therefore,
1 ~ P 1
[][]
IΓ3 = ΓP = -
P
(118)
a gL
3
1
2
[]
The function η will be obtained by first computing the element matrix A e and
$
[ ] for elements e = 1,... E,
[]
and the boundary matrix C P , [ΓP ], [Γ2P ], [Γ3P ] for
e
B
1
segments P = 1,... , N P . These matrices are assembled to obtain an NN system of
equations,
∑ ([ ]+ [ ]{η }+ ∑ [ ] η }+ ∑ ([ ]+ [ ]{η }+ ∑ [ ]+ ∑ [ ]= 0
B )$
Γ )$
C {$
Γ
Γ
e
e
e
P
P
P
P
P
P
P
A
D
Γ
C
1
2
3
Ω
Γ
Γ
Γ
C
Notice that
T
~ qr 2 η , -
η
~ qr 2 0 η , η
1
$
$
∑[ ]
{
}
T
= αa
=- a
P
(119)
D
0 1 $ A1 $ A2
s A2
s A1
Γ
where A1 and A2 are two points that connect the open boundary and coastal boundary and
∑ [ ] can
η / s. Therefore, term
P
D
the wall boundary condition, (9), applies to
be
$
Γ
∑ [ ] η }and then the assembled equation becomes
C {$
P
P
included into
C
C
[ 1 ] η} [ 2 ] ηC } [ 3 ] ηΓ} {f }
K {$ + K {$ + K {$ =
(120)
or
[ ] η} {f }
A {$ =
(121)
This linear system of equations may be solved to obtain η.
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