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

** Next:** Integral equation
** Up:** Applications of FMM to
** Previous:** Many penny-shaped cracks
*Ken-ichi Yoshida*

*2001-07-28*