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Algorithm

We briefly describe the usage of formulae presented here in each step in the algorithm of FM-BIEM with the hypersingular integral equation [resp. the regularised integral equation] (See chapter 2 for more details).
Steps 1-2. Same as the steps 1-2 in the algorithm described in chapter 2.
Step 3. Computation of the multipole moments:

In this step we use (3.23) [resp. (3.40)] for the computation of the multipole moments associated with leaves. Also, we use (3.24) [(3.32)] for M2M translations tracing the tree structure of cells upward (decreasing $l(\ge2)$).

Step 4. Computation of the local expansion: In this step we use (3.27) [(3.35)] for M2L translations and (3.29) [(3.37)] for L2L translations tracing the tree structure of cells downward (increasing $l(\ge2)$).

Step 5. Evaluation of the integral in (3.15): In this step we use (3.38) [(3.38)] for the direct computation and use (3.26) [(3.34)] for the evaluation of contributions with the local expansion.



Ken-ichi Yoshida
2001-07-28