Formulation {
  { Name cFormulation; Type FemEquation;
    Quantity {
	  { Name ln ; Type Local ; NameOfSpace airLinSpace; }
      { Name a ; Type Local ; NameOfSpace Hcurl_a_Mag_2D; }
      { Name ur; Type Local ; NameOfSpace Hregion_u_Mag_2D; }
      { Name I ; Type Global; NameOfSpace Hregion_u_Mag_2D [I]; }
      { Name U ; Type Global; NameOfSpace Hregion_u_Mag_2D [U]; }
      { Name istr ; Type Local ; NameOfSpace Hregion_i_Mag_2D ; }
      { Name Ustr ; Type Global ; NameOfSpace Hregion_i_Mag_2D [Ustr] ; }
      { Name Istr ; Type Global ; NameOfSpace Hregion_i_Mag_2D [Istr] ; }
	  { Name Uz; Type Global; 	NameOfSpace Hregion_Circ [Uz]; }
      { Name Iz; Type Global; 	NameOfSpace Hregion_Circ [Iz]; }
      { Name Iz_post; Type Global; 	NameOfSpace Hregion_Circ_Post [Iz_post]; }

	  If(Flag_MagTherm==2)
	  	  { Name T;  Type Local; NameOfSpace Hgrad_T; }
	  EndIf
    }
    Equation {
					 
	  If(Flag_MagTherm==2)

	  Galerkin { [ nu_nu0[{d a}, <T>[{T}]] * Dof{d a} , {d a} ]; In Region[{non_conducting_domain, conducting_domain, source_domain, stranded_source_domain}]; Jacobian JVol; Integration I1; }

		  If(bhNLFlag==1)			 
			  Galerkin { JacNL[ dhdb_NL[{d a}, <T>[{T}] ] * Dof{d a} , {d a} ]; In Region[{NL_domain}];
						 Jacobian JVol; Integration I1; }
		  EndIf
				 
      //Galerkin { [ - nu_nu0[{d a}, <T>[{T}]] * br[] * Complex[ Vector[ orientx[], orienty[], 0], Vector[ -Sign[direction[]]*orienty[], Sign[direction[]]*orientx[], 0] ] , {d a} ]; In Region[{magnet_domain}];
      //           Jacobian JVol; Integration I1; }
				 
	  Galerkin { DtDof [ sigma[<T>[{T}]] * Dof{a} , {a} ]; In Region[{conducting_domain, source_domain}];
                 Jacobian JVol; Integration I1; }
      Galerkin { [ sigma[<T>[{T}]] * Dof{ur} / GeomCoeff[] , {a} ]; In Region[{conducting_domain, source_domain}];
                 Jacobian JVol; Integration I1; }
      Galerkin { DtDof [ sigma[<T>[{T}]] * Dof{a} , {ur} ]; In Region[{conducting_domain, source_domain}];
                 Jacobian JVol; Integration I1; }
      Galerkin { [ sigma[<T>[{T}]] * Dof{ur} / GeomCoeff[] , {ur} ]; In Region[{conducting_domain, source_domain}];
                 Jacobian JVol; Integration I1; }
      Galerkin { DtDof [ 1.0/(Complex[1,1]* Sqrt[3.14*Freq/(nu_nu0[]*sigma[<T>[{T}]])]) * Dof{a} , {a} ]; In Region[{Sur_SIBC_B}];
                 Jacobian JSur; Integration I1; }	
				
      Galerkin { [ Fs[Sqrt[area[]*4/3.14]*Sqrt[3.14*Freq*sigma[<T>[{T}]]/(2*nu_nu0[])]] * Nc[]^(1-a_litz[])*Nc[]/(FillFactor[]*area[]^2*sigma[<T>[{T}]]) * Dof{istr} , {istr} ]  ; In Region[{stranded_source_domain}] ; Jacobian JVol; Integration I1; }
	    
	
				 
	  Else


	  Galerkin { [ nu_nu0[{d a}] * Dof{d a} , {d a} ]; In Region[{non_conducting_domain, conducting_domain, source_domain, stranded_source_domain}];
                 Jacobian JVol; Integration I1; }

		  If(bhNLFlag==1)			 
			  Galerkin { JacNL[ dhdb_NL[{d a} ] * Dof{d a} , {d a} ]; In Region[{NL_domain}];
						 Jacobian JVol; Integration I1; }
		  EndIf
		  				 
     // Galerkin { [ - nu_nu0[{d a}] * br[] * Complex[ Vector[ orientx[], orienty[], 0], Vector[ -Sign[direction[]]*orienty[], Sign[direction[]]*orientx[], 0] ] , {d a} ]; In Region[{magnet_domain}];
     //            Jacobian JVol; Integration I1; }
				 
      Galerkin { DtDof [ sigma[] * Dof{a} , {a} ]; In Region[{conducting_domain, source_domain}];
                 Jacobian JVol; Integration I1; }
      Galerkin { [ sigma[] * Dof{ur} / GeomCoeff[] , {a} ]; In Region[{conducting_domain, source_domain}];
                 Jacobian JVol; Integration I1; }
      Galerkin { DtDof [ sigma[] * Dof{a} , {ur} ]; In Region[{conducting_domain, source_domain}];
                 Jacobian JVol; Integration I1; }
      Galerkin { [ sigma[] * Dof{ur} / GeomCoeff[] , {ur} ]; In Region[{conducting_domain, source_domain}];
                 Jacobian JVol; Integration I1; }
      Galerkin { DtDof [ 1.0/(Complex[1,1]* Sqrt[3.14*Freq/(nu_nu0[]*sigma[])]) * Dof{a} , {a} ]; In Region[{Sur_SIBC_B}];
                 Jacobian JSur; Integration I1; }
				 
      Galerkin { [ Fs[Sqrt[area[]*4/3.14]*Sqrt[3.14*Freq*sigma[]/(2*nu_nu0[])]] * Nc[]^(1-a_litz[])*Nc[]/(FillFactor[]*area[]^2*sigma[]) * Dof{istr} , {istr} ]  ; In Region[{stranded_source_domain}] ; Jacobian JVol; Integration I1; }
	  
	  EndIf
	  
	  
      Galerkin { [ - Nc[]^(1-a_litz[])/area[] * Dof{istr} , {a} ]  ; In Region[{stranded_source_domain}] ; 
				 Jacobian JVol; Integration I1; }
				 
      Galerkin { DtDof [ Nc[]/area[] * Dof{a} , {istr} ]  ; In Region[{stranded_source_domain}] ; 
				 Jacobian JVol; Integration I1; }			 
	  
	  GlobalTerm { [ Dof{I} , {U} ]; In Region[{conducting_domain, source_domain}]; }
	  
	  GlobalTerm { [ Dof{Ustr}/GeomCoeff[] , {Istr} ] ; In Region[{stranded_source_domain}] ; }  
	  
	  Integral { [ 0 * Dof{ln} , {ln} ] ;
          In Region[{non_conducting_domain, conducting_domain, source_domain, stranded_source_domain}] ; Jacobian JVol ; Integration I1 ; }

	  GlobalTerm 	{ [ 0 * Dof{Uz}, 		{Iz} ];	        In circuit_domain; }
	  GlobalTerm	{ [ 0 * Dof{Iz},	{Iz} ];	        In circuit_domain; }
	  
      GlobalEquation { Type Network; NameOfConstraint ElectricalCircuit;
		{ Node {I};	Loop {U};       Equation {I}; 	In Region[{source_domain}]; }
		{ Node {Istr};	Loop {Ustr};       Equation {Ustr}; 	In Region[{stranded_source_domain}]; }
		{ Node {Iz}; 	Loop {Uz}; 	Equation {Uz}; 	In circuit_domain; }		
      }

	  GlobalTerm	{ [  Dof{Iz_post},	{Iz_post} ];	        In circuit_domain; }
	  GlobalTerm	{ [  -{Iz},	{Iz_post} ];	        In circuit_domain; }


    }
  }
}