Transfer your mesh from GMSH to Matlab

I believe examples are on of the best ways to learn, so I start from an example.

1- build your geometry in GMSH (you can easily do that by studying the first tutorial of the software)

2- Mesh the geometry by going to the Mesh tab and clicking on the 2D. This will build a triangular non structured mesh

3- Extract the mesh by going to File-Save Mesh, or you can use the hot key (Shift+Ctrl+S). This will give you a file with the same name as the project name and with the extension "MSH"

4- Open the file with Wordpad, Notepad or etc.

$MeshFormat

2.2 0 8

$EndMeshFormat

$Nodes

37

1 0 0 0

2 4 0 0

3 4 4 0

4 0 4 0

5 2 2 0

6 2.5 2 0

7 1.5 2 0

8 1.333333333330429 0 0

9 2.666666666663595 0 0

10 4 1.333333333330429 0

11 4 2.666666666663595 0

12 2.666666666669443 4 0

13 1.33333333333796 4 0

14 0 2.666666666669443 0

15 0 1.33333333333796 0

16 2.43301270189563 2.249999999994092 0

17 2.250000000005625 2.433012701888972 0

18 1.999999999999019 2.5 0

19 1.749999999993242 2.433012701888317 0

20 1.566987298104043 2.249999999993525 0

21 1.566987298103185 1.75000000000796 0

22 1.749999999991474 1.566987298112704 0

23 1.999999999998037 1.5 0

24 2.25000000000626 1.566987298111395 0

25 2.433012701896161 1.750000000006827 0

26 0.9761017850604321 2.346814881605136 0

27 3.02389821493962 1.65318511839525 0

28 2.334500907280026 3.134455102784824 0

29 1.665499092719324 0.8655448972157629 0

30 2.839249308207946 2.495807560436933 0

31 1.160750691791375 1.504192439564072 0

32 1.510100448723277 2.957936003268833 0

33 2.489899551276439 1.04206399673127 0

34 3.168083376431483 3.259385865977071 0

35 0.7639071134243337 3.194283510308682 0

36 3.236092886575931 0.8057164896913898 0

37 0.8319166235682255 0.7406141340235588 0

$EndNodes

$Elements

79

1 15 2 0 1 1

2 15 2 0 2 2

3 15 2 0 3 3

4 15 2 0 4 4

5 15 2 0 5 5

6 15 2 0 6 6

7 15 2 0 7 7

8 1 2 0 1 1 8

9 1 2 0 1 8 9

10 1 2 0 1 9 2

11 1 2 0 2 2 10

12 1 2 0 2 10 11

13 1 2 0 2 11 3

14 1 2 0 3 3 12

15 1 2 0 3 12 13

16 1 2 0 3 13 4

17 1 2 0 4 4 14

18 1 2 0 4 14 15

19 1 2 0 4 15 1

20 1 2 0 5 6 16

21 1 2 0 5 16 17

22 1 2 0 5 17 18

23 1 2 0 5 18 19

24 1 2 0 5 19 20

25 1 2 0 5 20 7

26 1 2 0 6 7 21

27 1 2 0 6 21 22

28 1 2 0 6 22 23

29 1 2 0 6 23 24

30 1 2 0 6 24 25

31 1 2 0 6 25 6

32 2 2 0 9 11 3 34

33 2 2 0 9 34 3 12

34 2 2 0 9 13 4 35

35 2 2 0 9 35 4 14

36 2 2 0 9 9 2 36

37 2 2 0 9 36 2 10

38 2 2 0 9 37 1 8

39 2 2 0 9 15 1 37

40 2 2 0 9 32 13 35

41 2 2 0 9 33 9 36

42 2 2 0 9 34 12 28

43 2 2 0 9 37 8 29

44 2 2 0 9 31 21 7

45 2 2 0 9 6 25 27

46 2 2 0 9 10 11 27

47 2 2 0 9 30 16 6

48 2 2 0 9 6 27 30

49 2 2 0 9 30 27 11

50 2 2 0 9 7 20 26

51 2 2 0 9 7 26 31

52 2 2 0 9 14 15 26

53 2 2 0 9 31 26 15

54 2 2 0 9 37 31 15

55 2 2 0 9 22 21 31

56 2 2 0 9 22 31 29

57 2 2 0 9 31 37 29

58 2 2 0 9 17 16 30

59 2 2 0 9 17 30 28

60 2 2 0 9 34 30 11

61 2 2 0 9 30 34 28

62 2 2 0 9 14 26 35

63 2 2 0 9 32 35 26

64 2 2 0 9 10 27 36

65 2 2 0 9 33 36 27

66 2 2 0 9 32 19 18

67 2 2 0 9 8 9 29

68 2 2 0 9 23 22 29

69 2 2 0 9 18 17 28

70 2 2 0 9 18 28 32

71 2 2 0 9 12 13 28

72 2 2 0 9 32 28 13

73 2 2 0 9 33 29 9

74 2 2 0 9 33 24 23

75 2 2 0 9 23 29 33

76 2 2 0 9 20 19 32

77 2 2 0 9 20 32 26

78 2 2 0 9 25 24 33

79 2 2 0 9 25 33 27

$EndElements

5- You can see the nodes from the line $Nodes to $EndNodes. The first number below $Nodes is the number of the nodes, The first number at the left column specifies the node number and the rest are the x,y and z position of the nodes (The nodes are highlighted in yellow). Copy the nodes into a separate "txt" file and name is as Nodes.txt.

6- The elements start from $Elements to $EndElements. In this example we are only interested in 2D elements, these elements start from the line in which the second column's value is 2. 32 2 2 0 9 11 3 34. Copy the elements into a separate "txt" file and name it as Elements.txt. The corresponding nodes of the element are the last three numbers, e.g. 32 2 2 0 9 11 3 3 4. 

7- Copy these two files into the working directory of your Matlab code.

8- Use the following code to transfer the data into Matlab:

----------------------------------------------------------

%----------- Description ---------

% Transfer Mesh from GMSH to Matlab

%---------------------------------

% Written by 

% Shah, 18 November 2011

clc

clear all

close all

load Elements.txt

load Nodes.txt

nrelm=size(Elements,1);

nnod=size(Nodes,1);

Edof=zeros(nrelm,4);

Ex=zeros(nrelm,3); Ey=Ex; Ez=Ex;

Edof(:,1)=sort(1:nrelm);

Elm(:,1)=sort(1:nrelm);

for i=1:nrelm

    Edof(i,2:7)=[2*Elements(i,6)-1 Elements(i,6)*2 2*Elements(i,7)-1 ...

        Elements(i,7)*2 2*Elements(i,8)-1 2*Elements(i,8)];  

    Elm(i,2:4)=Elements(i,6:8);  

    Ex(i,:)=[Nodes(Elm(i,2),2) Nodes(Elm(i,3),2) Nodes(Elm(i,4),2)];

    Ey(i,:)=[Nodes(Elm(i,2),3) Nodes(Elm(i,3),3) Nodes(Elm(i,4),3)];

    Ez(i,:)=[Nodes(Elm(i,2),4) Nodes(Elm(i,3),4) Nodes(Elm(i,4),4)];    

end

nrdof=max(max(Edof));

figure(1);

hold on;

for i=1:length(Edof(:,1));

    plot(Ex(i,[1:end 1]),Ey(i,[1:end 1]));

end

axis equal

------------------------------------------------------------------------------------------------

The output in Matlab looks like this:

This does not look a like good approximation of the geometry, a finer mesh would look like: