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We present a wavenumber-explicit convergence analysis of the hp finiteelement method applied to a class of heterogeneous Helmholtz problems withpiecewise analytic coefficients at large wavenumber $k$. Our analysis coversthe heterogeneous Helmholtz equation with Robin, exact Dirichlet-to-Neumann,and second order absorbing boundary conditions, as well as perfectly matchedlayers.

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