A robust discretization technique for three dimensional Helmholtz problems

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• Adrianna Gillman (University of Colorado Boulder)
• Tuesday 18 April 2023, 09:45-10:30
• Seminar Room 1, Newton Institute.

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MWSW03 - Computational methods for multiple scattering

he ability to robustly and efficiently solve Helmholtz problems has been plagued by the so-called pollution effect and the introduction of artificial resonances by the discretization.  The recently developed the Hierarchical Poincare-Steklov (HPS) method has demonstrated that it does not observe either of these shortcoming for two dimensional problems.  Additionally a robust coupling technique for scattering problem involving local deviations from constant coefficient which utilizes a Dirichlet-to-Neumann operator built by the HPS method has been developed.  In this presentation, we will demonstrate that the extension of the HPS method to three dimensional problems is just as robust as the two dimensional solution technique. We will also present ongoing work towards making the solution technique efficient for three dimensional problems.  For example, a three dimensional problem approximately 100 wavelengths in size can be solved to 4 digits of accuracy in 17 minutes with over 1 billion discretization points.  Additionally, a problem 50 wavelengths in size can be solved to 8 digits of accuracy in 26 minutes with the same number of discretization points.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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