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bempp / bempp-cl

A fast Python based just-in-time compiling boundary element library
http://www.bempp.com
MIT License
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Collocation Methods #49

Open tbetcke opened 4 years ago

tbetcke commented 4 years ago

Allow the discretisation of integral operators using collocation

pimanov commented 2 years ago

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 commented 2 years ago

If I understand well, "PS" would be defined similar to the "DP", 0 space, but with a different shapeset: https://github.com/bempp/bempp-cl/blob/3273fa97c8a13ee171b0bc45ec40567966588b3d/bempp/api/space/shapesets.py#L49 Am I correct? Would it be as simple as this?