复杂几何障碍物散射时域波场的cem - bem耦合模拟

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2023-03-09 DOI:10.1515/cmam-2022-0084

L. Desiderio, S. Falletta, M. Ferrari, L. Scuderi

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引用次数: 3

摘要

本文提出了一种基于曲面虚元法(CVEM)和边界元法(BEM)耦合的模拟均匀无限介质中障碍物散射波场的数值方法。特别地，我们考虑了边界上具有Dirichlet条件(声-软散射)的二维时域阻尼波动方程。为了将无限域简化为有限计算域，我们引入了一个人工边界，并在其上施加了边界积分非反射边界条件(BI-NRBC)。在内域采用CVEM与Crank-Nicolson时间积分器相结合的方法，在时间上采用卷积求积公式，在空间上采用配点法对BI-NRBC进行离散。我们给出了一些数值结果来测试所提出的方法的性能并突出其有效性，特别是在考虑具有复杂几何形状的障碍物时。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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CVEM-BEM Coupling for the Simulation of Time-Domain Wave Fields Scattered by Obstacles with Complex Geometries

Abstract In this paper, we present a numerical method based on the coupling between a Curved Virtual Element Method (CVEM) and a Boundary Element Method (BEM) for the simulation of wave fields scattered by obstacles immersed in homogeneous infinite media. In particular, we consider the 2D time-domain damped wave equation, endowed with a Dirichlet condition on the boundary (sound-soft scattering). To reduce the infinite domain to a finite computational one, we introduce an artificial boundary on which we impose a Boundary Integral Non-Reflecting Boundary Condition (BI-NRBC). We apply a CVEM combined with the Crank–Nicolson time integrator in the interior domain, and we discretize the BI-NRBC by a convolution quadrature formula in time and a collocation method in space. We present some numerical results to test the performance of the proposed approach and to highlight its effectiveness, especially when obstacles with complex geometries are considered.

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来源期刊

Computational Methods in Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.40

自引率

7.70%

发文量

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.