Integral Equations for Acoustic Scattering by Partially Impenetrable Composite Objects
Integral Equations for Acoustic Scattering by Partially Impenetrable Composite Objects
复制标题
部分不可穿透复合物体声散射的积分方程
DOI：
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复制
发表时间：
2014
影响因子：
0.8
通讯作者：
R. Hiptmair
中科院分区：
文献类型：
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作者：
X. Claeys;R. Hiptmair
本文研究了由Helmholtz方程的透射问题所产生的直接第一类边界积分方程，该方程具有分段常系数和Dirichlet边界条件.我们确定的必要条件和充分条件发生所谓的寄生共振，也就是说，失败的边界积分方程拥有独特的解决方案。继[A。Buffa和R. Hiptmair，Numer Math，100，1-19（2005）]，我们提出了一种对伪共振免疫的边界积分方程的修改版本。通过间隙构造，它将作为普遍适定的稳定的全局多迹公式的基础，该公式推广了[X]的方法。Claeys和R. Hiptmair，Commun Pure and Appl Math，66，1163-1201（2013）]到具有Dirichlet边界条件的情况。
We study direct first-kind boundary integral equations arising from transmission problems for the Helmholtz equation with piecewise constant coefficients and Dirichlet boundary conditions imposed on a closed surface. We identify necessary and sufficient conditions for the occurrence of so-called spurious resonances, that is, the failure of the boundary integral equations to possess unique solutions. Following [A. Buffa and R. Hiptmair, Numer Math, 100, 1–19 (2005)] we propose a modified version of the boundary integral equations that is immune to spurious resonances. Via a gap construction it will serve as the basis for a universally well-posed stabilized global multi-trace formulation that generalizes the method of [X. Claeys and R. Hiptmair, Commun Pure and Appl Math, 66, 1163–1201 (2013)] to situations with Dirichlet boundary conditions.
波传播和应用中的正问题和反问题
DOI：
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发表时间：
2013
期刊：
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影响因子：
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作者：
Graham, I.G.
通讯作者：
Graham, I.G.