Helmholtz transmission problem

luiz....@eac.ufsm.br

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Jul 27, 2020, 10:02:22 AM7/27/20

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Hello everyone,

I have been trying to solve a Helmholtz transmission problem with a complex wave number in the interior domain to represent porous materials. I noticed there is a commented function ("def transmission_operator") in the Helmholtz operators .py file and would like to know if there are major reasons for why it is not available or just that it was not yet functional. If such problems can be successfully solved with Bempp, are there informations or good literature you could share about this problem that could help implementation?

Thank you for all the help,

Best Wishes,

Luiz Augusto Alvim

Elwin

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Jul 27, 2020, 11:22:02 AM7/27/20

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Luiz,

For Helmholtz transmission problems you need to add the interior and exterior operators. In Bempp, you can take linear combinations of boundary integral operators and you can create block matrices. This functionality should be sufficient to solve Helmholtz transmission problems.

An example of a BEM formulation for Helmholtz transmission problems can be found here: https://arxiv.org/abs/1910.01011

Best,

Elwin

luiz....@eac.ufsm.br

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Jul 27, 2020, 12:10:23 PM7/27/20

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Hello Elwin,

I really appreciate your response, thanks for sending the paper. I will try to implement the presented formulation. Do you know if there are any Bempp parameters that I should consider tweaking for this model?

Luiz

Elwin

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Jul 27, 2020, 12:22:55 PM7/27/20

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Luiz,

Use the (complex-valued) wavenumber and impedance for the materials you consider. You can use the default Bempp parameters. When adding the exterior and interior Calderón operators, just be careful to scale the blocks of the interior operator with the correct impedance ratios.