From d5c099deb3ccf39e92e83a49024bdde61ca7ef4a Mon Sep 17 00:00:00 2001
From: Jon Doe <cgeuzaine@uliege.be>
Date: Sun, 1 Apr 2018 10:07:50 +0200
Subject: [PATCH] pp

---
 Magnetodynamics/Lib_MagStaDyn_av_2D_Cir.pro | 545 --------------------
 1 file changed, 545 deletions(-)
 delete mode 100644 Magnetodynamics/Lib_MagStaDyn_av_2D_Cir.pro

diff --git a/Magnetodynamics/Lib_MagStaDyn_av_2D_Cir.pro b/Magnetodynamics/Lib_MagStaDyn_av_2D_Cir.pro
deleted file mode 100644
index aedde5b..0000000
--- a/Magnetodynamics/Lib_MagStaDyn_av_2D_Cir.pro
+++ /dev/null
@@ -1,545 +0,0 @@
-// This is a template .pro file containing a general formulation for 2D
-// magnetostatic and magnetodynamic problems in terms of the magnetic vector
-// potential a (potentially coupled with the electric scalar potential v), with
-// optional circuit coupling.
-
-// Below are definitions of the constants (inside "DefineConstant"), groups
-// (inside "DefineGroup") and functions (inside "DefineFunction") that can be
-// redefined from outside this template.
-
-DefineConstant[
-  Flag_FrequencyDomain = 1, // frequency-domain or time-domain simulation
-  Flag_CircuitCoupling = 0, // consider coupling with external electric circuit
-  Flag_NewtonRaphson = 1, // Newton-Raphson or Picard method for nonlinear iterations
-  CoefPower = 0.5, // coefficient for power calculations
-  Freq = 50, // frequency (for harmonic simulations)
-  TimeInit = 0, // intial time (for time-domain simulations)
-  TimeFinal = 1/50, // final time (for time-domain simulations)
-  DeltaTime = 1/500, // time step (for time-domain simulations)
-  FE_Order = 1, // finite element order
-  Val_Rint = 0, // interior radius of annulus shell transformation region (Vol_Inf_Mag)
-  Val_Rext = 0 // exterior radius of annulus shell  transformation region (Vol_Inf_Mag)
-  NL_tol_abs = 1e-6, // absolute tolerance on residual for noninear iterations
-  NL_tol_rel = 1e-6, // relative tolerance on residual for noninear iterations
-  NL_iter_max = 20 // maximum number of noninear iterations
-];
-
-Group {
-  DefineGroup[
-    // The full magnetic domain:
-    Vol_Mag,
-
-    // Subsets of Vol_Mag:
-    Vol_C_Mag, // massive conductors
-    Vol_S0_Mag, // stranded conductors with imposed current densities js0
-    Vol_S_Mag, // stranded conductors with imposed current, voltage or circuit coupling
-    Vol_NL_Mag, // nonlinear magnetic materials
-    Vol_V_Mag, // moving massive conducting parts (with invariant mesh)
-    Vol_M_Mag, // permanent magnets
-    Vol_Inf_Mag, // annulus where a infinite shell transformation is applied
-
-    // Boundaries:
-    Sur_FluxTube_Mag, // boundary with Neumann BC
-    Sur_Perfect_Mag, // boundary of perfect conductors (non-meshed)
-    Sur_Imped_Mag // boundary of conductors approximated by a surface impedance
-                  // (non-meshed)
-  ];
-  If(Flag_CircuitCoupling)
-    DefineGroup[
-      SourceV_Cir, // voltage sources
-      SourceI_Cir, // current sources
-      Resistance_Cir, // resistors (linear)
-      Inductance_Cir, // inductors
-      Capacitance_Cir, // capacitors
-      Diode_Cir // diodes (treated as nonlinear resistors)
-    ];
-  EndIf
-}
-
-Function {
-  DefineFunction[
-    nu, // reluctivity (in Vol_Mag)
-    sigma, // conductivity (in Vol_C_Mag and Vol_S_Mag)
-    br, // remanent magnetic flux density (in Vol_M_Mag)
-    js0, // source current density (in Vol_S0_Mag)
-    dhdb, // Jacobian for Newton-Raphson method (in Vol_NL_Mag)
-    nxh, // n x magnetic field (on Sur_FluxTube_Mag)
-    Velocity, // velocity of moving part (in Vol_V_Mag)
-    Ns, // number of turns (in Vol_S_Mag)
-    Sc, // cross-section of windings (in Vol_S_Mag)
-    CoefGeos, // geometrical coefficient for 2D or 2D axi model (in Vol_Mag)
-    Ysur // surface admittance (on Sur_Imped_Mag)
-  ];
-  If(Flag_CircuitCoupling)
-    DefineFunction[
-      Resistance, // resistance values
-      Inductance, // inductance values
-      Capacitance // capacitance values
-    ];
-  EndIf
-}
-
-// End of definitions.
-
-Group{
-  // all linear materials
-  Vol_L_Mag = Region[ {Vol_Mag, -Vol_NL_Mag} ];
-  // all volumes + surfaces on which integrals will be computed
-  Dom_Mag = Region[ {Vol_Mag, Sur_FluxTube_Mag, Sur_Perfect_Mag, Sur_Imped_Mag} ];
-  If(Flag_CircuitCoupling)
-    // all circuit impedances
-    DomainZ_Cir = Region[ {Resistance_Cir, Inductance_Cir, Capacitance_Cir} ];
-    // all circuit sources
-    DomainSource_Cir = Region[ {SourceV_Cir, SourceI_Cir} ];
-    // all circuit elements
-    Domain_Cir = Region[ {DomainZ_Cir, DomainSource_Cir} ];
-  EndIf
-}
-
-Jacobian {
-  { Name Vol;
-    Case {
-      { Region Vol_Inf_Mag ;
-        Jacobian VolSphShell {Val_Rint, Val_Rext} ; }
-      { Region All; Jacobian Vol; }
-    }
-  }
-  { Name Sur;
-    Case {
-      { Region All; Jacobian Sur; }
-    }
-  }
-}
-
-Integration {
-  { Name Gauss_v;
-    Case {
-      { Type Gauss;
-        Case {
-          { GeoElement Point; NumberOfPoints  1; }
-          { GeoElement Line; NumberOfPoints  5; }
-          { GeoElement Triangle; NumberOfPoints  7; }
-          { GeoElement Quadrangle; NumberOfPoints  4; }
-          { GeoElement Tetrahedron; NumberOfPoints 15; }
-          { GeoElement Hexahedron; NumberOfPoints 14; }
-          { GeoElement Prism; NumberOfPoints 21; }
-        }
-      }
-    }
-  }
-}
-
-// Same FunctionSpace for both static and dynamic formulations
-FunctionSpace {
-  { Name Hcurl_a_2D; Type Form1P; // 1-form (circulations) on edges
-                                  // perpendicular to the plane of study
-    BasisFunction {
-      // \vec{a}(x) = \sum_{n \in N(Domain)} a_n \vec{s}_n(x)
-      //   without nodes on perfect conductors (where a is constant)
-      { Name s_n; NameOfCoef a_n; Function BF_PerpendicularEdge;
-        Support Dom_Mag; Entity NodesOf[All, Not Sur_Perfect_Mag]; }
-
-      // global basis function on boundary of perfect conductors
-      { Name s_skin; NameOfCoef a_skin; Function BF_GroupOfPerpendicularEdges;
-        Support Dom_Mag; Entity GroupsOfNodesOf[Sur_Perfect_Mag]; }
-
-      // additional basis functions for 2nd order interpolation
-      If(FE_Order == 2)
-        { Name s_e; NameOfCoef a_e; Function BF_PerpendicularEdge_2E;
-          Support Vol_Mag; Entity EdgesOf[All]; }
-      EndIf
-    }
-    GlobalQuantity {
-      { Name A; Type AliasOf; NameOfCoef a_skin; }
-      { Name I; Type AssociatedWith; NameOfCoef a_skin; }
-    }
-    Constraint {
-      { NameOfCoef a_n;
-        EntityType NodesOf; NameOfConstraint MagneticVectorPotential_2D; }
-
-      { NameOfCoef I;
-        EntityType GroupsOfNodesOf; NameOfConstraint Current_2D; }
-
-      If(FE_Order == 2)
-        { NameOfCoef a_e;
-          EntityType EdgesOf; NameOfConstraint MagneticVectorPotential_2D_0; }
-      EndIf
-    }
-  }
-}
-
-FunctionSpace {
-  // Gradient of Electric scalar potential (2D)
-  { Name Hregion_u_2D; Type Form1P; // same as for \vec{a}
-    BasisFunction {
-      { Name sr; NameOfCoef ur; Function BF_RegionZ;
-        // constant vector (over the region) with nonzero z-component only
-        Support Region[{Vol_C_Mag, Sur_Imped_Mag}];
-        Entity Region[{Vol_C_Mag, Sur_Imped_Mag}]; }
-    }
-    GlobalQuantity {
-      { Name U; Type AliasOf; NameOfCoef ur; }
-      { Name I; Type AssociatedWith; NameOfCoef ur; }
-    }
-    Constraint {
-      { NameOfCoef U;
-        EntityType Region; NameOfConstraint Voltage_2D; }
-      { NameOfCoef I;
-        EntityType Region; NameOfConstraint Current_2D; }
-    }
-  }
-
-  // Current in stranded coil (2D)
-  { Name Hregion_i_2D; Type Vector;
-    BasisFunction {
-      { Name sr; NameOfCoef ir; Function BF_RegionZ;
-        Support Vol_S_Mag; Entity Vol_S_Mag; }
-    }
-    GlobalQuantity {
-      { Name Is; Type AliasOf; NameOfCoef ir; }
-      { Name Us; Type AssociatedWith; NameOfCoef ir; }
-    }
-    Constraint {
-      { NameOfCoef Us;
-        EntityType Region; NameOfConstraint Voltage_2D; }
-      { NameOfCoef Is;
-        EntityType Region; NameOfConstraint Current_2D; }
-    }
-  }
-}
-
-If(Flag_CircuitCoupling)
-  // UZ and IZ for impedances
-  FunctionSpace {
-    { Name Hregion_Z; Type Scalar;
-      BasisFunction {
-        { Name sr; NameOfCoef ir; Function BF_Region;
-          Support Domain_Cir; Entity Domain_Cir; }
-      }
-      GlobalQuantity {
-        { Name Iz; Type AliasOf; NameOfCoef ir; }
-        { Name Uz; Type AssociatedWith; NameOfCoef ir; }
-      }
-      Constraint {
-        { NameOfCoef Uz;
-          EntityType Region; NameOfConstraint Voltage_Cir; }
-        { NameOfCoef Iz;
-          EntityType Region; NameOfConstraint Current_Cir; }
-      }
-    }
-  }
-EndIf
-
-
-// Static Formulation
-Formulation {
-  { Name MagSta_a_2D; Type FemEquation;
-    Quantity {
-      { Name a; Type Local; NameOfSpace Hcurl_a_2D; }
-      { Name ir; Type Local; NameOfSpace Hregion_i_2D; }
-    }
-    Equation {
-      Integral { [ nu[] * Dof{d a} , {d a} ];
-        In Vol_L_Mag; Jacobian Vol; Integration Gauss_v; }
-
-      If(Flag_NewtonRaphson)
-        Integral { [ nu[{d a}] * {d a} , {d a} ];
-          In Vol_NL_Mag; Jacobian Vol; Integration Gauss_v; }
-        Integral { [ dhdb[{d a}] * Dof{d a} , {d a} ];
-          In Vol_NL_Mag; Jacobian Vol; Integration Gauss_v; }
-        Integral { [ - dhdb[{d a}] * {d a} , {d a} ];
-          In Vol_NL_Mag; Jacobian Vol; Integration Gauss_v; }
-      Else
-        Integral { [ nu[{d a}] * Dof{d a}, {d a} ];
-          In Vol_NL_Mag; Jacobian Vol; Integration Gauss_v; }
-      EndIf
-
-      Integral { [ - nu[] * br[] , {d a} ];
-        In Vol_M_Mag; Jacobian Vol; Integration Gauss_v; }
-
-      Integral { [ - js0[] , {a} ];
-        In Vol_S0_Mag; Jacobian Vol; Integration Gauss_v; }
-
-      Integral { [ - (js0[]*Vector[0,0,1]) * Dof{ir} , {a} ];
-        In Vol_S_Mag; Jacobian Vol; Integration Gauss_v; }
-
-      Integral { [ nxh[] , {a} ];
-        In Sur_FluxTube_Mag; Jacobian Sur; Integration Gauss_v; }
-    }
-  }
-}
-
-// Dynamic Formulation (eddy currents)
-Formulation {
-  { Name MagDyn_a_2D; Type FemEquation;
-    Quantity {
-      { Name a; Type Local; NameOfSpace Hcurl_a_2D; }
-      { Name A_floating; Type Global; NameOfSpace Hcurl_a_2D [A]; }
-      { Name I_perfect; Type Global; NameOfSpace Hcurl_a_2D [I]; }
-
-      { Name ur; Type Local; NameOfSpace Hregion_u_2D; }
-      { Name I; Type Global; NameOfSpace Hregion_u_2D [I]; }
-      { Name U; Type Global; NameOfSpace Hregion_u_2D [U]; }
-
-      { Name ir; Type Local; NameOfSpace Hregion_i_2D; }
-      { Name Us; Type Global; NameOfSpace Hregion_i_2D [Us]; }
-      { Name Is; Type Global; NameOfSpace Hregion_i_2D [Is]; }
-
-      If(Flag_CircuitCoupling)
-        { Name Uz; Type Global; NameOfSpace Hregion_Z [Uz]; }
-        { Name Iz; Type Global; NameOfSpace Hregion_Z [Iz]; }
-      EndIf
-    }
-    Equation {
-      Integral { [ nu[] * Dof{d a} , {d a} ];
-        In Vol_L_Mag; Jacobian Vol; Integration Gauss_v; }
-
-      If(Flag_NewtonRaphson)
-        Integral { [ nu[{d a}] * {d a} , {d a} ];
-          In Vol_NL_Mag; Jacobian Vol; Integration Gauss_v; }
-        Integral { [ dhdb[{d a}] * Dof{d a} , {d a} ];
-          In Vol_NL_Mag; Jacobian Vol; Integration Gauss_v; }
-        Integral { [ - dhdb[{d a}] * {d a} , {d a} ];
-          In Vol_NL_Mag; Jacobian Vol; Integration Gauss_v; }
-      Else
-        Integral { [ nu[{d a}] * Dof{d a}, {d a} ];
-          In Vol_NL_Mag; Jacobian Vol; Integration Gauss_v; }
-      EndIf
-
-      Integral { [ - nu[] * br[] , {d a} ];
-        In Vol_M_Mag; Jacobian Vol; Integration Gauss_v; }
-
-      // Electric field e = -Dt[{a}]-{ur},
-      // with {ur} = Grad v constant in each region of Vol_C_Mag
-      Integral { DtDof [ sigma[] * Dof{a} , {a} ];
-        In Vol_C_Mag; Jacobian Vol; Integration Gauss_v; }
-      Integral { [ sigma[] * Dof{ur} / CoefGeos[] , {a} ];
-        In Vol_C_Mag; Jacobian Vol; Integration Gauss_v; }
-
-      Integral { [ - sigma[] * (Velocity[] /\ Dof{d a}) , {a} ];
-        In Vol_V_Mag; Jacobian Vol; Integration Gauss_v; }
-
-      Integral { [ - js0[] , {a} ];
-        In Vol_S0_Mag; Jacobian Vol; Integration Gauss_v; }
-
-      Integral { [ nxh[] , {a} ];
-        In Sur_FluxTube_Mag; Jacobian Sur; Integration Gauss_v; }
-
-      Integral { DtDof [  Ysur[] * Dof{a} , {a} ];
-        In Sur_Imped_Mag; Jacobian Sur; Integration Gauss_v; }
-      Integral { [ Ysur[] * Dof{ur} / CoefGeos[] , {a} ];
-        In Sur_Imped_Mag; Jacobian Sur; Integration Gauss_v; }
-
-      // When {ur} act as a test function, one obtains the circuits relations,
-      // relating the voltage and the current of each region in Vol_C_Mag
-      Integral { DtDof [ sigma[] * Dof{a} , {ur} ];
-        In Vol_C_Mag; Jacobian Vol; Integration Gauss_v; }
-      Integral { [ sigma[] * Dof{ur} / CoefGeos[] , {ur} ];
-        In Vol_C_Mag; Jacobian Vol; Integration Gauss_v; }
-      GlobalTerm { [ Dof{I} *(CoefGeos[]/Fabs[CoefGeos[]]) , {U} ]; In Vol_C_Mag; }
-
-      Integral { DtDof [ Ysur[] * Dof{a} , {ur} ];
-        In Sur_Imped_Mag; Jacobian Sur; Integration Gauss_v; }
-      Integral { [ Ysur[] * Dof{ur} / CoefGeos[] , {ur} ];
-        In Sur_Imped_Mag; Jacobian Sur; Integration Gauss_v; }
-      GlobalTerm { [ Dof{I} *(CoefGeos[]/Fabs[CoefGeos[]]) , {U} ]; In Sur_Imped_Mag; }
-
-      // js[0] should be of the form: Ns[]/Sc[] * Vector[0,0,1]
-      Integral { [ - (js0[]*Vector[0,0,1]) * Dof{ir} , {a} ];
-        In Vol_S_Mag; Jacobian Vol; Integration Gauss_v; }
-      Integral { DtDof [ Ns[]/Sc[] * Dof{a} , {ir} ];
-        In Vol_S_Mag; Jacobian Vol; Integration Gauss_v; }
-      Integral { [ Ns[]/Sc[] / sigma[] * (js0[]*Vector[0,0,1]) * Dof{ir} , {ir} ];
-        In Vol_S_Mag; Jacobian Vol; Integration Gauss_v; }
-      GlobalTerm { [ Dof{Us} / CoefGeos[] , {Is} ]; In Vol_S_Mag; }
-      // Attention: CoefGeo[.] = 2*Pi for Axi
-
-      GlobalTerm { [ - Dof{I_perfect} , {A_floating} ]; In Sur_Perfect_Mag; }
-
-      If(Flag_CircuitCoupling)
-	GlobalTerm { NeverDt[ Dof{Uz} , {Iz} ]; In Resistance_Cir; }
-        GlobalTerm { NeverDt[ Resistance[] * Dof{Iz} , {Iz} ]; In Resistance_Cir; }
-
-	GlobalTerm { [ Dof{Uz} , {Iz} ]; In Inductance_Cir; }
-	GlobalTerm { DtDof [ Inductance[] * Dof{Iz} , {Iz} ]; In Inductance_Cir; }
-
-	GlobalTerm { NeverDt[ Dof{Iz} , {Iz} ]; In Capacitance_Cir; }
-	GlobalTerm { DtDof [ Capacitance[] * Dof{Uz} , {Iz} ]; In Capacitance_Cir; }
-
-	GlobalTerm { NeverDt[ Dof{Uz} , {Iz} ]; In Diode_Cir; }
-	GlobalTerm { NeverDt[ Resistance[{Uz}] * Dof{Iz} , {Iz} ]; In Diode_Cir; }
-
-	GlobalTerm { [ 0. * Dof{Iz} , {Iz} ]; In DomainSource_Cir; }
-
-	GlobalEquation {
-	  Type Network; NameOfConstraint ElectricalCircuit;
-	  { Node {I};  Loop {U};  Equation {I};  In Vol_C_Mag; }
-	  { Node {Is}; Loop {Us}; Equation {Us}; In Vol_S_Mag; }
-	  { Node {Iz}; Loop {Uz}; Equation {Uz}; In Domain_Cir; }
-	}
-      EndIf
-
-    }
-  }
-}
-
-Resolution {
-  { Name MagDyn_a_2D;
-    System {
-      { Name Sys; NameOfFormulation MagDyn_a_2D;
-        If(Flag_FrequencyDomain)
-          Type ComplexValue; Frequency Freq;
-        EndIf
-      }
-    }
-    Operation {
-      If(Flag_FrequencyDomain)
-        Generate[Sys]; Solve[Sys]; SaveSolution[Sys];
-      Else
-        InitSolution[Sys]; // provide initial condition
-        TimeLoopTheta[TimeInit, TimeFinal, DeltaTime, 1.]{
-          // Euler implicit (1) -- Crank-Nicolson (0.5)
-          Generate[Sys]; Solve[Sys];
-          If(NbrRegions[Vol_NL_Mag])
-            Generate[Sys]; GetResidual[Sys, $res0];
-            Evaluate[ $res = $res0, $iter = 0 ];
-            Print[{$iter, $res, $res / $res0},
-              Format "Residual %03g: abs %14.12e rel %14.12e"];
-            While[$res > NL_tol_abs && $res / $res0 > NL_tol_rel &&
-                  $res / $res0 <= 1 && $iter < NL_iter_max]{
-              Solve[Sys]; Generate[Sys]; GetResidual[Sys, $res];
-              Evaluate[ $iter = $iter + 1 ];
-              Print[{$iter, $res, $res / $res0},
-                Format "Residual %03g: abs %14.12e rel %14.12e"];
-            }
-          EndIf
-          SaveSolution[Sys];
-        }
-      EndIf
-    }
-  }
-  { Name MagSta_a_2D;
-    System {
-      { Name Sys; NameOfFormulation MagSta_a_2D; }
-    }
-    Operation {
-      InitSolution[Sys];
-      Generate[Sys]; Solve[Sys];
-      If(NbrRegions[Vol_NL_Mag])
-        Generate[Sys]; GetResidual[Sys, $res0];
-        Evaluate[ $res = $res0, $iter = 0 ];
-        Print[{$iter, $res, $res / $res0},
-          Format "Residual %03g: abs %14.12e rel %14.12e"];
-        While[$res > NL_tol_abs && $res / $res0 > NL_tol_rel &&
-              $res / $res0 <= 1 && $iter < NL_iter_max]{
-          Solve[Sys]; Generate[Sys]; GetResidual[Sys, $res];
-          Evaluate[ $iter = $iter + 1 ];
-          Print[{$iter, $res, $res / $res0},
-            Format "Residual %03g: abs %14.12e rel %14.12e"];
-        }
-      EndIf
-      SaveSolution[Sys];
-    }
-  }
-}
-
-// Same PostProcessing for both static and dynamic formulations (both refer to
-// the same FunctionSpace from which the solution is obtained)
-PostProcessing {
-  { Name MagDyn_a_2D; NameOfFormulation MagDyn_a_2D;
-    PostQuantity {
-      // In 2D, a is a vector with only a z-component: (0,0,az)
-      { Name a; Value {
-          Term { [ {a} ]; In Vol_Mag; Jacobian Vol; }
-        }
-      }
-      // The equilines of az are field lines (giving the magnetic field direction)
-      { Name az; Value {
-          Term { [ CompZ[{a}] ]; In Vol_Mag; Jacobian Vol; }
-        }
-      }
-      { Name b; Value {
-          Term { [ {d a} ]; In Vol_Mag; Jacobian Vol; }
-        }
-      }
-      { Name norm_of_b; Value {
-          Term { [ Norm[{d a}] ]; In Vol_Mag; Jacobian Vol; }
-        }
-      }
-      { Name h; Value {
-          Term { [ nu[] * {d a} ]; In Vol_Mag; Jacobian Vol; }
-          Term { [ -nu[] * br[] ]; In Vol_M_Mag; Jacobian Vol; }
-        }
-      }
-      { Name js; Value {
-          Term { [ js0[] ]; In Vol_S0_Mag; Jacobian Vol; }
-          Term { [  (js0[]*Vector[0,0,1])*{ir} ]; In Vol_S_Mag; Jacobian Vol; }
-          Term { [ Vector[0,0,0] ]; In Vol_Mag; Jacobian Vol; } // to force a vector result out of sources
-        }
-      }
-      { Name j; Value {
-          Term { [ -sigma[] * (Dt[{a}]+{ur}/CoefGeos[]) ]; In Vol_C_Mag; Jacobian Vol; }
-          Term { [ js0[] ]; In Vol_S0_Mag; Jacobian Vol; }
-          Term { [ (js0[]*Vector[0,0,1])*{ir} ]; In Vol_S_Mag; Jacobian Vol; }
-          Term { [ Vector[0,0,0] ]; In Vol_Mag; Jacobian Vol; }
-          // Current density in A/m
-          Term { [ -Ysur[] * (Dt[{a}]+{ur}/CoefGeos[]) ]; In Sur_Imped_Mag; Jacobian Sur; }
-        }
-      }
-      { Name JouleLosses; Value {
-          Integral { [ CoefPower * sigma[]*SquNorm[Dt[{a}]+{ur}/CoefGeos[]] ];
-            In Vol_C_Mag; Jacobian Vol; Integration Gauss_v; }
-          Integral { [ CoefPower * 1./sigma[]*SquNorm[js0[]] ];
-            In Vol_S0_Mag; Jacobian Vol; Integration Gauss_v; }
-	  Integral { [ CoefPower * 1./sigma[]*SquNorm[(js0[]*Vector[0,0,1])*{ir}] ];
-            In Vol_S_Mag; Jacobian Vol; Integration Gauss_v; }
-          Integral { [ CoefPower * Ysur[]*SquNorm[Dt[{a}]+{ur}/CoefGeos[]] ];
-            In Sur_Imped_Mag; Jacobian Sur; Integration Gauss_v; }
-	}
-      }
-      { Name U; Value {
-          Term { [ {U} ]; In Vol_C_Mag; }
-          Term { [ {Us} ]; In Vol_S_Mag; }
-          If(Flag_CircuitCoupling)
-            Term { [ {Uz} ]; In Domain_Cir; }
-          EndIf
-        }
-      }
-      { Name I; Value {
-          Term { [ {I} ]; In Vol_C_Mag; }
-          Term { [ {Is} ]; In Vol_S_Mag; }
-          If(Flag_CircuitCoupling)
-            Term { [ {Iz} ]; In Domain_Cir; }
-          EndIf
-        }
-      }
-    }
-  }
-
-  { Name MagSta_a_2D; NameOfFormulation MagSta_a_2D;
-    PostQuantity {
-      { Name a; Value {
-          Term { [ {a} ]; In Vol_Mag; Jacobian Vol; }
-        }
-      }
-      { Name az; Value {
-          Term { [ CompZ[{a}] ]; In Vol_Mag; Jacobian Vol; }
-        }
-      }
-      { Name b; Value {
-          Term { [ {d a} ]; In Vol_Mag; Jacobian Vol; }
-        }
-      }
-      { Name h; Value {
-          Term { [ nu[] * {d a} ]; In Vol_Mag; Jacobian Vol; }
-        }
-      }
-      { Name j; Value {
-          Term { [ js0[] ]; In Vol_S0_Mag; Jacobian Vol; }
-          Term { [ (js0[]*Vector[0,0,1])*{ir} ]; In Vol_S_Mag; Jacobian Vol; }
-          Term { [ Vector[0,0,0] ]; In Vol_Mag; Jacobian Vol; }
-        }
-      }
-    }
-  }
-}
-- 
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