演算子積分法および高速多重極法を用いた新しい二次元時間領域動弾性境界要素法について

抄録

This paper presents a new time-domain Boundary Element Method (BEM) using the Operational Quadrature Method (OQM) and the Fast Multipole Method (FMM) in 2-D elastodynamics. In general, the use of direct time-domain BEM sometimes causes the instability of time-stepping solutions and needs much computational time and memory. To overcome these difficulties, in this paper, the Operational Quadrature Method developed by Lubich is applied to establish the stability behavior of the time-stepping scheme. Moreover, the Fast Multipole Method is adapted to improve the computational efficiency for large size problems. The formulation and numerical implementation of the new boundary element method, and the basic formulas for the fast multipole method such as the multipole expansion, the local expansion, and the translation relations of them in the fast multipole algorithm are presented. The accuracy, the computational efficiency and the applicability are checked by solving elastic wave scattering problems by cavities.