Convergence analysis of additive Schwarz for the Euler equations
Applied Numerical Mathematics
Applied Numerical Mathematics
Journal of Computational Physics
Analysis of a conjugated infinite element method for acoustic scattering
Computers and Structures
An analysis of the BEM-FEM non-overlapping domain decomposition method for a scattering problem
Journal of Computational and Applied Mathematics
Algebraic approach to absorbing boundary conditions for the Helmholtz equation
International Journal of Computer Mathematics - Distributed Algorithms in Science and Engineering
A damping preconditioner for time-harmonic wave equations in fluid and elastic material
Journal of Computational Physics
A posteriori error analysis for two non-overlapping domain decomposition techniques
Applied Numerical Mathematics
A parallel Aitken-additive Schwarz waveform relaxation suitable for the grid
Parallel Computing
Applied Numerical Mathematics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
Optimized Domain Decomposition Methods for the Spherical Laplacian
SIAM Journal on Numerical Analysis
A Robin-type non-overlapping domain decomposition procedure for second order elliptic problems
Advances in Computational Mathematics
A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation
Journal of Computational Physics
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
A sweeping preconditioner for time-harmonic Maxwell's equations with finite elements
Journal of Computational Physics
The Optimized Schwarz Method with a Coarse Grid Correction
SIAM Journal on Scientific Computing
A rapidly converging domain decomposition method for the Helmholtz equation
Journal of Computational Physics
Double sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem
Journal of Computational Physics
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The classical Schwarz method is a domain decomposition method to solve elliptic partial differential equations in parallel. Convergence is achieved through overlap of the subdomains. We study in this paper a variant of the Schwarz method which converges without overlap for the Helmholtz equation. We show that the key ingredients for such an algorithm are the transmission conditions. We derive optimal transmission conditions which lead to convergence of the algorithm in a finite number of steps. These conditions are, however, nonlocal in nature, and we introduce local approximations which we optimize for performance of the Schwarz method. This leads to an algorithm in the class of optimized Schwarz methods. We present an asymptotic analysis of the optimized Schwarz method for two types of transmission conditions, Robin conditions and transmission conditions with second order tangential derivatives. Numerical results illustrate the effectiveness of the optimized Schwarz method on a model problem and on a problem from industry.