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element_class_igfem.hh
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/**
* @file element_class_igfem.hh
* @author Aurelia Cuba Ramos <aurelia.cubaramos@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @date Thu May 22 13:50:46 2014
*
* @brief Specialization for interface-enriched finite elements
*
* @section LICENSE
*
* Copyright (©) 2010-2011 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/>.
*
*/
/* -------------------------------------------------------------------------- */
/* Interpolation */
/* -------------------------------------------------------------------------- */
template<InterpolationType interpolation_type>
class InterpolationElement<interpolation_type, _itk_igfem> {
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) {
AKANTU_DEBUG_TO_IMPLEMENT();
}
/// 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) {
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 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) {
AKANTU_DEBUG_TO_IMPLEMENT();
}
/// 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) {
AKANTU_DEBUG_TO_IMPLEMENT();
}
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);
};
/* -------------------------------------------------------------------------- */
/// define ElementClassProperty for parent elements
#define AKANTU_DEFINE_IGFEM_PARENT_ELEMENT_CLASS_PROPERTY(elem_type, \
geom_type, \
interp_type, \
regular_el_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 ElementType regular_element_type = regular_el_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; \
static const bool is_subelement = false; \
}
/// define ElementClassProperty for subelements
#define AKANTU_DEFINE_IGFEM_SUBELEMENT_CLASS_PROPERTY(elem_type, \
geom_type, \
interp_type, \
regular_el_type, \
parent_el_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 ElementType regular_element_type = regular_el_type; \
static const ElementType parent_element_type = parent_el_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; \
static const bool is_subelement = true; \
}
/* -------------------------------------------------------------------------- */
/* ElementClass */
/* -------------------------------------------------------------------------- */
template<ElementType element_type>
class ElementClass<element_type, _ek_igfem> :
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 the shape values for a given set of points in natural coordinates
static inline void computeShapes(const Matrix<Real> & natural_coord,
Matrix<Real> & N) {
ElementClass<ElementClassProperty<element_type>::regular_el_type>::computeShapes(natural_coord, N);
}
static inline void computeDNDS(const Matrix<Real> & natural_coord,
Tensor3<Real> & dnds) {
ElementClass<ElementClassProperty<element_type>::regular_el_type>::computeDNDS(natural_coord, dnds);
}
/// interpolate a field given (arbitrary) natural coordinates
static inline void interpolateOnNaturalCoordinates(const Vector<Real> & natural_coords,
const Matrix<Real> & nodal_values,
Vector<Real> & interpolated) {
ElementClass<ElementClassProperty<element_type>::regular_el_type>::interpolateonnaturalcoordinates(natural_coords, nodal_values, 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) {
ElementClass<ElementClassProperty<element_type>::regular_el_type>::gradientOnNaturalCoordinates(natural_coords, f, gradient);
}
/**
* 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) {
ElementClass<ElementClassProperty<element_type>::regular_el_type>::computeJMat(dnds, node_coords, 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) {
ElementClass<ElementClassProperty<element_type>::regular_el_type>::JMat(dnds, node_coords, 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) {
ElementClass<ElementClassProperty<element_type>::regular_el_type>::computeJacobian(natural_coords, node_coords, jacobians);
}
/// compute jacobian (or integration variable change factor) for a set of points
static inline void computeJacobian(const Tensor3<Real> & J,
Vector<Real> & jacobians) {
ElementClass<ElementClassProperty<element_type>::regular_el_type>::computeJacobian(J, jacobians);
}
/// compute jacobian (or integration variable change factor) for a given point
static inline void computeJacobian(const Matrix<Real> & J,
Real & jacobians) {
ElementClass<ElementClassProperty<element_type>::regular_el_type>::computeJacobian(J, 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) {
ElementClass<ElementClassProperty<element_type>::regular_el_type>::computeShapeDerivatives(J,dnds, 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){
ElementClass<ElementClassProperty<element_type>::regular_el_type>::computeNormalsOnNaturalCoordinates(coord, f, 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) {
ElementClass<ElementClassProperty<element_type>::regular_el_type>::inverseMap(real_coords, node_coords, natural_coords, tolerance);
}
public:
static AKANTU_GET_MACRO_NOT_CONST(Kind, _ek_igfem, 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]; }
private:
/// Type of the facet elements
static ElementType facet_type[];
/// type of element P1 associated
static ElementType p1_type;
};
/* -------------------------------------------------------------------------- */
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