An accurate boundary element method for the exterior elastic scattering problem in two dimensions
For researchers in computational wave scattering, this provides an accurate numerical method for elastic wave problems, though it is an incremental improvement over existing boundary element techniques.
The paper presents a Galerkin boundary element method for solving 2D exterior elastic wave scattering using the Burton-Miller formulation, with a new regularization for hyper-singular integrals and series expansions for weakly-singular operators. Numerical examples demonstrate effectiveness.
This paper is concerned with a Galerkin boundary element method solving the two dimensional exterior elastic wave scattering problem. The original problem is first reduced to the so-called Burton-Miller (\cite{BM71}) boundary integral formulation, and essential mathematical features of its variational form are discussed. In numerical implementations, a newly-derived and analytically accurate regularization formula (\cite{YHX}) is employed for the numerical evaluation of hyper-singular boundary integral operator. A new computational approach is employed based on the series expansions of Hankel functions for the computation of weakly-singular boundary integral operators during the reduction of corresponding Galerkin equations into a discrete linear system. The effectiveness of proposed numerical methods is demonstrated using several numerical examples.