弹性波传输问题的边界积分方程方法
首发时间:2020-04-03
摘要:本文介绍了一种求解二维可穿透有界障碍物的弹性波传输问题的Galerkin边界积分方程方法。首先将原问题归结为耦合边界积分方程组(BIES),并讨论了其变分形式的解的存在唯一性。其次设计算法进行数值模拟,在数值实现过程中,一方面采用正则化公式对超奇异边界积分算子进行数值计算,另一方面在Hankel函数级数展开的基础上,提出了一种计算弱奇异边界积分算子的新方法,最后通过数值算例验证了所提数值方法的有效性。
关键词: 计算数学 边界积分方程 弹性波传输问题 Galerkin 正则化公式
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Boundary Integral Equation Method for the Transmission Problem in Elasticity
Abstract:A galerkin boundary integral equation method is presented to solve the elastic wave transmission problem of two-dimensional penetrating bounded obstacles. First, the original problem is reduced to the coupled boundary integral equation set (bies), and the existence and uniqueness of the solution in its variational form are discussed. Finally, a new method for calculating the integral operator of weak singular boundary is proposed based on the expansion of hankel series. Finally, the validity of the proposed method is verified by numerical example.
Keywords: Computational Mathematics Boundary integral equation elastic wave transmission problem Regularization formula
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