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Zbl 1243.65144
Boubendir, Y.; Antoine, X.; Geuzaine, C.
A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation. (English)
[J] J. Comput. Phys. 231, No. 2, 262-280 (2012). ISSN 0021-9991

Summary: This paper presents a new non-overlapping domain decomposition method for the Helmholtz equation, whose effective convergence is quasi-optimal. These improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the Dirichlet to Neumann operator. A convergence theorem of the algorithm is established and numerical results validating the new approach are presented in both two and three dimensions.

MSC 2000:: *65N55 Multigrid methods; domain decomposition (BVP of PDE)
65N30 Finite numerical methods (BVP of PDE)
35J05 Laplace equation, etc.
65N12 Stability and convergence of numerical methods (BVP of PDE)

Keywords: Helmholtz equation; domain decomposition methods; finite elements; Padé approximants; convergence; algorithm; numerical results

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Zentralblatt MATH Berlin [Germany]