Collocation Methods

[tbetcke]

Allow the discretisation of integral operators using collocation

[pimanov]

How about implementing not only the Collocation method but the Nystrom method? I imagine the interface to the collocation method as a new function space, named for example "PS" - "Point Space", that can be used as a test space in the definition of an operator. Using "PS" as a domain space leads to the Nystrom method. The Nystrom method allows the calculation of most parts of matrix elements without integration as point-by-point interaction. It works well with FMM and Hierarchical matrices including Fast Direct Solvers.

[pescap]

If I understand well, "PS" would be defined similar to the "DP", 0 space, but with a different shapeset:

bempp-cl/bempp/api/space/shapesets.py

Line 49 in 3273fa9

return _np.ones((1, 1, local_coordinates.shape[1]), dtype=local_coordinates.dtype)

Am I correct? Would it be as simple as this?