[Getdp] Computing stored electrostatic energy

[Ruth Vazquez Sabariego]

The easiest way is to use global quantities.

You can use the following Function space:

FunctionSpace {
  { Name Hgrad_vf_Ele ; Type Form0 ;
    BasisFunction {
      // v = v  s  + v    s
      //      n  n    c,k  c,k
      { Name sn ; NameOfCoef vn ; Function BF_Node ;
        Support DomainCC_Ele ; Entity NodesOf[ All, Not SkinDomainC_Ele ] ; }
      { Name sck ;NameOfCoef vck ; Function BF_GroupOfNodes ;
        Support DomainCC_Ele ; Entity GroupsOfNodesOf[ SkinDomainC_Ele ] ; }
    }
    GlobalQuantity {
      { Name GlobalElectricPotential ; Type AliasOf        ; NameOfCoef vck ; }
      { Name GlobalElectricCharge    ; Type AssociatedWith ; NameOfCoef vck ; }
    }
    Constraint {
      { NameOfCoef vn ;
        EntityType NodesOf ; NameOfConstraint ElectricScalarPotential ; }

      { NameOfCoef GlobalElectricPotential ;
        EntityType GroupsOfNodesOf ; NameOfConstraint GlobalElectricPotential ; }
      { NameOfCoef GlobalElectricCharge ;
        EntityType GroupsOfNodesOf ; NameOfConstraint GlobalElectricCharge ; }
    }
  }
}

then formulation
Formulation {
  { Name Electrostatics_vf ; Type FemEquation ;
    Quantity {
      { Name v ; Type Local  ; NameOfSpace Hgrad_vf_Ele ; }
      { Name Q ; Type Global ;
        NameOfSpace Hgrad_vf_Ele [GlobalElectricCharge] ; }
      { Name V ; Type Global ;
        NameOfSpace Hgrad_vf_Ele [GlobalElectricPotential] ; }
    }
    Equation {
      Galerkin { [ epsr[] * Dof{d v} , {d v} ] ;
                 In DomainCC_Ele ;
                 Jacobian Vol ; Integration GradGrad ; }

      GlobalTerm { [ -Dof{Q}/eps0 / Length , {V} ] ; In SkinDomainC_Ele ; }
    }
  }
}


and the post-processing gives you directly the capacity:

PostProcessing {
  { Name EleSta_vf ; NameOfFormulation Electrostatics_vf ;
    PostQuantity {
      { Name v ; Value { Term { [ {v} ]                  ; Jacobian Vol; In DomainCC_Ele ; } } }
      { Name e ; Value { Term { [ -{d v} ]               ; Jacobian Vol; In DomainCC_Ele ; } } }
      { Name d ; Value { Term { [ -eps0*epsr[] * {d v} ] ; Jacobian Vol; In DomainCC_Ele ; } } }
      { Name em ; Value { Term { [ Norm[{d v}] / 1.e6 ] ; Jacobian Vol; In DomainCC_Ele ; } } } // Warning: in kV/mm
      { Name Q ; Value { Term { [ {Q} ] ; In SkinDomainC_Ele ; } } }
      { Name V ; Value { Term { [ {V} / 1.e3 ] ; In SkinDomainC_Ele ; } } } // Warning: in kV
      { Name C ; Value { Term { [ {Q}/{V} ] ; In SkinDomainC_Ele ; } } }
    }
  }
}

with domains:
Domain_Ele               Whole electric domain
DomainCC_Ele             Nonconducting regions
DomainC_Ele              Conducting regions (not used)
SkinDomainC_Ele          Skin of conducting regions (surfaces)


The other possibility is forgetting about the global quantities and define an integral quantity in the postprocessing.
 { Name Cpos ;
       Value {
          Integral { Type Global ;
            [ epsilon[] * SquNorm[-{d v}] ] ; In DomainCC_Ele ; Jacobian Vol ; Integration I1 ; }
        }
      }


HTH,
Ruth


—
Prof. Ruth V. Sabariego
KU Leuven
Dept. Electrical Engineering ESAT/Electa, EnergyVille
http://www.esat.kuleuven.be/electa
http://www.energyville.be

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On 28 Mar 2016, at 14:34, Geoffrey LOSSA [531522] <Geoffrey.LOSSA at umons.ac.be<mailto:Geoffrey.LOSSA at umons.ac.be>> wrote:

Dear all,

I’m looking to calculate the stored electrostatic energy in order to deduct some parasitic capacitance of a system (inductor).
What is the term or the expression to be integrated in the Getdp electrostatic formulation?

Thanks in advance for the help,

Geoffrey
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