The most important family of classes in the SpatialDomains library is the Geometry family, as can also be seen in the figure below. These classes are the representation of a (geometric) element in physical space}. It has been indicated before that every local element can be considered as an image of the standard element where the corresponding one-to-one mapping can be represented as an elemental standard spectral/hp expansion. As such, a proper encapsulation should at least contain data structures that represent such an expansion in order to completely define the geometry of the element. Therefore, we have equipped the classes in the Geometry family with the following data structures:
Note that although the latter data structure is not necessary to define the geometry, it contains information inherent to the iso-parametric representation of the element that can later be used in e.g. the LocalRegions library. Again, the StdExpansion object can be defined in the abstract base class Geometry. However, for every shape-specific geometry class, it needs to be initialised according to the corresponding StdRegions class (e.g. for the QuadGeom class, it needs to be initialised as an StdQuadExp object).
1.7.1
