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