[Getdp] @D axisymmetric electrostatic problem

[Nacho Andres]

Yes sure,
Have a look to the pro file that I attached.
Best Regards,
Nacho

On Wed, 2005-04-06 at 16:14, Patrick Dular wrote:
> Nacho,
> 
> Could you send a example illustrating what you explain? Thank you.
> 
> Patrick

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/* ------------------------------------------------------------------------
   File "EleStat.v_toy.pro"

   Toy to play before Photoelectric Emission Effect on Lageos

   This program expresses the formulation part of the problem
   Created by N at cho Andres, Feb, 2004
   ------------------------------------------------------------------------

   ------------------------------------------------------------------------
   Input:

    * Global Groups
        ConductingDomain             Conducting regions 
        WholeDomain                  Including Surfaces+Lines+Points

    * Function
        sigma[]                 Conductivity of several components
        CoLat[]                 CoLatitude w.r.t. Sun's direction
        IllPhotoFunc[]          B.C. for the illuminated part of the 
                                outer surface
        DarkPhotoFunc[]         idem for the dark part

    * Neumann Boundary Conditions
        1. Photoelectric condition at the external boundary of the sphere
        2. Axis of Symmetry normal derivative must be null
        3. At the interface between two materials the weak formulation 
           implicitly solves for the continuity is problem

------------------------------------------------------------------------ */

Group {
  DefineGroup [ ConductingDomain ];
  DefineGroup [ WholeDomain ];
  DefineGroup [ Surfaces ];
}



Function {
  DefineFunction [ sigma ];
  DefineFunction [ CoLat ]; 
  DefineFunction [ IllPhotoFunc ]; 
  DefineFunction [ DarkPhotoFunc ];
}

// Quoting Cristophe:
//
// << Contrary to a Dirichlet condition where you directly set the value of
//    some degrees of freedom, here you define a new integration term on the
//    boundary, where the unknowns have to be interpolated and integrated. You
//    thus need to add the region on which you do that integration to the
//    'Support' of your 'FunctionSpace' >>
//
// In my case this implies that SurfIll, SurfDark and SymAx (Physical Surfaces 
// appearing in the Neumann condition should appear in the 'Support' of my 
// 'FunctionSpace')

FunctionSpace {
  { Name PhEl_v_Ele; Type Form0;
    BasisFunction {
      // v = v_n * s_n   ,  for all nodes
      { Name sn; NameOfCoef vn; Function BF_Node;
        Support Region[{ConductingDomain,SurfIll,SurfDark,SymAx}] ; Entity NodesOf[ All ]; 
      }
       // { Name s2; NameOfCoef v2n; Function BF_Edge;
       //   Support Region[{ConductingDomain,SurfIll,SurfDark,SymAx}] ;  Entity EdgesOfTreeIn[Surfaces, StartingOn Surfaces]; }
       // { Name s2; NameOfCoef v2n; Function BF_Node_2E;
       //   Support Region[{ConductingDomain,SurfIll,SurfDark,SymAx}] ; Entity NodesOf[ All ]; }
    }
    Constraint {
      { NameOfCoef vn; EntityType NodesOf; NameOfConstraint FloatingP; }
      // { NameOfCoef v2n; EntityType NodesOf; NameOfConstraint FloatingP; }
    }
  }
}


Formulation {
  { Name PhEl_v; Type FemEquation;
    Quantity {
      { Name v; Type Local; NameOfSpace PhEl_v_Ele; }
     }
    Equation {
      Galerkin { [ sigma[] * Dof{d v} , {d v} ]; In ConductingDomain;
                 Jacobian JVolAxiSqu; Integration GradGrad; }
// For the Neumann B.C.
      Galerkin { [ DarkPhotoFunc[] , {v} ]; In SurfDark;
                 Jacobian JSurAxi; Integration GradGrad; }
      Galerkin { [ IllPhotoFunc[CoLat[X[],Y[]]] , {v} ]; 
                 In SurfIll; Jacobian JSurAxi; Integration GradGrad; }
    }
  }
}

Resolution {
  { Name PhEl_v_res;
    System {
      { Name Sys_Ele; NameOfFormulation PhEl_v; }
    }
    Operation { 
      Generate[Sys_Ele]; Solve[Sys_Ele]; SaveSolution[Sys_Ele];
    }
  }
}


PostProcessing {
  { Name EleSta_v; NameOfFormulation PhEl_v;
    Quantity {
      { Name BC1;
        Value {
          Local { [ IllPhotoFunc[CoLat[X[],Y[]]] ]; In SurfIll; Jacobian JSurAxi; }
        }
      }
      { Name BC2;
         Value {
         Local { [ DarkPhotoFunc[] ]; In SurfDark; Jacobian JSurAxi; }
        }
      }
      { Name BC3;
        Value {
          Local { [ {v} ]; In SymAx; Jacobian JLin; }
        }
      }
      { Name Int;
        Value {
          Local { [ Normal[] * {d v} ]; In Surfaces; Jacobian JSurAxi; }
        }
      }
      { Name v; 
        Value { 
          Local { [ {v} ]; In ConductingDomain; Jacobian JVolAxiSqu; } 
          Local { [ {v} ]; In SymAx; Jacobian JLin; }
          Local { [ {v} ]; In SurfIll; Jacobian JSurAxi; }
          Local { [ {v} ]; In SurfDark; Jacobian JSurAxi; }
        }
      }
      { Name e; 
        Value { 
          Local { [ -{d v} ]; In ConductingDomain; Jacobian JVolAxiSqu; }
        }
      }
      { Name j; 
        Value { 
          Local { [ -sigma[] * {d v} ]; In ConductingDomain; Jacobian JVolAxiSqu; } 
        } 
      }
      { Name Nj;
        Value {
          Local { [ Norm[ -sigma[] * {d v}] ]; In ConductingDomain; Jacobian JVolAxiSqu; }
        }
      }
    }
  }
}