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Three-dimensional scattering of elastic waves by a crack

In this section we discuss an application of FM-BIEM to three-dimensional scattering of elastic waves by a crack. As far as we know, an application of FMM to three-dimensional elastodynamics is found only in Fujiwara[22]. Fujiwara uses Rokhlin's diagonal form and his FMM formulation requires 6 moments for the double-layer potential. On the other hand, we use Wigner 3-j symbols for the FMM formulation because we are interested in low frequency problems and in our formulation the number of the multipole moments is 4. In order to discretise the hypersingular BIE we use collocation method and piecewise constant shape functions. In this section we deal with low frequency problems assuming that the wave field is time-harmonic and that the time factor is $e^{-i\omega t}$.

This material in this section is from Yoshida et al.[85]


Ken-ichi Yoshida