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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) 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 (


Ken-ichi Yoshida