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Multipole moment

Let Sy, a subset of S, be a union of boundary elements $S_L(L=1
\ldots N)$ and $\mbox{\boldmath$\space x $ }$ be sufficiently far from Sy that the inequality $\vert\overrightarrow{O\mbox{\boldmath$\space x $ }}\vert > \vert\overrightarrow{O\mbox{\boldmath$\space y $ }}\vert \ (\mbox{\boldmath$\space y $ }\in S_y)$ is valid (See Fig.2.5).

Using (2.2), one can evaluate the integral in (2.1) on Sy as follows:

$\displaystyle \int_{S_y} K(\mbox{\boldmath$ x $ },\mbox{\boldmath$ y $ }) \varp...
...h$ y $ }) dS
=\sum_{i} \phi_i(\overrightarrow{O\mbox{\boldmath$ x $ }}) M_i(O),$     (2.3)

where Mi(O) is a multipole moment centred at O defined as
$\displaystyle M_i(O) = \sum_{L=1}^{N} \int_{S_L} \psi_i(\overrightarrow{O\mbox{\boldmath$ y $ }}) \varphi(\mbox{\boldmath$ y $ }) dS.$     (2.4)

Ken-ichi Yoshida