3.2 Expansions

This section defines the polynomial expansions used on each of the defined geometric composites and variables. Expansion entries specify the number of modes and the expansion type, or a full list of data of basis type, number of modes, points type and number of points. The short-hand version has the following form


or, if we have more then one variable we can apply the same basis to all using


The expansion basis can also be specified in detail as a combination of one-dimensional bases, and thus the user is able to, for example, increase the quadrature order. For tet elements this takes the form:

2   BASISTYPE="Modified_A,Modified_B,Modified_C" 
3   NUMMODES="3,3,3" 
4   POINTSTYPE="GaussLobattoLegendre,GaussRadauMAlpha1Beta0,GaussRadauMAlpha2Beta0" 
5   NUMPOINTS="4,3,3" 
6   FIELDS="u" />

and for prism elements:

2   BASISTYPE="Modified_A,Modified_A,Modified_B" 
3   NUMMODES="3,3,3" 
4   POINTSTYPE="GaussLobattoLegendre,GaussLobattoLegendre,GaussRadauMAlpha1Beta0" 
5   NUMPOINTS="4,4,3" 
6   FIELDS="u" />

The expansions can be defined with a list of <E> elements (e.g., to represent different polynomial orders for different variables or to address different composites). The user can define a default expansion field by entering <E> tags without the FIELDS attribute. The default expansion is used to define any variables not explicitly listed in the <E> entries. In the following example, the default expansion is used to define the expansions for the composites C[0], C[1] and C[2]:


The expansions of each field should be defined only once for each composite.