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Numerical Examples

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