Evaluating EFIE with test = trial

[Raymond van Venetië]

Hi,

I want to calculate the matrix belonging to the EFIE discretized with Raviart Thomas test and trial spaces, so I've tried:

rwg_space = bempp.api.function_space(grid, "RWG",0)
efie = bempp.api.operators.boundary.maxwell.electric_field(rwg_space, rwg_space, rwg_space, k)

It appears, however, that this is not a valid choice, and that I have to take my test space equal to a Nedelec curl-conforming space, i.e.

rwg_space = bempp.api.function_space(grid, "RWG", 0)
snc_space = bempp.api.function_space(grid, "SNC", 0)
efie = bempp.api.operators.boundary.maxwell.electric_field(rwg_space, rwg_space, snc_space, k)

Is it possible to circumvent this restriction? Or is the latter somehow equivalent to what I wish to calculate?

Thanks in advance!

Raymond

[Matthew Scroggs]

Hi Raymond,

The operators for Maxwell are usually defined using the twisted inner product (integral of u dot (normal cross v)). However, as SNC functions are equal to "normal cross RWG", this inner product is equivalent to using the l2 inner product (integral of u dot v) with u in RWG and v in SNC.

In Bempp, we use the latter notation, so use SNC functions for the dual/test spaces. This is equivalent to testing using RWG spaces if you are using the twisted product.

This is commented on in the paper Software framework for ... (open access: https://www.sciencedirect.com/science/article/pii/S0898122117304789?via%3Dihub) just after theorem 1.

Hope this helps,

Matthew