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
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
|
/*********************************************************************
*
* Gmsh tutorial 1
*
* Variables, elementary entities (points, lines, surfaces), physical
* entities (points, lines, surfaces)
*
*********************************************************************/
// The simplest construction in Gmsh's scripting language is the
// `affectation'. The following command defines a new variable `lc':
lc = 1e-2;
// This variable can then be used in the definition of Gmsh's simplest
// `elementary entity', a `Point'. A Point is defined by a list of four numbers:
// three coordinates (X, Y and Z), and a characteristic length (lc) that sets
// the target element size at the point:
Point(1) = {0, 0, 0, lc};
// The distribution of the mesh element sizes is then obtained by interpolation
// of these characteristic lengths throughout the geometry. Another method to
// specify characteristic lengths is to use a background mesh (see `t7.geo' and
// `bgmesh.pos').
// We can then define some additional points as well as our first curve. Curves
// are Gmsh's second type of elementery entities, and, amongst curves, straight
// lines are the simplest. A straight line is defined by a list of point
// numbers. In the commands below, for example, the line 1 starts at point 1 and
// ends at point 2:
Point(2) = {.1, 0, 0, lc} ;
Point(3) = {.1, .3, 0, lc} ;
Point(4) = {0, .3, 0, lc} ;
Line(1) = {1,2} ;
Line(2) = {3,2} ;
Line(3) = {3,4} ;
Line(4) = {4,1} ;
// The third elementary entity is the surface. In order to define a simple
// rectangular surface from the four lines defined above, a line loop has first
// to be defined. A line loop is a list of connected lines, a sign being
// associated with each line (depending on the orientation of the line):
Line Loop(1) = {4,1,-2,3} ;
// We can then define the surface as a list of line loops (only one here, since
// there are no holes--see `t4.geo'):
Plane Surface(1) = {1} ;
// At this level, Gmsh knows everything to display the rectangular surface 6 and
// to mesh it. An optional step is needed if we want to associate specific
// region numbers to the various elements in the mesh (e.g. to the line segments
// discretizing lines 1 to 4 or to the triangles discretizing surface 1). This
// is achieved by the definition of `physical entities'. Physical entities will
// group elements belonging to several elementary entities by giving them a
// common number (a region number).
// We can for example group the points 1 and 2 into the physical entity 1:
Physical Point(1) = {1,2} ;
// Consequently, two punctual elements will be saved in the output mesh file,
// both with the region number 1. The mechanism is identical for line or surface
// elements:
MY_LINE = 2;
Physical Line(MY_LINE) = {1,2} ;
Physical Line("My second line (automatic physical id)") = {3} ;
Physical Line("My third line (physical id 5)", 5) = {4} ;
Physical Surface("My surface") = {1} ;
// All the line elements created during the meshing of lines 1 and 2 will be
// saved in the output mesh file with the physical id 2. The elements from line
// 3 will be saved in the output mesh file with an automatic physical id,
// associated with the label "My second line (automatic physical id)". The
// elements from line 4 will be saved with physical id 5, associated with the
// label "My third line (physical id 5)". And finally, all the triangular
// elements resulting from the discretization of surface 6 will be given an
// automatic physical id associated with the label "My surface").
// Note that if no physical entities are defined, then all the elements in the
// mesh will be saved "as is", with their default orientation.
|
