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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) chip as
the CPU. In FMM, we truncate the infinite series in
(3.22) [(3.30)] and
(3.26) [(3.34)] taking 10
terms. Namely we take 121 [363] multipole moments and coefficients of
the local expansion into consideration. Because of the relations in
(3.25) [(3.33)] and
(3.28) [(3.36)] we store 66 [198]
multipole moments and coefficient of the local expansion. Also, we set
the maximum number of boundary elements in a leaf 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[62]. In GMRES
we terminate the iteration when the relative error is less than
10^{-5}. In this thesis we mainly use BLAS, LAPACK and SLATEC as
mathematical libraries. These are available from Netlib
(http://www.netlilb.org/).

*Ken-ichi Yoshida*

*2001-07-28*