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element_class.hh
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/**
* @file element_class.hh
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Jun 18 2010
* @date last modification: Fri Jul 04 2014
*
* @brief Declaration of the ElementClass main class and the
* Integration and Interpolation elements
*
* @section LICENSE
*
* Copyright (©) 2014 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 GaussIntergrationType gauss_integration_type = _git_not_defined;
static const UInt minimal_integration_order = 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 GaussIntergrationType gauss_integration_type = gauss_int_type; \
static const UInt minimal_integration_order = 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<GaussIntergrationType git_class, UInt max_order>
struct GaussIntegrationTypeData {
/// quadrature points in natural coordinates
static Real quad_positions[];
/// weights for the Gauss integration
static Real quad_weights[];
/// Number of quadrature points per element
static UInt nb_quadrature_points;
};
template<ElementType type, UInt order = ElementClassProperty<type>::minimal_integration_order>
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;
};
/* -------------------------------------------------------------------------- */
#include "element_class_tmpl.hh"
/* -------------------------------------------------------------------------- */
#include "element_classes/element_class_point_1_inline_impl.cc"
#include "element_classes/element_class_segment_2_inline_impl.cc"
#include "element_classes/element_class_segment_3_inline_impl.cc"
#include "element_classes/element_class_triangle_3_inline_impl.cc"
#include "element_classes/element_class_triangle_6_inline_impl.cc"
#include "element_classes/element_class_tetrahedron_4_inline_impl.cc"
#include "element_classes/element_class_tetrahedron_10_inline_impl.cc"
#include "element_classes/element_class_quadrangle_4_inline_impl.cc"
#include "element_classes/element_class_quadrangle_8_inline_impl.cc"
#include "element_classes/element_class_hexahedron_8_inline_impl.cc"
#include "element_classes/element_class_hexahedron_20_inline_impl.cc"
#include "element_classes/element_class_pentahedron_6_inline_impl.cc"
#include "element_classes/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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