Mapping Namespace Reference

Namespace for mappings from reference elements to physical elements, etc. More...

Classes
class	Linear
	Mapping of a unit hypercube to a parallelotope — can also be used for simplices. More...

Detailed Description

Namespace for mappings from reference elements to physical elements, etc.

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Mappings of a hyEdge_dimT dimensional unit square to a subset of a subset of the real numbers to the power space_dimT heavily reliy on QR decomposition. Additionally, there are four different types of normals:

• The normals of the unit square in hyEdge_dimT dimensions.
• The normals of R times the unit square in hyEdge_dimT dimensions (called local_normal).
• The normals of QR times the unit square within the planar spanned by the columns of the transformation matrix (denoted inner normals) in space_dimT dimensions.
• The orthonormal vectors to the planar spanned by the transformation matrix (outer normals).

The QR decomposition has a special normalization, i.e., the matrix Q suffices det(Q) = +1, i.e. Q describes a movement (no mirrioring), and R has non-negative diagonal entries — except for the entry (0,0) which may have negative sign. Thus, the sign of entry (0,0) describes, whether matrix a is orientation preserving or not.

Authors

Guido Kanschat, Heidelberg University, 2019–2020.

Andreas Rupp, Heidelberg University, 2019–2020.