# Shifted Laplace preconditioners for the Helmholtz equations

@article{Vuik2003ShiftedLP, title={Shifted Laplace preconditioners for the Helmholtz equations}, author={Cornelis Vuik and Yogi A. Erlangga}, journal={Reports of the Department of Applied Mathematical Analysis}, year={2003} }

In this paper, we present a numerical method to solve the time-harmonic wave equation in 2D heterogeneous media. The underlying equation governs wave propagations and scattering phenomena arising in acoustic and optical problems. In particular, we look for solutions of the Helmholtz equation discretized by a finite difference method. Since the number of gridpoints per wavelength should be sufficiently large to result in acceptable solutions, for very high wavenumbers the discrete problem…

## 7 Citations

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Several numerical aspects and difficulties for solving a large linear system, derived from the Helmholtz equation, are overviewed and the numerical and exact solution of the one-dimensional HBVP in cases when the wavenumber and the source term are both real-valued is given.

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- PhysicsOCEANS 2015 - MTS/IEEE Washington
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The rapid growth of renewable energy from offshore sources has raised concerns that underwater noise from construction and operation of offshore devices may interfere with communication of marine…

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Dans cette these on considere des algorithmes de Schwarz appliques aux problemes harmoniques heterogenes (Maxwell et Helmholtz) en deux et trois dimensions. On fait l'etude pour une decomposition en…

### A PRECONDITIONED METHOD FOR THE SOLUTION OF THE ROBBINS PROBLEM FOR THE HELMHOLTZ EQUATION

- Computer Science, MathematicsThe ANZIAM Journal
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The approach taken in this paper is to preconditions this linear system with a sine transform based preconditioner and then solve it using the generalized minimum residual method (GMRES).

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