Betcke, T;
Gander, MJ;
Phillips, J.;
(2012)
Block Jacobi relaxation for plane wave discontinuous Galerkin methods.
In:
Domain Decomposition Methods in Science and Engineering XXI.
Springer
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Abstract
In recent years plane wave approximation methods have become popular for the solution of Helmholtz problems, where instead of standard polynomial basis functions plane waves are used on each element to approximate the solution. One possibility to enforce inter-element continuity conditions for these basis functions is to use the plane wave discontinuous Galerkin Method (PWDG). In this paper we investigate block Jacobi relaxation methods for the PWDG. We show that for a certain choice of flux parameters in the PWDG block Jacobi is identical to a Schwarz method with standard impedance boundary conditions. This result motivates a simple algebraic decomposition method whose numerical performance is demonstrated for various wavenumbers. For high-frequency problem it is important to choose optimized transmission conditions between subdomains, and a first result of how to modify fluxes to incorporate optimized transmission conditions is presented.
| Type: | Proceedings paper |
|---|---|
| Title: | Block Jacobi relaxation for plane wave discontinuous Galerkin methods |
| Event: | Domain Decomposition Methods in Science and Engineering XXI |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | http://www.springer.com |
| Language: | English |
| Additional information: | Preprint submitted to Domain Decomposition Methods in Science and Engineering XXI. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1379539 |
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