# [Getdp] Integration in 2D and 2D axisymmetry

Frederic Trillaud Pighi ftrillaudp at pumas.iingen.unam.mx
Tue Jun 10 13:07:36 CEST 2014

```Dear all,

The question is the following, how does the Integral function computes the integral on Jacobian VolAxi and Jacobian Vol?

I have implemented a 2D axisymmetric magnetic problem (a solenoid). While I tried to compute the area of the solenoidal coil on the Jacobian definition VolAxi in the post-processing stage, it comes out wrong. However, if I define Jacobian Vol, the area comes out right. It should be mentioned that if I use either the definition of the Jacobian Vol or VolAxi in the Formulation to integrate the current density, the results do not seem to be affect. I am puzzled!!

{
Name jacobianNDRegionZ;
Case
{
{
Region All;
Jacobian Vol;
}
}
}
{
Name jacobianNDRegion;
Case
{
{
Region infiniteBoundaryDomain;
}
{
Region All;
Jacobian VolAxi;
}
}
}

Correct -> {Name computedCoilSurface; Value{Integral {[1]; In inductorDomain; Jacobian jacobianNDRegionZ; Integration basicIntegration;}}}
Wrong -> {Name computedCoilSurface; Value{Integral {[1]; In inductorDomain; Jacobian jacobianNDRegion; Integration basicIntegration;}}}

In formulation:

{
Name potentialVectorFormulation;
Type FemEquation;
Quantity
{
{
Name A;
Type Local;
NameOfSpace potentialVectorFunctionSpace;
}
{
Name Je;
Type Local;
NameOfSpace sourceFunctionSpace;
}
}
Equation
{
Galerkin // magnetic solution domain (entire domain)
{
[nu[]*Dof{Curl A}, {Curl A}];
In electromagneticSolutionDomain;
Jacobian jacobianNDRegion;
Integration basicIntegration;
}
Galerkin // Induction in inductor domain
{
DtDof[sigma[Dt[{A}], {Curl A}]*Dof{A}, {A}];
In inductorDomain;
Jacobian jacobianNDRegion;
Integration basicIntegration;
}
Galerkin // Inductor domain (conductors)
{
[-Dof{Je}, {A}];
In inductorDomain;
Jacobian jacobianNDRegion; // or Jacobian jacobianNDRegionZ; does not seem to affect result
Integration basicIntegration;
}
}
}

Best,

Frederic
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