A simple implementation of PML for second-order elastic wave equations
When modeling time-domain elastic wave propagation in an unbound space, the standard perfectly matched layer (PML) is straightforward for the first-order partial differential equations (PDEs); by contrast, the PML requires tremendous re-constructions of the governing equations in the second-order PD...
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Veröffentlicht in: | Computer physics communications 2020-01, Vol.246, p.106867, Article 106867 |
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Sprache: | eng |
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Zusammenfassung: | When modeling time-domain elastic wave propagation in an unbound space, the standard perfectly matched layer (PML) is straightforward for the first-order partial differential equations (PDEs); by contrast, the PML requires tremendous re-constructions of the governing equations in the second-order PDE form, which is however preferable, because of much less memory and time consumption. Therefore, it is imperative to explore a simple implementation of PML for the second-order system. In this work, we first systematically extend the first-order Nearly PML (NPML) technique into second-order systems, implemented by the spectral element and finite difference time-domain algorithms. It merits the following advantages: the simplicity in implementation, by keeping the second-order PDE-based governing equations exactly the same; the efficiency in computation, by introducing a set of auxiliary ordinary differential equations (ODEs). Mathematically, this PML technique effectively hybridizes the second-order PDEs and first-order ODEs, and locally attenuates outgoing waves, thus efficiently avoid either spatial or temporal global convolutions. Numerical experiments demonstrate that the NPML for the second-order PDE has an excellent absorbing performance for elastic, anelastic and anisotropic media in terms of the absorption accuracy, implementation complexity, and computation efficiency. |
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ISSN: | 0010-4655 1879-2944 |
DOI: | 10.1016/j.cpc.2019.106867 |