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H Hu Vnh
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nx = 4 % number elements in x-direction ny = 3 % number elements in y-direction
i = 1, j = 1:nx (j = 1,2,3,4) Elements = 1 2 7 6 (1)
2 3 8 7 (2)
3 4 9 8 (3)
4 5 10 9 (4)
i = 2, j = 1:nx (j = 1,2,3) Elements = 6 7 12 11 (5)
7 8 13 12 (6)
8 9 14 13 (7)
9 10 15 14 (8)
i = 2, j = 1:nx (j = 1,2,3) Elements = 11 12 17 16 (9)
12 13 18 17 (10)
13 14 19 18 (11)
14 15 20 19 (12)
nx+1
nx+1
Cng sai = j
Cng sai
i =
j = 1:nx
i = 1:ny
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
16 17 18 19 20
21 22 23 24 25
u tin ta xt vng lp chnh tm mi tng quan gia cc nt ca phn t khi
i = 1 : ny
Ta xt mi tng quan gia cc nt ca cc phn t u tin khi i = 1 : ny (1,2,3,4)
y ta thy:
khi i = 1 th: nt1 = 1, nt2 = 2, nt3 = 7, nt4 = 6;
khi i = 2 th: nt1 = 6, nt2 = 7, nt3 = 12, nt4 = 11;
khi i = 3 th: nt1 = 11, nt2 = 12, nt3 = 17, nt4 = 16;
khi i = 4 th: nt1 = 16, nt2 = 17, nt3 = 22, nt4 = 21;
Nhn vo s thay i khi i = 1:ny ta thy s th t ca nt tng theo cp s cng v
c cng sai l 5 hay cng sai = (nx+1)*(i - 1) (*)
Tip theo ta xt cc mi tng quan vng lp con khi j = 1:nx
Ta xt mi tng quan gia cc nt ca cc phn t khi j = 1, 2, 3, 4
y ta thy:
Khi j = 1 th: nt1 = 1, nt2 = 2, nt3 = 7, nt4 = 6;
Khi j = 2 th: nt1 = 2, nt2 = 3, nt3 = 8, nt4 = 7;
Khi j = 3 th: nt1 = 3, nt2 = 4, nt3 = 9, nt4 = 8;
Khi j = 4 th: nt1 = 4, nt2 = 5, nt3 = 10, nt4 = 9;
Nhn vo s thay i khi j = 1:nx ta thy s th t ca nt cng tng theo cp s
cng v c cng sai l 1 hay cng sai = j (**)
Kt hp gia (*) v (**) ta c cch gn cc s th t thay i theo qui lut nh sau:
- Gi s nt u tin ca phn t th nht l a
th nt th 2 ca phn t l b = a+1
nt th 3 ca phn t l c = b+(nx+1)
V nt th t ca phn t l d = c1
- V a l nt th nht ca phn t nn khi i =1:ny th a phi tng theo cp s cng
vi cng sai l (nx+1)*(i 1) theo tnh cht ca (*). V theo tnh cht ca (**)
khi j = 1:nx th a cng phi tng theo cp s cng vi cng sai l j
a = (nx+1)*(i - 1) +j
- Tng t b, c, d cng tun theo tnh cht ca (*) v (**) nn
- b = a+1 = (nx+1)*(i 1) +j + 1
- c = b+(nx+1) = (nx+1)*(i 1) +j + 1 + (nx+1) = (nx+1) *i+j+1
- d = c 1 = (nx+1) *i+j+1 1 = (nx+1) *i+j+1
Nh vy vng lp kt ni phn t s c thc hin nh sau
for i = 1:nx (i = 1,2,3,4)
for j = 1:ny (j = 1,2,3,4)
Elements = [ Elements; (nx+1)*(i-1)+j (nx+1)*(i-1)+j+1 (nx+1)*i+j+1 nx*i+j+i ]
end
end
- a = (nx+1)*(i 1) +j
- b = a+1 = (nx+1)*(i 1) +j + 1
- c = b+(nx+1) = (nx+1)*(i 1) +j + 1 + (nx+1) = (nx+1) *i+j+1
- d = c 1 = (nx+1) *i+j+1 1 = (nx+1) *i+j+1
Elements = [ ];
a b c d
nx = 4 % number elements in x-direction ny = 3 % number elements in y-direction
i =
j = 1:nx
i = 1:ny
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
16 17 18 19 20
21 22 23 24 25
i = 1, j = 1:nx (j = 1,2,3,4) Elements = 1 7 6 (1)
1 2 7 (2)
2 8 7 (3)
2 3 8 (4) 3 9 8 (5) 3 4 9 (6) 4 10 9 (7) 4 5 10 (8)
i = 2, j = 1:nx (j = 1,2,3,4) Elements = 6 12 11 (9)
6 7 12 (10)
7 13 12 (11)
7 8 13 (12) 8 14 13 (13) 8 9 14 (14) 9 15 14 (15) 9 10 15 (16)
j = 2
j = 1
j = 3
j = 4
Vi cch lp lun tng t ta cng c c cch kt ni cc phn t nh sau
for i = 1:nx (i = 1,2,3,4)
for j = 1:ny (j = 1,2,3,4)
Elements = [ Elements; (nx+1)*(i-1)+j (nx+1)*i+j+1 (nx+1)*i+j % element 1
(nx+1)*(i-1)+j (nx+1)*(i-1)+j+1 (nx+1)*i+j+1 ] % element 2
end
end
Elements = [ ];
Ch : khi i = 1, j = 1:nx th mi vng lp qua j s cho ta hai phn t