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A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation. (English) Zbl 1243.65144
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:
65N55Multigrid methods; domain decomposition (BVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
65N12Stability and convergence of numerical methods (BVP of PDE)
Software:
GetDP
References:
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