[Getdp] Method of moments

Lars Rindorf lhr at com.dtu.dk
Tue Jan 15 18:33:59 CET 2008

Dear all 
I'm working on a simple method of moments which involves a Greens function. A simplified model for the problem involves a formulation
  { Name form_neumann; Type FemEquation;
    Quantity {
      { Name E;  Type Local;     NameOfSpace scalar;}
      { Name E2; Type Integral ; NameOfSpace scalar;
        [ Helmholtz[]{2D,k0} * {E} ];
        In feed; Jacobian Jac ; Integration I1 ; }
    Equation {
      Galerkin {      [ Dof{E},{E} ]; In Domain; Integration I1; Jacobian Jac;}
      Galerkin {      [ -inc[],{E} ]; In Domain; Integration I1; Jacobian Jac;}
      Galerkin {      [ {E2},{E} ]; In Domain2D; Integration I1; Jacobian Jac;}
The problem is 2D. "feed" is a 1D boundary. "inc[]" is the incoming field. Domain is the union of the 2D domain (Domain2D) and the 1D domain (feed).

The problem is that the Green's function integral E2 is evaluated once during initialization of the problem, and it is not included in the discretization of the matrix. I have tried making a coupled model. This seems to be able to work, but it is not very elegant from a mathematical point of view. I have come rather stuck in the problem. 
Does anyone know how to make it work?
Kind regards
Lars Rindorf