局部粗糙表面时变声散射问题的PML方法的适定性和收敛性分析

IF 1 4区 数学 Q3 MATHEMATICS, APPLIED
Hongxia Guo, Guanghui Hu
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引用次数: 0

摘要

我们的目的是分析和计算声波在有界障碍物和局部摄动非自交曲线下的时变散射。通过明确定义的透明边界条件,将散射问题等效地转化为截断有界域中波动方程的初边值问题。建立了约简问题的适定性和稳定性。数值上,我们采用完全匹配层(PML)格式来模拟摄动波的传播。通过在半圆形PML中设计一种特殊的吸收介质,证明了截断初边值问题的适定性和稳定性。最后,我们证明了PML解在物理域中指数收敛于精确解。数值结果验证了吸波介质参数和吸波介质厚度的指数收敛性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Well-Posedness and Convergence Analysis of PML Method for Time-Dependent Acoustic Scattering Problems Over a Locally Rough Surface
We aim to analyze and calculate time-dependent acoustic wave scattering by a bounded obstacle and a locally perturbed non-selfintersecting curve. The scattering problem is equivalently reformulated as an initial-boundary value problem of the wave equation in a truncated bounded domain through a well-defined transparent boundary condition. Well-posedness and stability of the reduced problem are established. Numerically, we adopt the perfect matched layer (PML) scheme for simulating the propagation of perturbed waves. By designing a special absorbing medium in a semi-circular PML, we show the well-posedness and stability of the truncated initial-boundary value problem. Finally, we prove that the PML solution converges exponentially to the exact solution in the physical domain. Numerical results are reported to verify the exponential convergence with respect to absorbing medium parameters and thickness of the PML.
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来源期刊
CiteScore
2.40
自引率
7.70%
发文量
54
期刊介绍: The highly selective international mathematical journal Computational Methods in Applied Mathematics (CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.
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