Determine hueristic settings for ACA about acoustics HOT 10 CLOSED

First trial involved running the sphere and changing only the approximation tolerance from 1e-2 to 1e-10.

Findings were that 1e-2 does not yield accurate results and the rest do, but there is little to no change in the accuracy between 1e-4 and 1e-10.

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Second trial is changing the number of octree levels while holding approximation tolerance at 1e-4 to see for what number of unknowns and number of octree levels will, generally, lead to the lowest compression ratio thus the fastest runtime

Only the 19000 element sphere benefits from 4 octree levels. Next, try more elements.

at 43000 elements 5 levels is much slower still.

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try tuning reltol of gmres to push error down

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lowering reltol of gmres and aca approximation tol isnt lowering the error much. maybe I need to increase the number of inner iterations of gmres.

https://iterativesolvers.julialinearalgebra.org/stable/linear_systems/gmres/#GMRES

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I am seeing strange behavior with the convergence of the error for the sphere for the most refined meshes.

There is non-convergence for the last two meshes shown above. Check out the condition numbers of the Z matrix at those corresponding wavelengths. For this plot lambda = 350 * approximate element edge length. I would think resonances wouldn't be an issue here, but running my resonance test should tell me if the condition number spikes at these wavelengths compared to the wavelengths used in the first three runs.

Next Steps:

• run resonance test on problematic wavelenths
• run resonance test on good wavelengths
• compare resonance test results
• run old solver on 19000 element mesh and compare error with ACA results

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The condition number of the Z matrix is mostly stable in these wavelength regimes. Time to run the 19000 mesh with the non-fast solver.

Additionally, I ran the old solver on 19000 element mesh and the error was ~1.5e-3 which is on trend with the log fit line. So there must be a problem with ACA that is causing the convergence of the error to break at 19000 elements.

Next Steps:

• Run with higher ACA tolerances and see if there is a difference in error

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Ran with a mesh of over 70000 elements

Looks like the error continues along its path with the more refined mesh.

Next steps:

• Remesh with approimately the same number of elements as the 40000 mesh, but slightly different and rerun

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Remeshing showed results on trend with convergence rate so I think it was just a funky mesh

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Last step in this issue is running some tests on a rectangular strip

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issue completed in #80

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