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In-Depth Information
The following interpolation and restriction matrix applies to the example under
consideration:
2
2
4
3
5
3
2
2
4
3
5
3
x 1
x 1
x 1
1
1
0
0
0
1
4
5
4
5
0
2
4
3
5
2
4
3
5
2
4
3
5
2
4
3
5
y 1
y 1
y 1
y 1
x 2
x 2
x 2
1
1
0
0
0
1
I 1 ^
, I 0 ^
y ¼
¼
0
x ¼
y 2
y 2
y 2
y 2
2
4
3
5
2
4
3
5
x 3
x 3
x 3
1
1
0
0
0
1
0
2
3
2
4
3
5
2
4
3
5
x 1
x 1
x 1
2
4
3
5
2
4
3
5
1
4
1
4
1
4
1
4
4
5
0
0
2
3
0
00 1
2
00 1
2
x 2
x 2
x 2
4
5
¼
,
2
4
3
5
1
2
1
2
2
3
0
x 3
x 3
x 3
00
4
5
001
where the preconditioner C 1 is derived as follows:
2
4
2
4
3
5
2
4
3
5
3
5
1
4
1
4
1
4
1
4
1 þ
0
0
1
4
1
4
1
4
1
4
2
2
4
3
5
3
2
2
4
3
5
3
1 þ
0
0
x 1
e
x 1
x 1
x 1
e
0
0
4
5
4
5
x 1
e
1
2
00 1
2
x 1
2
3
001 þ
2
4
3
5
2
4
3
5
1
2
1
2
x 2
e
x 2
x 2
x 2
e
1 þ
0
2
3
2
3
4
5
C 1
^
x 2
e
1
4
1
4
1
4
1
4
x ¼
¼
:
0
1 þ
0
1
2
1
2
x 2
4
5
4
5
2
4
3
5
1 þ
0
2
4
3
5
x 3
e
x 3
x 3
x 3
e
1
4
1
4
1
4
1
4
0
1 þ
0
x 3
e
001 þ 1
x 3
00 1
2
1
2
001 þ
0
0
β l , t were set to a constant 1. We should
now take a brief look at the method of operation of the preconditioner. Thus, an
update via the action x 1 leads to an update of the actions x 1 themselves and also x 2 in
accordance with:
For simplicity's sake all scaling factors
x 1 ,
1
4
1
4 x 1 :
x 1 ¼
x 2 ¼
e
1 þ
e
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