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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 (3.53) and (3.54) are computed numerically with Gaussian quadrature. The sums in the finite series (3.52) [(3.66)] and (3.59) [(3.73)] are truncated at 10 terms. Namely we take 484 [1452] multipole moments and coefficients of the local expansion into consideration in FM-BIEM with the hypersingular integral equation [the reguralised integral equation]. Because of the relations in (3.55) [(3.69)], (3.56) [(3.70)], (3.62) [(3.76)] and (3.63) [(3.77)] we store 264 [792] multipole moments and coefficient of the local expansion. 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[62]. In GMRES the iteration is stopped when the relative error is below 10-5.



 
next up previous contents
Next: One penny-shaped crack Up: Crack problems for three-dimensional Previous: Algorithm
Ken-ichi Yoshida
2001-07-28