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Discretisation of the regularised integral equation with piecewise constant shape functions

Discretising the regularised integral equation (3.16) with piecewise constant shape functions, one obtains the following equation:
 
$\displaystyle -\frac{\partial u^{\infty}(\mbox{\boldmath$ x $ })}{\partial n_x}...
...al G(\mbox{\boldmath$ x $ }-\mbox{\boldmath$ y $ })}{\partial y_p} dy_l \phi_J,$     (3.38)

where SJ is a plane element in S and $\phi_J$ represents $\phi$on SJ. In (3.38) the right-hand screw convention is applied to the direction of the integration along $\partial S_J$. We use (3.38) for the direct computation instead of (3.16). In the similar way the multipole moment $\widetilde{M}_{j,n,m}(O)$ in (3.31) is rewritten as
 
$\displaystyle \widetilde{M}_{j,n,m}(O) = \sum_{L} \oint_{\partial S_L} e_{jpl}
...
...l R_{n,m}(\overrightarrow{O\mbox{\boldmath$ y $ }})}{\partial y_p} dy_l \phi_L,$     (3.39)

where SL is a plane element in Sy and $\phi_L$ represents $\phi$on SL.

Ken-ichi Yoshida
2001-07-28