三次元スカラー波動および弾性波動問題における演算子積分時間領域境界要素法

抄録

This paper presents a Operational Quadrature time-domain Boundary Element Method (OQBEM) in 3-D scalar and elastic wave problems. Time-domain Boundary Element Method (BEM) is known as a suitable numerical approach for transient analysis of scalar and elastic waves in an infinite or half space domain, since BEM can deal with an infinite region without any modification. However, the use of direct time-domain BEM sometimes causes the instability of time-stepping solutions. To overcome this difficulty, a new time-domain BEM (OQ-BEM) for 3-D scalar and elastic wave problems is developed in conjunction with Operational Quadrature Method (OQM), which was proposed by Lubich to obtain stable solutions in a time-stepping scheme. In OQ-BEM, the convolution integrals in boundary integral equations are numerically approximated by quadrature formulas, whose weights are computed by using the Laplace transform of the fundamental solutions of a linear multistep method. As numerical examples, wave scattering solutions obtained by the OQ-BEM are shown and the accuracy of the method is confirmed to validate the proposed method.