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Three-dimensional scattering of scalar waves by cracks

In this section we discuss an application of FM-BIEM to three-dimensional scattering of scalar waves by cracks. Acoustic and electromagnetic scattering problems are interesting subjects in engineering and therefore many researchers have investigated such problems using FMM. However, most of them use Rokhlin's diagonal form which have numerical instabilities in dealing with static problems and low frequency problems. If one implements the original FMM for scattering problems to avoid these problems one uses the Wigner-3j symbols for the FMM formulation. In literature, however, numerical implementations of FMM with the Wigner-3j symbols are scarcely found because of the complexity for treatment. Therefore, we investigate the use of Wigner-3j symbols in the implementation of the original FMM for low frequency problems and carry out numerical experiments. In order to discretise the hypersingular BIE we use collocation method and piecewise constant shape functions. In this section we assume that the wave field is time-harmonic and the time factor is $e^{-i\omega t}$.

The material in this section is from Yoshida et al.[86]


 
next up previous contents
Next: Integral equation Up: Applications of FMM to Previous: Many penny-shaped cracks
Ken-ichi Yoshida
2001-07-28