minor improvements

Electrostatic/microstrip.pro

 /* -------------------------------------------------------------------
    Tutorial 1 : electrostatic field of a microstrip
 
+   Features:
+   - Physical and abstract regions
+   - Scalar FunctionSpace with Dirichlet constraint
+   - Galerkin term for stiffness matrix
+
    To compute the solution in a terminal: 
        getdp microstrip -solve EleSta_v
        getdp microstrip -pos Map
@@ -11,12 +16,9 @@
        Run (button at the bottom of the left panel)
 
    The microstrip.pro file describes the finite element (FE) model.
-   
    ------------------------------------------------------------------- */
 
-
-
-Group { // CG utiliser le mot-cle Regions {} ? 
+Group { 
   /* One starts by giving explicit meaningful names to 
      the Physical regions defined in the "microstrip.msh" mesh file. 
      There are 2 volume regions and 3 surface regions in this model. */ 
@@ -65,30 +67,34 @@ Constraint {
 }
 
 Group{
-  /* The domain of definition lists all regions on which the unknown field "v" is defined.
+  /* The domain of definition of a FunctionSpace lists all regions 
+     on which a field is defined.
 
-     Contrary Vol_xxx and Sur_xxx regions, which contain only volume or surface regions, resp.,
-     Dom_xxx regions may contain both volume and surface regions. 
+     Contrary to Vol_xxx and Sur_xxx regions, 
+     which contain only volume or surface regions, resp.,
+     domains of definition Dom_xxx regions may contain both volume and surface regions. 
      Hence the use of the prefixes Vol_, Sur_ and Dom_ to avoid confusions.*/
 
   Dom_Hgrad_v_Ele =  Region[ {Vol_Dielectric_Ele, Sur_Dir_Ele, Sur_Neu_Ele} ];
 }
 
 FunctionSpace {
-  /* The function space in which we shall pick the electric scalar potential v solution
+  /* The function space in which we shall pick the electric scalar potential "v" solution
      is definied by 
      - a domain of definition ("Dom_Hgrad_v_Ele")
      - a type ("Form0" means scalar field)
      - a set of scalar basis functions ("BF_Node" means nodal basis functions)
      - a constraint (here the Dirichlet boundary conditions) 
 
-     The FE representation of the unknown fields now reads
+     The FE representation of the unknown field "v" reads
      
      v = Sum_k sn_k vn_k 
 
      where the "vn_k" are the nodal values and "sn_k" the basis functions.
-     Not all nodal values are unknowns of the problem, due to the "Constraint"
-     which assigns particular values to the nodes of the region "Sur_Dir_Ele". */
+     Not all nodal values are unknowns of the FE problem, due to the "Constraint"
+     which assigns particular values to the nodes of the region "Sur_Dir_Ele". 
+     GetDP deals with that automatically on basis of the definition of the FunctionSpace.
+  */
 
   { Name Hgrad_v_Ele; Type Form0;
     BasisFunction {
@@ -111,7 +117,7 @@ Jacobian {
 }
 
 Integration {
-  { Name GradGrad ;
+  { Name Int ;
     Case { {Type Gauss ;
             Case { { GeoElement Triangle    ; NumberOfPoints  4 ; }
                    { GeoElement Quadrangle  ; NumberOfPoints  4 ; } }
@@ -135,7 +141,7 @@ Formulation {
 
      The Galerkin{} statement is a symbolic representation of this weak formulation term. 
      The first argument represents the density to be integrated over finite elements,
-     the result of which being the bilinear form, i.e., the matrix 
+     the result of which being the bilinear form, i.e., the element-based matrix 
      that will be assembled in the linear system of FE equations. 
      
      What is a bit confusing is that the two comma-separated arguments of the bracket [] 
@@ -152,7 +158,7 @@ Formulation {
 
      to highlight the symmetry.
      But the second argument of the density is always reserved for the trial functions
-     and the the Dof operator should therefore be there systematically.
+     and the Dof{} operator should therefore always be there.
      It can thus be made implicit and, according to the GetDP syntax, it must be omitted.
      Hence the final expression of the density below. 
    */
@@ -163,7 +169,7 @@ Formulation {
     Equation {
       Galerkin { [ epsr[] * Dof{d v} , {d v} ]; 
 	In Vol_Dielectric_Ele; 
-	Jacobian Vol; Integration GradGrad; }
+	Jacobian Vol; Integration Int; }
     }
   }
 }
@@ -182,6 +188,23 @@ Resolution {
 
 eps0 = 8.854187818e-12;  // permittivity of empty space
 
+/* Post-processing is done in two parts.
+   The first part defines, in terms of the Formulation,
+   which itself refers to the FunctionSpace, 
+   a number of quantities that can be evaluated at the postprocessing stage.
+   The three quantities defined here are :
+   - the scalar vector potential
+   - the electric fied
+   - the electric displacement
+   The second part consists in defining groups of post-processing operations,
+   which can be invoked separately. 
+   The first group is invoked by default when Gmsh is run interactively.
+   Each Operation specifies 
+   - a quantity to be eveluated, 
+   - the region on which the evaluation is done,
+   - the name of the output file.
+   The generated post-processing files are automatically displayed by Gmsh
+   if the "Merge result automatically" option is enabled (which is the default). */
 
 PostProcessing {
   { Name EleSta_v; NameOfFormulation Electrostatics_v;