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FIGURE 9.5
Boundary element discretization for three-dimensional problems.
is the number of “cells” with volume (area)
V
s
which are the blocks to form the total body
and are needed for the volume (area) integration. Note that these cells are different from
the elements in the finite element method in that they involve no unknown nodal values
and are used for integration purposes only. Substitution of the expressions
u
∗
=
1
/
r
and
q
∗
=−
r
3
into Eq. (9.32) leads to an expression for three-dimensional problems. In this
case,
S
i
becomes the area of the element.
Let
u
r
k
a
k
/
v
j
is the nodal value of
u
in the global numbering scheme. After
the numerical integration of Eqs. (9.32), a system of linear equations is obtained
(ξ
j
)
=
v
j
,
where
M
M
1
H
ij
v
i
1
G
ij
q
i
c
v
+
=
+
B
j
(9.34)
j
i
=
i
=
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