[Getdp] Problems with mixed periodic and Dirichlet boundary conditions

[de Rosny Julien]

Hello,

I would like to simulate the wave propagation inside a waveguide with a 
periodic structure inside it.
I simplified the problem with the simulation of the homogeneous 
Helmholtz equ. with Dirichlet boundary conditions on the top & bottom 
and periodic on the left and right.
To that end, I set the following constrains :

Constraint{
     { Name CL;
         Case{
     // periodic BND cond. between TOP & Bottom
     {Region L1 ;
         Type LinkCplx ; RegionRef L3;
         Coefficient  Complex[1,0];
         Function Vector[$X,$Y+Sqrt[2],$Z] ;
         }

//     periodic BND cond. between left & right
//      {Region L4 ;
//        Type LinkCplx ; RegionRef L2;
//        Coefficient  Complex[1,0];
//        Function Vector[$X+1,$Y,$Z] ;
//        }

          //{ Region L1; Type Assign; Value 000. ;}
            // { Region L3; Value 000. ;}
          // Dirichelt BND condition on the bottom and top
            { Region L2; Type Assign;  Value 0000. ;}
            { Region L4; Type Assign; Value 0000. ;}
       }
     }
}

But it gives wrong results (not periodic on top/bottom and not null on 
left/right borders). See attached files.
The code works well if now I only use  Dirichlet or periodic boundary 
constrains for the 4 sides.

Any idea what is wrong?

Thanks.
Regards.

Julien de Rosny

-- 
Julien de Rosny
Directeur de recherche CNRS
Institut Langevin -UMR 7587
ESPCI - CNRS
1 rue Jussieu
75231 Paris Cedex 05
tel : +33 1 180963052

-------------- next part --------------
Group{
  S = Region[100]; //rectangle
  L1= Region[{103}]; // bottom bnd
  L2= Region[{104}]; //right bnd
  L3= Region[{105}]; //top bnd
  L4= Region[{106}]; // left bnd
  Domain=Region[{S,L1,L2,L3,L4}];
  DPEC=Region[{L1,L3}];
  }

Constraint{
    { Name CL;
        Case{
    // periodic BND cond. between TOP & Bottom      
    {Region L1 ; 
        Type LinkCplx ; RegionRef L3;
        Coefficient  Complex[1,0];
	    Function Vector[$X,$Y+Sqrt[2],$Z] ;
        }

//     periodic BND cond. between left & right  
//      {Region L4 ; 
//        Type LinkCplx ; RegionRef L2;
//        Coefficient  Complex[1,0];
//	    Function Vector[$X+1,$Y,$Z] ;
//        }
    
         //{ Region L1; Type Assign; Value 000. ;}
           // { Region L3; Value 000. ;}
         // Dirichelt BND condition on the bottom and top
           { Region L2; Type Assign;  Value 0000. ;}
           { Region L4; Type Assign; Value 0000. ;} 
      }
    }
}


// =========
// JACOBIAN
// =========
Jacobian {
  { Name JVol ; Case { { Region All ; Jacobian Vol ; } } }
  { Name JSur ; Case { { Region All ; Jacobian Sur ; } } }
}

// ======================
// INTEGRATION PARAMETERS
// ======================
Integration {
  { Name I1 ;
    Case {
      { Type Gauss ;
        Case {
          { GeoElement Point ; NumberOfPoints  1 ; }
          { GeoElement Line ; NumberOfPoints  4 ; }
          { GeoElement Triangle ; NumberOfPoints  6 ; }
          { GeoElement Quadrangle ; NumberOfPoints 7 ; }
          { GeoElement Tetrahedron ; NumberOfPoints 15 ; }
          { GeoElement Hexahedron ; NumberOfPoints 34 ; }
        }
      }
    }
  }
}

// ==============
// FUNCTION SPACE
// ==============

FunctionSpace{
  {Name H_grad; Type Form0;
    BasisFunction{
      {Name uuuuu; NameOfCoef ui; Function BF_Node;
       Support Domain;Entity NodesOf[All];}
    }
    Constraint {
      { NameOfCoef ui; EntityType EdgesOf ; NameOfConstraint CL; }
  }
  }
}//End FunctionSpace

// ============
// FORMULATIONS
// ============
Formulation {
  // Formulation for a Dirichlet boundary condition
  { Name Helmholtz; Type FemEquation;
    Quantity{
      { Name u ; Type Local; NameOfSpace H_grad;}
    }
    Equation{
      //Helmholtz equation
      Galerkin{[Dof{Grad u}, {Grad u}];
	In S; Jacobian JVol; Integration I1;}
      Galerkin{DtDtDof[Dof{u}, {u}];
	In S; Jacobian JVol; Integration I1;}
      
}   
  }
}//End Formulation

Resolution{
  {Name Scattering;
    System{ {Name A; NameOfFormulation Helmholtz; Type Complex; } }
    Operation{
      GenerateSeparate[A];
      EigenSolve[A, 10, .1, 0,$EigenvalueReal > 0];
      SaveSolutions[A] ;
    }
  }
} // End Resolution


PostProcessing{
  {Name Wave; NameOfFormulation Helmholtz;
    Quantity {
      {Name u; Value {Local { [{u}] ; In S; Jacobian JVol; }}}
} // End Postprocessing.
}}

PostOperation{
  {Name Wave; NameOfPostProcessing Wave ;
    Operation {
      Print [u, OnElementsOf Domain, File "u.pos"];
    }
  }
} // End PostOperation
-------------- next part --------------
lc=0.01;
Lx=1/2;
Ly=1/2*Sqrt[2];
Point(1) = {-Lx,-Ly,0,lc};
Point(2) = {+Lx,-Ly,0,lc};
Point(3) = {+Lx,+Ly,0,lc};
Point(4) = {-Lx,+Ly,0,lc};
Line(1) = {1,2};
Line(2) = {2,3};
Line(3) = {3,4};
Line(4) = {4,1};
Line Loop(5) ={1,2,3,4};
Plane Surface(6)= {5};
Physical Surface(100)={6};
Physical Line(103)={1};
Physical Line(104)={2};
Physical Line(105)={-3};
Physical Line(106)={-4};