Stable multiscale Petrov-Galerkin finite element method for high frequency acoustic scattering

D. Gallistl, D. Peterseim

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45 Citations (Scopus)


We present and analyze a pollution-free Petrov–Galerkin multiscale finite element method for the Helmholtz problem with large wave number as a variant of Peterseim (2014). We use standard continuous finite elements at a coarse discretization scale as trial functions, whereas the test functions are computed as the solutions of local problems at a finer scale . The diameter of the support of the test functions behaves like for some oversampling parameter . Provided is of the order of and is sufficiently small, the resulting method is stable and quasi-optimal in the regime where is proportional to . In homogeneous (or more general periodic) media, the fine scale test functions depend only on local mesh-configurations. Therefore, the seemingly high cost for the computation of the test functions can be drastically reduced on structured meshes. We present numerical experiments in two and three space dimensions.
Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalComputer methods in applied mechanics and engineering
Publication statusPublished - 2015
Externally publishedYes

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