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1.5.1 General remarks

The program is divided into three main, mutually exclusive, applications :

1. the CONSTRUCTION application: used for editing and creating the geometry (contours);

2. the PREP_MESH application: used for editing and defining the mesh for the contours, the references of the lines, points and subdomains;

3. the EDIT_MESH application: used for editing and creating a triangular or quadrangular mesh.

In each of the applications, we can also have access to the following menus:

• GENERAL used among other things for moving from one application to another, for saving or restoring a database, for making hard and soft screen copies, for re-executing a run or for quitting Emc...

• GRAPHIC SCREEN MANAGEMENT used for handling database display,

• CALCULATOR used for entering numerical data, which can be the result of an expression, whenever necessary, or to display certain values such as the radius of a circle or an arc of a circle, the length of an arc or of a segment...

• SELECT used for defining the type of element that we wish to select, for example, coordinate, point, line, circle, arc, segment, spline... This menu is application dependent since the ITEMs to be selected vary according to the application.

Each main application has a specific menu of its own. All applications are driven by LL1 grammars.

 
Figure 1.9: Depiction of the screen 

The screen (figure 1.9) is divided into 9 zones: 5 are menus   ((1), (2), (4), (7), (6)), 3 are display zones ((8), (9), (5)) , the center zone is for graphics.

The GENERAL, CALCULATOR, SCREEN MANAGEMENT menus are fixed and application independent. The APPLICATION and SELECT menus obviously depend on the current application.

The program is interactive, all entries are made with the mouse and keyboard. The mouse is used to select menu ITEMS, as well as graphic elements. Graphic elements can only be selected after the desired type of element has been chosen in the SELECT menu. The keyboard is used to enter text, for example file names, as well as short cuts (ITEMS of certain menus have keyboard equivalents).

The CONSTRUCTION application

This application is used to define the geometric contours  of the domain with the help of points, segments, arcs of circles and splines. Additionally, two other construction entities are useful in certain cases: straight lines and circles. These last two entities are only used in the CONSTRUCTION application.

All these entities, except splines, can be constructed by using elementary geometry theorems. When there are multiple solutions, ambiguities are removed by using the following heuristic method: the selected points are close to the points of tangency of the elements (point, line, circle, arc, segment).

A spline is a -curve passing through a series of points. It is closed if the first and last points coincide.

All these entities can be duplicated by using the following affine transformations: symmetry, rotation, homothety, translation.

Moreover, it is possible to:

• round off angles,
• divide segments, arcs, splines with points, segments, arcs, splines,
• destruct entities using the GENERAL menu.

The PREP_MESH application

At this point the connex components of the boundaries of the subdomains  of are known. We will call these connex components simply components.

This application is used to define the discretization of the entities defining the boundaries of the domain and subdomains (boundary of materials). It is also used to define the reference numbers of the subdomains, lines and points, with the aim of entering various physical data, for example, several boundary conditions, several materials.

This application is also used to create a data file so as to interface with the MODULEF mesh generator APNOXX, by defining the subdomains as a list of components where the first component is the exterior component---the other components being the components of the holes---plus internal lines and internal points to be enforced.

The EDIT_MESH application

When moving to this application, it is possible to modify the default value  of certain parameters of the mesh generator. The program constructs a triangular or grid quadrangular mesh of the subdomains defined in the previous step, or of all subdomains if none has been defined.

At the point, we can edit the mesh by:

• adding internal vertices to subdomains

• suppressing vertices or subdomains

• swapping internal edges of a quadrilateral

• moving vertices

• regularizing the mesh or making it Delaunay

• quadrangulating the mesh

• transforming subdomains with symmetries, rotations, homotheties, translations

• modifying the references of vertices, edges and subdomains (regions)

• saving or restoring a mesh under different formats: MESH,  the Emc internal structure; the MODULEF NOPO  structure; a simplified structure and so on

• cracking lines of the mesh: the points situated on each side of the lines are duplicated

• renumbering so as to decrease the size of the profile of the or finite element matrices.

A very simple detailed example

For a change, we are going to mesh a unit circle instead of a square. First, we must construct the circle, i.e. a arc, then define the discretization of the arc and finally construct the mesh. These three phases correspond respectively to the three applications CONSTRUCTION, PREP_MESH and EDIT_MESH. Here is the list of steps to be taken.

1. Run emc2, then enter the machine-dependent number of the graphic peripheral device. After initialization we are implicitly in the construction application and the selection mode is mouse point (MOUSE P). To construct the arc:
   1. click the ARC item on top of the construction menu,
   2. click the CENTER item of the same menu to define the center,
   3. click the XY POINT item of the select menu,

       
      Figure 1.10: The unit circle 
      

       
      Figure 1.11: The discretized unit circle 
      

       
      Figure 1.12: The meshed unit circle 
      

   4. enter 0=0= on the keyboard. This sets the center at point (0,0),
   5. click the RADIUS item on top of the select menu,
   6. enter 1= on the keyboard, which sets the radius to 1 (the radius state variable is set to 1 and displayed on the bottom of the screen).
   a arc of circle centered at (0,0) with a radius of 1 is displayed. Note: although the angle state variable is equal to 0, the angle of the arc is actually ( ).
2. The circle is small, around 2cm, because the implicit scale is equal to 1. To see it full screen (figure 1.10), click SHOW_ALL in the screen management menu (top right).

3. Now we have constructed the circle and we switch to the PREP_MESH application by clicking on the corresponding item of the general menu.

   To define the number of points in the arc:

   1. click on NB_INTERVAL
   2. enter the number of intervals 10=
   3. select the arc by clicking in the ARC item of the select menu (bottom)
   4. click near the arc in the graphic window.
   The points generated appear on the screen (figure 1.11). We construct the mesh by moving to the EDIT_MESH application. For this, we click the EDIT_MESH item in the general menu, then type (CR) four times to use the default options in response to the four questions posed by the program. The meshed circle appears on the screen (figure 1.12). The mesh can be saved with the SAVE item of the general menu, by entering:
   1. the type of mesh to be saved, for example by typing am_fmt(CR)
   2. the name of the prefix of the mesh by typing circle<return>
   thus a file entitled circle.am_fmt containing the mesh is generated.

A less trivial example

Construction of a mesh between 8 circles tangent to the 3 dotted circles (cf. figure 1.13). The arcs are divided in the neighborhood of the points of ``near tangency" for future mesh refinement. The different stages are shown in figures 1.13,1.14 and 1.15 and enlargements of the mesh in figures 1.16 and 1.17. Figure 1.17 shows a very strong zoom (around 360 times) around a point of near tangency.

 
Figure 1.13: The geometry of the domain 

 
Figure 1.14: The discretization of contours 

 
Figure 1.15: Display of the whole mesh 

 
Figure 1.16: A first zoom 

 
Figure 1.17: Zoom around one of the points of near tangency