eigen::MatrixBase<D1> & Xs,
	const Eigen::MatrixBase<D2> & N_);

	/// compute the shape values for a given point in natural coordinates
	template <class D1, class D2,
	aka::enable_if_t<aka::are_vectors<D1, D2>::value> * = nullptr>
	static inline void computeShapes(const Eigen::MatrixBase<D1> & /Xs/,
	Eigen::MatrixBase<D2> & /N_/) {
	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
	*/
	template <class D>
	static inline void computeDNDS(const Eigen::MatrixBase<D> & Xs,
	Tensor3Base<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 D1, class D2>
	static inline void computeDNDS(const Eigen::MatrixBase<D1> & /Xs/,
	Eigen::MatrixBase<D2> & /dNdS/) {
	AKANTU_TO_IMPLEMENT();
	}

	/**
	* compute @f$ @f$

	**/
	static inline void computeD2NDS2(const Matrix<Real> & natural_coord,
	Tensor3<Real> & d2nds2);

	/**
	* compute @f$ B_{ij} = \frac{\partial N_j}{\partial S_i} @f$ the
	* second 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 computeD2NDS2(const vector_type & /unused/,
	matrix_type & /unused/) {
	AKANTU_TO_IMPLEMENT();
	}

	/// compute jacobian (or integration variable change factor) for a given point
	/// in the case of spatial_dimension != natural_space_dimension
	template <class D>
	static inline Real computeSpecialJacobian(const Eigen::MatrixBase<D> &) {
	AKANTU_TO_IMPLEMENT();
	}

	/// interpolate a field given (arbitrary) natural coordinates
	template <class Derived1, class Derived2>
	static inline decltype(auto) interpolateOnNaturalCoordinates(
	const Eigen::MatrixBase<Derived1> & natural_coords,
	const Eigen::MatrixBase<Derived2> & nodal_values) {
	using interpolation = InterpolationProperty<interpolation_type>;
	Eigen::Matrix<Real, interpolation::nb_nodes_per_element, 1> shapes;
	computeShapes(natural_coords, shapes);

	Matrix<Real, Eigen::Dynamic, 1> res;
	res.noalias() = interpolate(nodal_values, shapes);

	return res;
	}

	/// interpolate a field given the shape functions on the interpolation point
	template <class Derived1, class Derived2>
	static inline auto
	interpolate(const Eigen::MatrixBase<Derived1> & nodal_values,
	const Eigen::MatrixBase<Derived2> & shapes);

	/// interpolate a field given the shape functions on the interpolations points
	template <class Derived1, class Derived2, class Derived3>
	static inline void
	interpolate(const Eigen::MatrixBase<Derived1> & nodal_values,
	const Eigen::MatrixBase<Derived2> & Ns,
	const Eigen::MatrixBase<Derived3> & interpolated);

	/// compute the gradient of a given field on the given natural coordinates
	template <class D1, class D2, class D3>
	static inline void
	gradientOnNaturalCoordinates(const Eigen::MatrixBase<D1> & natural_coords,
	const Eigen::MatrixBase<D2> & f,
	const Eigen::MatrixBase<D3> & dfds);

	public:
	static constexpr auto getShapeSize() {
	return InterpolationProperty<interpolation_type>::nb_nodes_per_element;
	}
	static constexpr auto getShapeDerivativesSize() {
	return (InterpolationProperty<interpolation_type>::nb_nodes_per_element *
	InterpolationProperty<interpolation_type>::natural_space_dimension);
	}
	static constexpr auto getNaturalSpaceDimension() {
	return InterpolationProperty<interpolation_type>::natural_space_dimension;
	}
	static constexpr auto getNbNodesPerInterpolationElement() {
	return InterpolationProperty<interpolation_type>::nb_nodes_per_element;
	}
	};

	/* -------------------------------------------------------------------------- */
	/* Integration */
	/* -------------------------------------------------------------------------- */
	template <GaussIntegrationType git_class, Int 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,
	Int n = ElementClassProperty<type>::polynomial_degree>
	class GaussIntegrationElement {
	static constexpr InterpolationType itp_type =
	ElementClassProperty<type>::interpolation_type;
	using interpolation_property = InterpolationProperty<itp_type>;

	public:
	static constexpr Int getNbQuadraturePoints();
	static constexpr auto getQuadraturePoints();
	static constexpr auto 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
	*/
	template <class D1, class D2>
	static inline decltype(auto)
	computeJMat(const Eigen::MatrixBase<D1> & dnds,
	const Eigen::MatrixBase<D2> & node_coords);

	/**
	* 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
	*/
	template <class D>
	static inline void computeJMat(const Tensor3Base<Real> & dnds,
	const Eigen::MatrixBase<D> & node_coords,
	Tensor3Base<Real> & J);

	/// compute the jacobians of a serie of natural coordinates
	template <class D1, class D2, class D3>
	static inline void
	computeJacobian(const Eigen::MatrixBase<D1> & natural_coords,
	const Eigen::MatrixBase<D2> & node_coords,
	Eigen::MatrixBase<D3> & jacobians);

	/// compute jacobian (or integration variable change factor) for a set of
	/// points
	template <class D>
	static inline void computeJacobian(const Tensor3Base<Real> & J,
	Eigen::MatrixBase<D> & jacobians);

	/// compute jacobian (or integration variable change factor) for a given point
	template <class D>
	static inline Real computeJacobian(const Eigen::MatrixBase<D> & J);

	/// compute shape derivatives (input is dxds) for a set of points
	static inline void computeShapeDerivatives(const Tensor3Base<Real> & J,
	const Tensor3Base<Real> & dnds,
	Tensor3Base<Real> & shape_deriv);

	/// compute shape derivatives (input is dxds) for a given point
	template <class D1, class D2, class D3>
	static inline void
	computeShapeDerivatives(const Eigen::MatrixBase<D1> & J,
	const Eigen::MatrixBase<D2> & dnds,
	Eigen::MatrixBase<D3> & shape_deriv);

	/// compute the normal of a surface defined by the function f
	template <class D1, class D2, class D3>
	static inline void
	computeNormalsOnNaturalCoordinates(const Eigen::MatrixBase<D1> & coord,
	const Eigen::MatrixBase<D2> & f,
	Eigen::MatrixBase<D3> & normals);

	/// get natural coordinates from real coordinates
	template <class D1, class D2, class D3,
	aka::enable_if_vectors_t<D1, D3> * = nullptr>
	static inline void inverseMap(const Eigen::MatrixBase<D1> & real_coords,
	const Eigen::MatrixBase<D2> & node_coords,
	const Eigen::MatrixBase<D3> & natural_coords,
	Int max_iterations = 100,
	Real tolerance = 1e-10);

	/// get natural coordinates from real coordinates
	template <class D1, class D2, class D3,
	aka::enable_if_matrices_t<D1, D3> * = nullptr>
	static inline void inverseMap(const Eigen::MatrixBase<D1> & real_coords,
	const Eigen::MatrixBase<D2> & node_coords,
	const Eigen::MatrixBase<D3> & natural_coords_,
	Int max_iterations = 100,
	Real tolerance = 1e-10);

	public:
	static constexpr auto getKind() { return element_kind; }
	static constexpr auto getSpatialDimension() {
	return ElementClassProperty<element_type>::spatial_dimension;
	}

	using element_class_extra_geom_property =
	ElementClassExtraGeometryProperties<element_type>;

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

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

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