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##

Numerical integration on

In this paper, integrals on the unit sphere are computed numerically
via the Gauss-Legendre quadrature in direction and the
trapezoidal quadrature rule in direction in the following
manner:

where
is a function,
and are the
arccosine of the th abscissa and th weight of the
-point Gauss-Legendre quadrature,
and
.
In the numerical evaluation of the integral in Eq. (9), the
coefficients of the local expansion are computed at the finite
sample points on the unit sphere, i.e. a finite set of
given
by
and . Also, we need to prepare multipole
moments for the same set of
to obtain the coefficients of
local expansion using Eqs. (10) and (11).

** Next:** Translation of multipole and
** Up:** FM-BIEM
** Previous:** Multipole moments and coefficients
2001-12-14