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The application of the BEM to elastodynamics started in the late 1960s. Cruse and Rizzo (1968) transformed elastodynamic problems into stationary problems using the Laplace transform. Niwa et al. (1971) and Manolis and Beskos (1981) obtained more accurate results with the Fourier transform. The BEM applied directly in the time domain started in 1978 with Cole et al. (1978) and has been developed quickly and adopted widely because of its directness (Antes, 1985; Banerjee et al., 1986; Ahmad and Banerjee, 1988). Nardini and Brebbia (1983a, b) put forward another boundary element technique, which directly applied the fundamental solution of statics to elastodynamics and selected interpolation functions to obtain the invariable system matrices that correspond to the stiffness and mass matrices that arise when the FEM is applied Wong and Jennings (1975) applied the BEM to numerically calculate the effects of canyon topography on seismic SH-waves.

As a subset of elastodynamic problems, the scalar seismic wave equation is widely applied in geophysics. This chapter introduces the two primary methods of the BEM for solving elastodynamic and scalar wave equation problems in both the time and frequency domains. Some practical examples are also given.

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