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Boundary infinite elements for the Helmholtz equation in exterior domains. (English) Zbl 0911.76035

Summary: We present a novel approach to the development of infinite element formulations for exterior problems of time-harmonic acoustics. This approach is based on a functional which provides a general framework for domain-based computation of exterior problems. Special cases include non-reflecting boundary conditions (such as the DtN method). A feature of this formulation is the lack of integration over the unbounded domain, simplifying the task of discretization. The original formulation is generalized to account for derivative discontinuities across infinite element boundaries, typical of standard infinite element approximations. Continuity between finite elements and infinite elements is enforced weakly, precluding compatibility requirements. Various infinite element approximations for two-dimensional configurations with circular interfaces are presented. Numerical results demonstrate a good performance of this scheme.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76Q05 Hydro- and aero-acoustics
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