Update microstrip.pro

Electrostatics/microstrip.pro

@@ -104,10 +104,10 @@ Group{
 
 FunctionSpace {
   /* The function space in which we shall pick the electric scalar potential "v"
-     solution is definied by
+     solution is defined by
      - a domain of definition (the "Support": "Dom_Hgrad_v_Ele")
      - a type ("Form0" means scalar field)
-     - a set of scalar basis functions ("BF_Node" means nodal basis functions)
+     - a set of basis functions ("BF_Node" means scalar nodal basis functions)
      - a set of entities to which the basis functions are associated ("Entity":
        here all the nodes of the domain of definition "NodesOf[All]")
      - a constraint (here the Dirichlet boundary conditions)
@@ -116,11 +116,11 @@ FunctionSpace {
 
      v(x,y) = Sum_k vn_k sn_k(x,y)
 
-     where the "vn_k" are the nodal values (connectors) and "sn_k(x,y)" the
-     nodal basis functions.  Not all connectors are unknowns of the FE problem,
-     due to the "Constraint", which assigns particular values to the nodes of
-     the Ground and Electrode regions. GetDP deals with that automatically on
-     basis of the definition of the FunctionSpace. */
+     where the "vn_k" coefficients are the nodal values (connectors) and
+     "sn_k(x,y)" the nodal basis functions.  Not all connectors are unknowns of
+     the FE problem, due to the "Constraint", which assigns particular values to 
+     the nodes of the Ground and Electrode regions. GetDP deals with that
+     automatically on basis of the definition of the FunctionSpace. */
 
   { Name Hgrad_v_Ele; Type Form0;
     BasisFunction {
@@ -128,7 +128,7 @@ FunctionSpace {
         Support Dom_Hgrad_v_Ele; Entity NodesOf[ All ]; }
       // using "NodesOf[All]" instead of "NodesOf[Dom_Hgrad_v_Ele]" is an
       // optimization, which allows GetDP to not explicitly build the list of
-      // all nodes
+      // all the nodes
     }
     Constraint {
       { NameOfCoef vn; EntityType NodesOf; NameOfConstraint Dirichlet_Ele; }
@@ -140,8 +140,8 @@ Jacobian {
   /* Jacobians are used to specify the mapping between elements in the mesh and
      the reference elements (defined in standardized unit cells) over which
      integration is performed. "Vol" represents the classical 1-to-1 mapping
-     between elements of identical geometrical dimension, i.e. in this case a
-     reference triangle/quadrangle onto triangles/quadrangles in the z=0 plane
+     between identical spatial dimensions, i.e. in this case a reference
+     triangle/quadrangle onto triangles/quadrangles in the z=0 plane
      (2D <-> 2D). "Sur" would be used to map the reference triangle/quadrangle
      onto triangles/quadrangles in a 3D space (2D <-> 3D), or to map the
      reference line segment onto segments in 2D space (1D <-> 2D). "Lin" would
@@ -178,15 +178,15 @@ Formulation {
      (-Div(epsilon Grad v) , v')_Vol_Ele = 0
 
      holds for all so-called "test-functions" v', where (.,.)_D denotes an inner
-     product over the domain D. If the test-functions v' are differentiable,
+     product over a domain D. If the test-functions v' are differentiable,
      integration by parts using Green's identity leads to finding v such that
 
      (epsilon Grad v, Grad v')_Vol_Ele + (epsilon n.Grad v, v')_Bnd_Vol_Ele = 0
 
      holds for all v', where Bnd_Vol_Ele is the boundary of Vol_Ele. In our
-     microstrip example this surface term vanishes, as either there is no test
-     function v' (on the Dirichlet boundary) or the "epsilon n.Grad v" is zero
-     (on the homogeneous Neumann boundary). We are thus eventually looking for
+     microstrip example this surface term vanishes, as there is either no test
+     function v' (on the Dirichlet boundary), or "epsilon n.Grad v" is zero
+     (on the homogeneous Neumann boundary. We are thus eventually looking for
      functions v in the function space Hgrad_v_Ele such that
 
      (epsilon Grad v, Grad v')_Vol_Ele = 0