ShapesP13D Class Reference

#include <ShapesEvaluatedP13D.h>

Inheritance diagram for ShapesP13D:

Public Types
typedef ShapesEvaluated__ < P13D, Tet_1::Bulk >	Bulk
typedef ShapesEvaluated__ < P12D, Triangle_1::Bulk >	Faces
typedef ShapesEvaluated__ < P13D, Tet_1::FaceOne >	FaceOne
typedef ShapesEvaluated__ < P13D, Tet_1::FaceTwo >	FaceTwo
typedef ShapesEvaluated__ < P13D, Tet_1::FaceThree >	FaceThree
typedef ShapesEvaluated__ < P13D, Tet_1::FaceFour >	FaceFour
Static Public Attributes
static const Shape *const	P13D = new Linear<3>(ShapesP13D::bctMap)
static const Shape *const	P12D = new Linear<2>
Static Protected Attributes
static const size_t	bctMap [] = {0,1,3,2}

Detailed Description

ShapesEvaluatedP13D.h DG++.

Created by Ramsharan Rangarajan.

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. Shape functions for P13D elements: Linear functions on tetrahedra.

It containes two types of traces 1) ShapesP13D::Faces are linear functions on triangles and their dofs are those associated with the nodes of the triangular face.

2) ShapesP13D::FaceOne, ShapesP13D::FaceTwo, ShapesP13D::FaceThree and ShapesP13D::FaceFour are the full set of linear shape functions in the elements evaluated at quadrature points in each one of the faces. Instead of having 3 dofs per field per face, there are 3 dofs per field per face. Some of these values are trivially zero, i.e., those of the shape function associated to the node opposite to the face where the quadrature point is. As was the done in ShapesP12D, these are provided since ocassionally it may be necessary to have the same number of dofs as the bulk fields. In the most general case of arbitrary bases, there is generally no shape function that is zero on the face, and hence bulk and trace fields have the same number of dofs.