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FIGURE 9.4
Boundary element discretization for two-dimensional problems.
For a two-dimensional problem with
u
∗
=
and
q
∗
=
(
−
r
2
ln
(
1
/
r
)
r
i
a
i
/
)
r
2
N
i
dS
v
i
ln
1
r
N
i
dS
q
i
b
ln
1
r
dV
M
M
S
r
k
a
k
cu
(ξ
j
)
+
−
=
−
S
i
S
i
V
s
i
=
1
i
=
1
s
=
1
(9.33)
where
c
is given in Eq. (9.29),
j
is the number of a node in the global numbering scheme,
ξ
j
is the point on which node
j
is located,
S
i
is the length of the
i
th element,
r
is the distance
from the point
j
to a point on
S
i
,r
k
is a component of
r
in the direction of a coordinate
axis,
a
k
is a direction cosine of the boundary,
M
is the number of boundary elements, and
S
ξ
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