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A Domain Decomposition Method for the Exterior Helmholtz Problem

✍ Scribed by Romeo F. Susan-Resiga; Hafiz M. Atassi

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 320 KB
Volume: 147
Category: Article
ISSN: 0021-9991
DOI: 10.1006/jcph.1998.6094

No coin nor oath required. For personal study only.

✦ Synopsis

A new domain decomposition method is presented for the exterior Helmholtz problem. The nonlocal Dirichlet-to-Neumann (DtN) map is used as a nonreflecting condition on the outer computational boundary. The computational domain is divided into nonoverlapping subdomains with Sommerfeld-type conditions on the adjacent subdomain boundaries to ensure uniqueness. An iterative scheme is developed, where independent subdomain boundary-value problems are obtained by applying the DtN operator to values from the previous iteration. The independent problems are then discretized with finite elements and can be solved concurrently. Numerical results are presented for a two-dimensional model problem, and both the solution accuracy and convergence rate are investigated.

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