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This paper describes a fast boundary integral equation method (BIEM) for elastodynamic problems in 2D in time domain for solving very large scale initial-boundary value problems which can not 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.

Keywords: Boundary Integral Equation Method, Elastodynamics, Fast Solution Method, Plane Wave Time Domain Algorithm, Iterative Solution Method, GMRES, Scattering Problem

Toru Takahashi