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
       getdp microstrip -pos Cut

   To compute the solution interactively from the Gmsh GUI:
       File > Open > microstrip.pro
       Run (button at the bottom of the left panel)
   ------------------------------------------------------------------- */

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. */

  Air = Region[101];
  Diel1 = Region[111];

  Ground = Region[120];
  Electrode = Region[121];
  SurfInf = Region[130];

  /* We now define abstract regions to be used below
     in the definition of the scalar electric potential formulation:

     Vol_Dielectric_Ele : dielectric volume regions where
                          "Div ( epsr[] Grad v)" is solved
     Sur_Dir_Ele        : Dirichlet boundary condition (v imposed)
     Sur_Neu_Ele        : Neumann bondary condition ( epsr[] n.Grad v = 0 )

     Vol_xxx groups contain only volume elements of the mesh (triangles here).
     Sur_xxx groups contain only surface elements of the mesh (lines here).
  */

  Vol_Dielectric_Ele = Region[ {Air, Diel1} ];
  Sur_Dir_Ele = Region[ {Ground, Electrode} ];
  Sur_Neu_Ele = Region[ {SurfInf} ];
}

Function {
  /* Material laws (here the relative permittivity)
     are defined piecewise in terms of the above defined physical regions */

  epsr[Air] = 1.;
  epsr[Diel1] = 9.8;
}

Constraint {
  /* As for material laws, the Dirichlet boundary condition
     is defined piecewise.
     The constraint "Dirichlet_Ele" is invoked in the FunctionSpace below */

  { Name Dirichlet_Ele; Type Assign;
    Case {
      { Region Ground; Value 0.; }
      { Region Electrode; Value 1.e-3; }
    }
  }
}

Group{
  /* The domain of definition of a FunctionSpace lists all regions