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14
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12
10
8
m=1
m=2
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6
4
2
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10
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4
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12
CG Iterations
10
8
6
4
2
2
10
3
4
10
Number of Edges n
10
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I
II
III
IV
V
0.5
0.45
convergence rate
0.4
0.35
0.3
0.25
0.2
0.15
0
1
2
3
4
5
6
7
boundary width
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I
II
III
IV
V
0.16
convergence rate
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
1
2
3
4
5
6
7
boundary width
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V1
V2
V3
V5
W1
W2
W3
W5
80
70
# Multigrid Iterations
60
50
40
30
20
10
0
2
10
3
10
4
10
Number of Edges
5
6
10
10
) $- %
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2
10
Mesh
Mesh
Mesh
Mesh
Mesh
Mesh
0
10
−2
10
I
II
III
IV
V
VI
−4
10
−6
k
||e ||
A
10
−8
10
−10
10
−12
10
−14
10
−16
10
1
2
3
4
5
6
Iteration Steps
7
8
9
) $1 2 @C$! C$!
C$A
10
C$!
22 #"'"' , )! %/#' "0# ! %&#$ --
2
10
Mesh
Mesh
Mesh
Mesh
Mesh
Mesh
1
10
0
Euklidean Norm of the Residual
10
I
II
III
IV
V
VI
−1
10
−2
10
−3
10
−4
10
−5
10
−6
10
−7
10
1
2
3
4
5
6
Iteration Steps
7
) $< @C$! C$!
8
9
10
C$! C$A
2
10
Mesh
Mesh
Mesh
Mesh
Mesh
Mesh
0
10
−2
10
I
II
III
IV
V
VI
−4
10
−6
||ek||
A
10
−8
10
−10
10
−12
10
−14
10
−16
10
−18
10
1
2
3
4
Iteration Steps
5
6
) $5 2 @C-! C$!
C$A
7
C$!
2 -1
2
10
Mesh
Mesh
Mesh
Mesh
Mesh
Mesh
1
10
0
10
I
II
III
IV
V
VI
Euklidean Norm of the Residual
−1
10
−2
10
−3
10
−4
10
−5
10
−6
10
−7
10
−8
10
1
2
3
4
Iteration Steps
5
) $* @C-! C$!
6
C$! C$A
7
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20
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15
10
5
0
0
0.1
0.2
0.3
0.4
0.5
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0.6
0.7
0.8
0.9
1
0.9
1
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120
100
µ
80
60
40
20
0
0
0.1
0.2
0.3
0.4
0.5
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0.6
0.7
0.8
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