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