Defines a set of shape functions. More...
#include <shapeset.h>
Inheritance diagram for Hermes::Hermes2D::Shapeset:
Public Types | |
| typedef double(* | shape_fn_t )(double, double) |
| Shape-function function type. Internal. | |
Public Member Functions | |
| int | get_order (int index, ElementMode2D mode) const |
| virtual Shapeset * | clone ()=0 |
| int | get_num_components () const |
| Returns 2 if this is a vector shapeset, 1 otherwise. | |
| int | get_max_order () const |
| Returns the maximum poly degree for all shape functions. | |
| virtual int | get_max_index (ElementMode2D mode)=0 |
| Returns the highest shape function index. | |
| int | get_vertex_index (int vertex, ElementMode2D mode) const |
| Returns the index of a vertex shape function associated with the specified vertex. | |
| int | get_edge_index (int edge, int ori, int order, ElementMode2D mode) const |
| virtual SpaceType | get_space_type () const =0 |
| Returns space type. | |
Protected Member Functions | |
| int * | get_bubble_indices (int order, ElementMode2D mode) const |
| Returns a complete set of indices of bubble functions for an element of the given order. | |
| int | get_num_bubbles (int order, ElementMode2D mode) const |
| Returns the number of bubble functions for an element of the given order. | |
| int | get_constrained_edge_index (int edge, int order, int ori, int part, ElementMode2D mode) const |
| double | get_value (int n, int index, double x, double y, int component, ElementMode2D mode) |
| double | get_fn_value (int index, double x, double y, int component, ElementMode2D mode) |
| double | get_dx_value (int index, double x, double y, int component, ElementMode2D mode) |
| double | get_dy_value (int index, double x, double y, int component, ElementMode2D mode) |
| double | get_dxx_value (int index, double x, double y, int component, ElementMode2D mode) |
| double | get_dyy_value (int index, double x, double y, int component, ElementMode2D mode) |
| double | get_dxy_value (int index, double x, double y, int component, ElementMode2D mode) |
| double2 * | get_ref_vertex (int vertex, ElementMode2D mode) |
| Returns the coordinates of the reference domain vertices. | |
| virtual int | get_id () const =0 |
| Returns shapeset identifier. Internal. | |
| double * | calculate_constrained_edge_combination (int order, int part, int ori, ElementMode2D mode) |
| double * | get_constrained_edge_combination (int order, int part, int ori, int &nitems, ElementMode2D mode) |
| void | free_constrained_edge_combinations () |
| Releases all cached coefficients. | |
| double | get_constrained_value (int n, int index, double x, double y, int component, ElementMode2D mode) |
Protected Attributes | |
| shape_fn_t *** | shape_table [6] |
| int ** | vertex_indices |
| int *** | edge_indices |
| int *** | bubble_indices |
| int ** | bubble_count |
| int ** | index_to_order |
| double2 | ref_vert [H2D_MAX_SOLUTION_COMPONENTS][H2D_MAX_NUMBER_VERTICES] |
| int | max_order |
| int | num_components |
| int | ebias |
| first edge function. More... | |
| double ** | comb_table |
| int | table_size |
Friends | |
| template<typename Scalar > | |
| class | DiscreteProblem |
| template<typename Scalar > | |
| class | Solution |
| class | CurvMap |
| class | RefMap |
| template<typename Scalar > | |
| class | RefinementSelectors::H1ProjBasedSelector |
| template<typename Scalar > | |
| class | RefinementSelectors::L2ProjBasedSelector |
| template<typename Scalar > | |
| class | RefinementSelectors::HcurlProjBasedSelector |
| template<typename Scalar > | |
| class | RefinementSelectors::OptimumSelector |
| class | PrecalcShapeset |
| template<typename Scalar > | |
| class | Form |
| template<typename Scalar > | |
| class | MatrixForm |
| template<typename Scalar > | |
| class | VectorForm |
| template<typename Scalar > | |
| class | Space |
| template<typename Scalar > | |
| class | H1Space |
| template<typename Scalar > | |
| class | L2Space |
| template<typename Scalar > | |
| class | HcurlSpace |
| template<typename Scalar > | |
| class | HdivSpace |
| void | check_leg_tri (Shapeset *shapeset) |
| void | check_gradleg_tri (Shapeset *shapeset) |
Detailed Description
Defines a set of shape functions.
This class stores mainly the definitions of the polynomials for all shape functions, but also their polynomial degrees, their types (vertex, edge, bubble), and contains mechanisms for the calculation and storage of constrained shape functions.
The class returns shape function values for both triangles and quads, depending on what mode is requested.
Each shape function is assigned a unique number - 'index'. For standard shape functions, index is positive and not greater than the value returned by get_max_index(). Negative index values are reserved for constrained shape functions. These are special edge functions designed to fit standard edge functions along a portion of an edge, used in the construction of FE spaces on meshes with hanging nodes.
The usage of Shapeset is simple: you first obtain the index of the shape function you are interested in, be it a vertex function for a given vertex, or an edge function of a given order, etc. Then you call one of the functions get_fn_value(), get_dx_value(), etc. All shape functions are defined on the reference domain. For triangles, this is the standard triangle (-1,-1), (1,-1), (-1,1), and for quads this is the square (-1,1)^2.
The polynomial degree (or 'order') is an integer typically in the range[1-10] for H1 shapesets and[0-10] for H(curl) shapesets. Quadrilaterals are allowed to have different orders in the x and y directions (of the reference domain). The 'order' for quads thus has to be formed with the macro H2D_MAKE_QUAD_ORDER(), see h2d_common.h.
Vertex shape functions in H1 shapesets are also regarded as edge functions of orders 0 and 1. This simplifies constraint calculations and BC projections.
Shape functions are always Real-valued.
Definition at line 86 of file shapeset.h.
Member Function Documentation
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numbering of edge intervals: (the variable 'part')
-+- -+- -+- | | 13 | | 5 | -+- | | 12 | 1 | -+- -+- finer interval: | | 11 | | 4 | -+- p = (p + 1) * 2 (+1) | | 10 | -+- -+- -+- ... etc. | | 9 | | 3 | -+- | | 8 | 0 | -+- -+- | | 7 | | 2 | -+- | | 6 | -+- -+- -+- Constrained edge functions are constructed by subtracting the linear part (ie., two vertex functions) from the constraining edge function and expressing the rest as a linear combination of standard edge functions. This function determines the coefficients of such linear combination by forming and solving a simple linear system.
Definition at line 26 of file shapeset.cpp.
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Returns the coefficients for the linear combination forming a constrained edge function. This function performs the storage (caching) of these coefficients, so that they can be calculated only once.
Definition at line 101 of file shapeset.cpp.
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Returns the index of a constrained edge function. 'part' is 0 or 1 for edge halves, 2, 3, 4, 5 for edge quarters, etc. See shapeset.cpp.
Definition at line 211 of file shapeset.cpp.
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Constructs the linear combination of edge functions, forming a constrained edge function.
Definition at line 148 of file shapeset.cpp.
| int Hermes::Hermes2D::Shapeset::get_edge_index | ( | int | edge, |
| int | ori, | ||
| int | order, | ||
| ElementMode2D | mode | ||
| ) | const |
Returns the index of an edge function associated with the specified edge and of the requested order. 'ori' can be 0 or 1 and determines edge orientation (this is for shapesets with non-symmetric edge functions).
Definition at line 183 of file shapeset.cpp.
Referenced by Hermes::Hermes2D::RefMap::set_active_element(), and Hermes::Hermes2D::RefMap::untransform().
| int Hermes::Hermes2D::Shapeset::get_order | ( | int | index, |
| ElementMode2D | mode | ||
| ) | const |
Returns the polynomial degree of the specified shape function. If on quads, it returns encoded orders. The orders has to be decoded through macros H2D_GET_H_ORDER and H2D_GET_V_ORDER.
Definition at line 223 of file shapeset.cpp.
Referenced by Hermes::Hermes2D::PrecalcShapeset::set_active_shape().
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Obtains the value of the given shape function. (x,y) is a coordinate in the reference domain, component is 0 for Scalar shapesets and 0 or 1 for vector shapesets.
Definition at line 231 of file shapeset.cpp.
Member Data Documentation
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first edge function.
2 for H1 shapesets, 0 for H(curl) shapesets. It is the order of the
Definition at line 161 of file shapeset.h.
The documentation for this class was generated from the following files:
