Journal Article

A Robust and High Precision Algorithm for Elastic Scattering Problems from Cornered Domains

Lai, Jun, Yao, Jianan, Xie, Baoling

2024

Overview

The Navier equation is the governing equation of elastic waves, and computing its solution accurately and rapidly has a wide range of applications in geophysical exploration, materials science, etc. In this paper, we focus on the efficient and high-precision numerical algorithm for the time harmonic elastic wave scattering problems from cornered domains via the boundary integral equations in two dimensions. The approach is based on the combination of Nyström discretization, analytical singular integrals and kernel-splitting method, which results in a high-order solver for smooth boundaries. It is then combined with the recursively compressed inverse preconditioning (RCIP) method to solve elastic scattering problems from cornered domains. Numerical experiments demonstrate that the proposed approach achieves high accuracy, with stabilized errors close to machine precision in various geometric configurations. The algorithm is further applied to investigate the asymptotic behavior of density functions associated with boundary integral operators near corners, and the numerical results are highly consistent with the theoretical formulas.

• Publisher: Springer US,Springer Nature B.V
• Subject: Algorithms / Asymptotic properties / Boundary integral method / Boundary value problems / Computational Mathematics and Numerical Analysis / Decomposition / Domains / Eigenvalues / Elastic scattering / Elastic waves / Integral equations / Integrals / Mathematical and Computational Engineering / Mathematical and Computational Physics / Mathematics / Mathematics and Statistics / Methods / Nondestructive testing / Numerical analysis / Operators (mathematics) / Preconditioning / Radiation / Robustness (mathematics) / Smooth boundaries / Theoretical / Wave scattering