论文标题
弹性障碍物散射问题的高度准确的边界积分方法
A highly accurate boundary integral method for the elastic obstacle scattering problem
论文作者
论文摘要
考虑通过嵌入在二维中的均质和各向同性弹性培养基中的刚性障碍物来散射时间谐波平面波。在本文中，提出了一种新颖的边界积分公式，并为弹性障碍物散射问题开发了其高度准确的数值方法。更具体地说，基于Helmholtz的分解，模型问题被简化为与单数内核的耦合边界积分方程。为了处理退化的积分运算符，构建了正规化系统。通过使用三角搭配方法研究了边界积分系统的半二聚体和全discrete方案。在某些适当的Sobolev空间中为数值方案建立了收敛性。对平滑和非平滑障碍物进行了数值实验，以证明该方法的出色性能。
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate numerical method is developed for the elastic obstacle scattering problem. More specifically, based on the Helmholtz decomposition, the model problem is reduced to a coupled boundary integral equation with singular kernels. A regularized system is constructed in order to handle the degenerated integral operators. The semi-discrete and full-discrete schemes are studied for the boundary integral system by using the trigonometric collocation method. Convergence is established for the numerical schemes in some appropriate Sobolev spaces. Numerical experiments are presented for both smooth and nonsmooth obstacles to demonstrate the superior performance of the proposed method.
