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Studies of domain-based formulations for computing exterior problems of acoustics. (English) Zbl 0818.76040
The propagation and decay of acoustic waves in exterior domains is an essential ingredient in the study of fluid-structure interaction. A strategy must be devised to compute solutions over domains which are unbounded. Exact impedance conditions at an artificial external boundary are specified by the Dirichlet-to-Neumann (DtN) method, yielding an equivalent problem that is suitable for domain-based computation. The DtN boundary condition is non-reflective, giving rise to exact (and thereby unique) solutions. The truncated DtN operator fails to inhibit the reflection of higher modes, so that non-unique solutions may occur at their harmonics. Numerical studies examine the dependence of the conditioning of finite element coefficient matrices on the number of terms in the truncated DtN operator vs. the wave number non- dimensionalized by each of the length scales. Analytic results regarding the number of terms sufficient for unique solutions are confirmed.

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