Symmetric Boundary-Finite Element Discretization of Time Dependent Acoustic Scattering by Elastic Obstacles with Piezoelectric Behavior
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- 作者：Tonatiuh Sánchez-Vizuet ; Francisco-Javier Sayas
- 关键词：Time ; domain boundary integral equations ; Convolution quadrature ; Scattering ; Coupling BEM/FEM ; Piezoelectricity
- 刊名：Journal of Scientific Computing
- 出版年：2017
- 出版时间：March 2017
- 年：2017
- 卷：70
- 期：3
- 页码：1290-1315
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Algorithms; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theoretical, Mathematical and Computational Physics;
- 出版者：Springer US
- ISSN：1573-7691
- 卷排序：70
文摘
A coupled BEM/FEM formulation for the transient interaction between an acoustic field and a piezoelectric scatterer is proposed. The scattered part of the acoustic wave is represented in terms of retarded layer potentials while the elastic displacement and electric potential are treated variationally. This results in an integro-differential system. Well posedness of a general Galerkin semi-discretization in space of the problem is shown in the Laplace domain and translated into explicit stability bounds in the time domain. Trapezoidal-rule and BDF2 convolution quadrature are used in combination with matching time stepping for time discretization. Second order convergence is proven for the BDF2-based method. Numerical experiments are provided for BDF2 and trapezoidal rule based time evolution.