An accurate boundary element method for the exterior elastic scattering problem in two dimensions. (English) Zbl 1380.74059
Summary: 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 boundary integral formulation [A. J. Burton and G. F. Miller, Proc. R. Soc. Lond., Ser. A 323, 201–210 (1971; Zbl 0235.65080)], and essential mathematical features of its variational form are discussed. In numerical implementations, a newly-derived and analytically accurate regularization formula [the third author et al., SIAM J. Numer. Anal. 55, No. 5, 2361–2393 (2017; Zbl 1386.35056)] 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.
MSC:
| 74J20 | Wave scattering in solid mechanics |
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
Keywords:
boundary element method; elastic wave; Burton-Miller formulation; hypersingular boundary integral operatorReferences:
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