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On perfectly
matched layers of nonlocal wave equations in unbounded
multiscale media
Yu Du and Jiwei Zhang |
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Vol. 17 (2022), No. 4, 343–364
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Abstract |
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A nonlocal perfectly matched layer (PML) is formulated for the nonlocal wave equation in the whole real axis, and numerical discretization is designed for solving the reduced PML problem on a bounded domain. The nonlocal PML poses challenges not faced in PDEs. For example, there is no derivative in nonlocal models, which makes it impossible to replace derivatives with complex ones. Here we provide a way of constructing the PML for nonlocal models, which decays the waves exponentially impinging in the layer and makes reflections at the truncated boundary very tiny. To numerically solve the nonlocal PML problem, we design the asymptotically compatible (AC) scheme for a spatially nonlocal operator by combining Talbot’s contour and a Verlet-type scheme for time evolution. The accuracy and effectiveness of our approach are illustrated by various numerical examples. |
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Keywords
nonlocal wave equation, asymptotically compatible (AC)
scheme, perfectly matched layer (PML), artificial/absorbing
boundary condition (ABC), multiscale media
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Milestones
Received: 7 November 2021
Revised: 16 March 2022
Accepted: 21 March 2022
Published: 18 February 2023
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Authors |
| Yu Du | |
| Department of Mathematics Xiangtan University Yuhu District, Xiangtan, Hunan China |
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| Jiwei Zhang | |
| School of Mathematics and
Statistics Wuhan University Wuhan, Hubei China |
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