Geometry Namespace Reference

A namespace containing classes describing hypergraph geometries. More...

Classes
class	File
	Hypergraph geometry based on an input file. More...
class	UnitCube
	Define the geometry of a unit cube that is subdivided into several orthotopes. More...

Detailed Description

A namespace containing classes describing hypergraph geometries.

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One of the advantages of this software package is the strict discrimination between the topology and the geometry of the domain \(\Omega\). Thus, one can exemplarily define a single topology (the one of a cube) to approximate PDEs that live on the cube's boundary and PDEs that live on a sphere, since their topology is the same. However, different geometries have to be defined, since these obviously are not equal. Thus, all parts of the code that involve communication and/or solving systems of equations are reusable in a much more general (than the standard) sense. Beyond that, absurd (on first sight) domains can be defined easily. This also covers variously periodic domains, for example.

There are four different types of normals specified (cf. the respective mapping):

• The normals of the reference element.
• The normals of of the transformed element which is still an element of the hyEdge_dimT dimensional space, but already has the shape of the physical element (called local_normal).
• The space_dimT dimensional normals of the phyiscal element located within the planar (or curve if curved elements are allowed) which is spanned by the element.
• The orthonormal vectors to the planar/curve spanned by phyiscal element (outer normals).

Authors

Guido Kanschat, Heidelberg University, 2019–2020.

Andreas Rupp, Heidelberg University, 2019–2020.