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