Iterative schemes for high order compact discretizations to the exterior Helmholtz equation
| Autor: | Eli Turkel, Yogi A. Erlangga |
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| Rok vydání: | 2012 |
| Předmět: |
Numerical Analysis
Helmholtz equation Iterative method Preconditioner Applied Mathematics Mathematical analysis Krylov subspace Sommerfeld radiation condition System of linear equations Computer Science::Numerical Analysis Mathematics::Numerical Analysis Computational Mathematics Multigrid method Biconjugate gradient stabilized method Modeling and Simulation Analysis Mathematics |
| Zdroj: | ESAIM: Mathematical Modelling and Numerical Analysis. 46:647-660 |
| ISSN: | 1290-3841 0764-583X |
| DOI: | 10.1051/m2an/2011063 |
| Popis: | We consider high order finite difference approximations to the Helmholtz equation in an exterior domain. We include a simplified absorbing boundary condition to approximate the Sommerfeld radiation condition. This yields a large, but sparse, complex system, which is not self-adjoint and not positive definite. We discretize the equation with a compact fourth or sixth order accurate scheme. We solve this large system of linear equations with a Krylov subspace iterative method. Since the method converges slowly, a preconditioner is introduced, which is a Helmholtz equation but with a modified complex wavenumber. This is discretized by a second or fourth order compact scheme. The system is solved by BICGSTAB with multigrid used for the preconditioner. We study, both by Fourier analysis and computations this preconditioned system especially for the effects of high order discretizations. |
| Databáze: | OpenAIRE |
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