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<p>Perfectly Matched Layers (PML) has become a very common method for the numerical approximation of wave and wave-like equations on unbounded domains. This technique allows one to obtain accurate solutions while working on a finite computational domain, and the technique is relatively simple to implement. Results concerning the accuracy of the PML method have been obtained, but mostly with regard to problems at a fixed frequency. In this paper we provide very explicit time-domain bounds on the accuracy of PML for the inhomogeneous two-dimensional wave equation with a particular type of forcing term, and illustrate our conclusions with some numerical examples.</p>

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Perfectly matched layers in time domain. A simplified two-dimensional error analysis

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • Kurt M. Bryan,
  • Michael S. Vogelius

摘要

Perfectly Matched Layers (PML) has become a very common method for the numerical approximation of wave and wave-like equations on unbounded domains. This technique allows one to obtain accurate solutions while working on a finite computational domain, and the technique is relatively simple to implement. Results concerning the accuracy of the PML method have been obtained, but mostly with regard to problems at a fixed frequency. In this paper we provide very explicit time-domain bounds on the accuracy of PML for the inhomogeneous two-dimensional wave equation with a particular type of forcing term, and illustrate our conclusions with some numerical examples.