2次元時間域動弾性問題に対する高速境界積分方程式法

抄録

This paper describes a fast boundary integral equation method (BIEM) for elastodynamic problems in 2 D in time domain for solving very large scale initial-boundary value problems which cannot be analyzed with the conventional BIEM within an affordable amount of time. At first, we derive a plane wave expansion of the fundamental solution of elastodynamic problems. This expansion formula enables us to construct a fast algorithm for evaluating the layer potentials in BIE which uses the multilevel plane wave time domain (PWTD) algorithm, that was originally developed by A. Ergin and M. Lu et al, in scalar wave problems. Finally, a fast solution method is obtained with the help of this algorithm and an Iterative solver for linear algebraic equations. Some numerical examples show that the proposed method solves large scale problems faster than the conventional one.