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We can efficiently evaluate the integral in (2.1) using the
multipole moments alone. However, in order to enhance this efficiency
we use the local expansion in FMM.
Suppose that one can expand
as follows:



(2.8) 
where
is a function,
is a certain coefficient of
the expansion and
is a certain point such that the inequality
is valid (See
Fig.2.5).
Substituting (2.8) into (2.3), one can
evaluate the integral in (2.1) as follows:
where
is the coefficient of the local expansion centred
at
given by



(2.10) 
This formula (2.10) is used to translate the multipole moments
centred at O to the coefficients of the local expansion centred at
(See Fig.2.5) and this translation is called ``M2L
(Multipole moment to(2) Local expansion) translation''.
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Up: Formulation for FMBIEM
Previous: M2M translation
Kenichi Yoshida
20010728