Numerical analysis of high frequency wave scattering via semiclassical analysis: a case study with non-uniform meshes

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• Jeffrey Galkowski (UCL)
• Thursday 06 February 2025, 15:00-16:00
• Centre for Mathematical Sciences, MR14.

If you have a question about this talk, please contact Matthew Colbrook.

In recent years, semiclassical analysis has significantly advanced our understanding of numerical algorithms for high-frequency wave scattering. This talk will begin with an overview of how semiclassical methods have influenced the theory of numerical methods for frequency-domain wave problems. As a case study, we will then focus on the finite element method (FEM), a classical approach for approximating solutions to high-frequency scattering problems. In FEM , the solution is typically approximated using piecewise polynomials of degree p on a mesh of width h. A fundamental question is then: how should h be chosen (as a function of the frequency, k) so that the error in the numerical solution is small? It has been known since the seminal work of Babuska and Ihlenberg that the natural conjecture hk<

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