论文标题
光谱Galerkin方法用于解决多个开放弧的弹性波散射问题
Spectral Galerkin method for solving elastic wave scattering problems with multiple open arcs
论文作者
论文摘要
我们研究了无界域上的弹性时谐波散射问题，其边界由有限的脱节有限的开放弧（或裂纹）组成。具体而言，我们提出了一种快速光谱Galerkin方法，用于求解分别由Dirichlet和Neumann边界条件引起的相关的弱和超细边界积分方程（BIE）。由此产生的比斯的离散化基础采用加权的Chebyshev多项式，以捕获解决方案的边缘行为。我们表明，当假设源和弧的几何形状分析性时，这些碱基确保了多项式程度的指数收敛。数值示例证明了所提出的方法与弧数和波数的数量的准确性和鲁棒性。
We study the elastic time-harmonic wave scattering problems on unbounded domains with boundaries composed of finite collections of disjoints finite open arcs (or cracks) in two dimensions. Specifically, we present a fast spectral Galerkin method for solving the associated weakly- and hyper-singular boundary integral equations (BIEs) arising from Dirichlet and Neumann boundary conditions, respectively. Discretization bases of the resulting BIEs employ weighted Chebyshev polynomials that capture the solutions' edge behavior. We show that these bases guarantee exponential convergence in the polynomial degree when assuming analyticity of sources and arcs geometries. Numerical examples demonstrate the accuracy and robustness of the proposed method with respect to number of arcs and wavenumber.
