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We consider an infinite space which contains one penny-shaped crack
having the radius and the unit normal vector of
. We compute the crack opening displacement when the
crack is subject to a plane longitudinal wave of the normal incidence
from the direction. The wavenumber and Poisson's ratio are set
to be and , respectively. This problem has been
solved with the conventional BIEM with Crout's method and with multilevel
FM-BIEMs with both Wigner-3j symbols and diagonal forms. The
numerical results obtained by these methods were essentially
identical. Fig.1 plots the total CPU time vs the number of
unknowns. In Fig.1 the lines marked `Crout', `FMM-Wigner3j' and
`FMM-diag' indicate the CPU times required by the conventional BIEM
with Crout's method, FM-BIEM with Wigner-3j symbols and FM-BIEM with
diagonal forms, respectively. This figure shows that FM-BIEM with
diagonal forms is faster than that with Wigner-3j symbols.

2001-12-14