# [Getdp] Method of moments

Olivier Castany castany at quatramaran.ens.fr
Wed Jan 16 23:12:11 CET 2008

```>   { 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.

I think you should add the keyword "Dof" in the definition of the integral quantity and in the equations :

{ Name form_neumann; Type FemEquation;
Quantity {
{ Name E;  Type Local;     NameOfSpace scalar;}
{ Name E2; Type Integral ; NameOfSpace scalar;
[ Helmholtz[]{2D,k0} * Dof{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 {      [ Dof{E2},{E} ]; In Domain2D; Integration I1; Jacobian Jac;}
}
}

Let me know if it works, I'm interested.

Bye,

O.C.

```