Regularized integral equation methods for elastic scattering problems in three dimensions
Regularized integral equation methods for elastic scattering problems in three dimensions
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DOI：
10.1016/j.jcp.2020.109350
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发表时间：
2019-09
期刊：
影响因子：
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通讯作者：
O. Bruno;Tao Yin
中科院分区：
文献类型：
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作者：
O. Bruno;Tao Yin
本文提出了三维空间中封闭和开放表面弹性波散射数值模拟的新方法。所提出的方法利用了新的积分公式以及最近针对声学情况引入的高效高阶奇异积分方法 [13] 的弹性上下文的扩展。为了获得在少量迭代中收敛的迭代求解器 (GMRES) 的公式，我们从理论上和计算上研究了与弹性波 Calderón 关系相关的各种算子的谱的特征，包括它们的一些可能的组成和组合。特别是，通过依赖复合算子 NS 的特征值远离零和无穷大这一事实，提出了针对闭曲面情况的新的唯一可解的低 GMRES 迭代积分公式。为了光谱质量以及精度和效率，为开放表面方程引入相应的低 GMRES 迭代方程还需要使用经典积分算子的加权版本来匹配边缘处未知密度的奇异性。几个数值例子证明了所提出方法的准确性和效率。
This paper presents novel methodologies for the numerical simulation of scattering of elastic waves by both closed and open surfaces in three-dimensional space. The proposed approach utilizes new integral formulations as well as an extension to the elastic context of the efficient high-order singular-integration methods [13] introduced recently for the acoustic case. In order to obtain formulations leading to iterative solvers (GMRES) which converge in small numbers of iterations we investigate, theoretically and computationally, the character of the spectra of various operators associated with the elastic-wave Calderón relation—including some of their possible compositions and combinations. In particular, by relying on the fact that the eigenvalues of the composite operatorNSare bounded away from zero and infinity, new uniquely-solvable, low-GMRES-iteration integral formulation for the closed-surface case are presented. The introduction of corresponding low-GMRES-iteration equations for the open-surface equations additionally requires, for both spectral quality as well as accuracy and efficiency, use of weighted versions of the classical integral operators to match the singularity of the unknown density at edges. Several numerical examples demonstrate the accuracy and efficiency of the proposed methodology.