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Algorithm for the new FM-BIEM

The algorithm for the new version of FMM is given as follows:

Steps 1-3. Same as the steps 1-3 in the algorithm described in 3.2.
Step 4. Computation of the coefficients of the exponential expansion:

Compute the coefficients of the exponential expansion at each cell using (4.13)-(4.18) and (4.19), taking the origin at the centroid of the cell.

Step 5. Computation of the coefficients of the local expansion:

We compute the coefficients of the local expansion of cells of level l, starting from l=2 and increasing l. In the evaluation of the coefficients of the local expansion of a level l cell C, we first consider the contribution from the interaction list of C, to which a cell C' is assumed to belong. Depending on the position of C' relative to C, we use (4.20) to shift the centre of the exponential expansion of C' from the centroid of C' to that of C. Next convert the contributions from all the cells in the uplist, downlist, northlist, southlist, eastlist and westlist to the coefficients of the local expansion via (4.21), (4.22)-(4.27) and add them together to obtain the contributions to the coefficients of the local expansion of C from the interaction list of C. To these we add the coefficients of the local expansion of the parent of C with the origin shifted from the centroid of the parent to that of C via (3.29) to obtain the coefficients of the local expansion of C.

Step 6. Evaluation of the integral in (3.15): This step is the same as the step 5 in the algorithm describe in 3.2.


next up previous contents
Next: Numerical examples Up: Crack problems for three-dimensional Previous: Rotation of coefficients
Ken-ichi Yoshida
2001-07-28