Issue: Improved Modal Basis for Triangles

[alilasemi]

Problem

The current modal basis for triangles, the hierarchic basis, has issues with poor conditioning at high polynomial order. Using orthogonal bases on triangles could be useful (for example - to simplify the inverse mass matrix multiply, or for exactly integrating source terms in Strang splitting), therefore an improved modal triangle basis could be useful.

Suggestion Solution

There may be a fix to this basis that improves the conditioning. Another fix could be to implement the Gram-Schmidt basis, since it is straightforward and very well conditioned (identity mass matrix).