[Getdp] [Gmsh] ¿how to express a weak formulation for an integral operator?

[Luis Saavedra]

Dear Community,

i'm attempting to express this week formulation (in LaTeX notation):

\Int_{\Omega} T(x,y) v(x,y) dxdy = 
\Int_{\Omega}\Int_{\Omega}(1/r).(grad' u(x',y'))(grad v(x,y)) dxdydx'dy'

where:

u = u(x',y') is the unknown function,
v = v(x,y) is a test function,
T is a known function,
r = || (x-x')^2 + (y-y')^2 ||, and
grad' is the gradient with respect to de x', y' variables.

it would be something as this:

Formulation {
  {Name WeekIEM; Type FemEquation;
    Quantity {
      { Name  v; Type Local;  NameOfSpace  TestSpace; }
    }
    Equation {
      Galerkin { [[ (1/r) , Dof{Grad v} ], {Grad v}] ; In Omega ; 
Jacobian Vol ; Integration Int ; }
      Galerkin { [ -T[],{v}] ; In Omega ; Jacobian Vol ; Integration Int ; }
    }
}

but I know that this will not work.

I like very much the free software GetDP, is my made dream reality, i'm 
very grateful with you.

Thanks for all and best regards,
Luis Saavedra.

Santiago Chile.