K-0311 3次元時間域動弾性問題に対する高速境界積分方程式法(S02-1 境界要素法とその周辺技術(1))(S02 境界要素法とその周辺技術)

Abstract

In this article, we propose a fast boundary integral equation method (BIEM) for elastodynamic problems in 3D in time domain by extending the formulation for 2D problems developed by present authors recently. In order to obtain a fast solution method, we need to construct a fast algorithm for evaluating the layer potentials in BIE and combine it with an iterative solver for linear algebraic equations. As in 2D problems, we construct the fast algorithm using the plane wave expansions of the single and double layer kernels for elastodynamic problems and the hierarchical system of time-space domain. The fast method obtained here is expected to reduce the computational costs from O(N^2_S N^2_t) required for conventional BIEM to O(N_Slog^2N-S N^2_t) and to solve very large scale initial-boundary value problems where N_S and N_t are the spatial and temporal degrees of freedom, respectively.