Perfectly Matched Layers for Time-Harmonic Second Order Elliptic Problems
Abstract
The main goal of this work is to give a review of the Perfectly Matched Layer (PML) technique for time-harmonic problems. Precisely, we focus our attention on problems stated in unbounded domains, which involve second order elliptic equations writing in divergence form and, in particular, on the Helmholtz equation at low frequency regime. Firstly, the PML technique is introduced by means of a simple porous model in one dimension. It is emphasized that an adequate choice of the so called complex absorbing function in the PML yields to accurate numerical results. Then, in the two-dimensional case, the PML governing equation is described for second order partial differential equations by using a smooth complex change of variables. Its mathematical analysis and some particular examples are also included. Numerical drawbacks and optimal choice of the PML absorbing function are studied in detail. In fact, theoretical and numerical analysis show the advantages of using non-integrable absorbing functions. Finally, we present some relevant real life numerical simulations where the PML technique is widely and successfully used although they are not covered by the standard theoretical framework.
Additional Information
© CIMNE, Barcelona, Spain 2010. Received: 8 August 2009. Accepted: 8 August 2009. Published online: 13 February 2010. This work has been partially supported by Ministerio de Ciencia e Innovación of Spain under grant number MTM2008-02483. Moreover, the first and third author were partially supported by Xunta de Galicia under grant number PGIDIT-07- PXIB105257-PR. The fourth author was partially supported by FONDAP and BASAL projects CMM, Universidad de Chile (Chile).Additional details
- Eprint ID
- 17677
- DOI
- 10.1007/s11831-010-9041-6
- Resolver ID
- CaltechAUTHORS:20100305-134528276
- MTM2008-02483
- Ministerio de Ciencia e Innovación of Spain
- PGIDIT-07-PXIB105257-PR
- Xunta de Galicia
- FONDAP and BASAL projects CMM, Universidad de Chile (Chile)
- Created
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2010-03-12Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field