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The proposed techniques have been implemented in Fortran 77 and
have been tested on a computer having a DEC Alpha 21264(500 MHz) as the
CPU. The integrals in the multipole moments in (14) and
(15) are computed numerically with Gaussian quadrature. The
sums in the finite series (13) and
(18) are truncated at 10 terms and the series in
(46), (47), (50) and (51) are
computed with the 109 point generalised Gaussian quadrature formula in
Yarvin and Rokhlin[23]. The maximum number of boundary elements
in a leaf is set to be 100. To solve the resulting matrix equation we
use the preconditioned GMRES and adopt the block diagonal matrix
corresponding to the leaves as the preconditioner according to Nishida
and Hayami[26]. In GMRES the iteration is stopped when the
relative residual norm is below 10^{-5}.

*Ken-ichi Yoshida*

*2001-03-26*