Wavenumber-explicit stability and convergence analysis of hp finite element discretizations of Helmholtz problems in piecewise smooth media

09/08/2022

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by   M. Bernkopf, et al.

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We present a wavenumber-explicit convergence analysis of the hp finite element method applied to a class of heterogeneous Helmholtz problems with piecewise analytic coefficients at large wavenumber k. Our analysis covers the heterogeneous Helmholtz equation with Robin, exact Dirichlet-to-Neumann, and second order absorbing boundary conditions, as well as perfectly matched layers.