Feature Linear Basis functions #102
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This allows a singularity extraction strategy for the doublelayer, doublelayertransposed and hypersingular operator for triangles close together (for specific pairings of patch and pyramid functions).
Added functions so that all combinations of patch and pyramid functions can be used with Sauter integrals for the common face/edge/certex case and a singularity extraction rule for the near singular case. Not clear why DoubleQuadStrat performs better for common vertex than singularity extraction. For triangles close together singularity extraction appears to perform better as is expected.
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I released a new version of WiltonInts with your additions. Could you modify the Project.toml in this PR to depend on this new version? I have been working in parallel on enabling the SauterSchwab rules for the HH3D Hypersinguler etc. could you bring your PR in accordance to this work (I think most of what is in |
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Thank you for your work! I am now finally finding time to look into the changes you made. |
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For Helmholtz problems, there was so missing support for the singular or near singular integrals when linear basis functions are used.
In this pull request,
I tested the functions by comparing the SauterSchwab, Wilton, and DoubleQuad integrals for the common face/edge/vertex cases and making sure they give similar results, also under the assumption that the Wilton strategy should give results closer to the SauterSchwab strategy than the DoubleQuad does. However, there are some cases where where the DoubleQuad performs better, and I am not sure why that is, it's marked in the code as a comment.
For seperated triangles, I also compare to a reference value that was calculated with the HCubature package.
To get the correct signs in all expressions, this relies on pull request #14 in the WiltonInts84 package.