Formulation {

 { Name stranded_sigma_formulation; Type FemEquation ;
    Quantity {
      { Name e0  ; Type Local ; NameOfSpace Hregion_u0_3D ; } //stranded conductor effective sigma computation
	  { Name I0  ; Type Global ; NameOfSpace Hregion_u0_3D [I0] ; }
      { Name U0  ; Type Global ; NameOfSpace Hregion_u0_3D [U0] ; }
	  If(Flag_MagTherm==3)
	  	  { Name T;  Type Local; NameOfSpace Hgrad_T; }
	  EndIf
    }
    Equation {
	If(Flag_MagTherm==3)
      Galerkin { [ sigma[<T>[{T}]] * Dof{e0} , {e0} ] ;
        In Region[{stranded_source_domain}] ; Jacobian JVol ; Integration I1 ; }
	Else
      Galerkin { [ sigma[] * Dof{e0} , {e0} ] ;
        In Region[{stranded_source_domain}] ; Jacobian JVol ; Integration I1 ; }
	EndIf
      GlobalTerm {  [ - Dof{I0}, {U0} ] ; In Region[{SurStr_CURRENT_B_CH}]; }
    }
  }
	  
	  
  { Name cFormulation ; Type FemEquation ;
    Quantity {
	  { Name ln ; Type Local ; NameOfSpace airLinSpace; }
      { Name a  ; Type Local ; NameOfSpace Hcurl_a_3D ; }
	  
      { Name e  ; Type Local ; NameOfSpace Hregion_u_3D ; }
	  If (#Sur_RESISTANCE_B_List())
		{ Name eResistance ; Type Local ; NameOfSpace Hregion_u_3D[eResistance] ; }
	  EndIf

	  { Name I  ; Type Global ; NameOfSpace Hregion_u_3D [I] ; }
      { Name U  ; Type Global ; NameOfSpace Hregion_u_3D [U] ; }	  
	  { Name Istr  ; Type Global ; NameOfSpace Hregion_u_3D [Istr] ; }
      { Name Ustr  ; Type Global ; NameOfSpace Hregion_u_3D [Ustr] ; }
	  { Name I_post  ; Type Global ; NameOfSpace Hregion_u_3D_Post [I_post] ; }

      { Name estr  ; Type Local ; NameOfSpace Hregion_uStrInd_3D ; }
	  { Name Istr_ind  ; Type Global ; NameOfSpace Hregion_uStrInd_3D [Istr_ind] ; }
      { Name Ustr_ind  ; Type Global ; NameOfSpace Hregion_uStrInd_3D [Ustr_ind] ; }
	  
      { Name e0  ; Type Local ; NameOfSpace Hregion_u0_3D ; } //stranded conductor effective sigma computation

	  If(Flag_MagTherm==3)
	  	  { Name T;  Type Local; NameOfSpace Hgrad_T; }
	  EndIf
    } 
				 
    Equation {
				 
	If(Flag_MagTherm==3)
	  
      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 { [1.0/(Complex[1,1]* Sqrt[3.14*Freq/(nu_nu0[]*sigma[<T>[{T}]])]) * Dof{e} , {a} ]; In Region[{Sur_SIBC_B}];
                 Jacobian JSur; Integration I1; }		  
      Galerkin { DtDof [ 1.0/(Complex[1,1]* Sqrt[3.14*Freq/(nu_nu0[]*sigma[<T>[{T}]])]) * Dof{a} , {e} ]; In Region[{Sur_SIBC_B}];
                 Jacobian JSur; Integration I1; }	
      Galerkin { [ 1.0/(Complex[1,1]* Sqrt[3.14*Freq/(nu_nu0[]*sigma[<T>[{T}]])]) * Dof{e} , {e} ]; In Region[{Sur_SIBC_B}];
                 Jacobian JSur; Integration I1; }
				 
	   Galerkin { [ nu_nu0[Norm[{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 ; }
				
   //   Galerkin { [ - nu_nu0[Norm[{d a}], <T>[{T}]] * br[] * Complex[ Vector[ orientx[], orienty[], orientz[]], Vector[ -Sign[direction[]]*orienty[], Sign[direction[]]*orientx[], orientz[]] ] , {d a} ]; In Region[{magnet_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 { DtDof[ sigma[<T>[{T}]] * Dof{a} , {a} ] ;
        In Region[{conducting_domain, source_domain}] ; Jacobian JVol ; Integration I1 ; }
      Galerkin { [ sigma[<T>[{T}]] * Dof{e} , {a} ] ;
        In Region[{conducting_domain, source_domain}] ; Jacobian JVol ; Integration I1 ; }

      Galerkin { DtDof[ sigma[<T>[{T}]] * Dof{a} , {e} ] ;
        In Region[{conducting_domain, source_domain}] ; Jacobian JVol ; Integration I1 ; }
      Galerkin { [ sigma[<T>[{T}]] * Dof{e} , {e} ] ;
        In Region[{conducting_domain, source_domain}] ; Jacobian JVol ; Integration I1 ; }
		
	  Else
	  
      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 { [1.0/(Complex[1,1]* Sqrt[3.14*Freq/(nu_nu0[]*sigma[])]) * Dof{e} , {a} ]; In Region[{Sur_SIBC_B}];
                 Jacobian JSur; Integration I1; }		  
      Galerkin { DtDof [ 1.0/(Complex[1,1]* Sqrt[3.14*Freq/(nu_nu0[]*sigma[])]) * Dof{a} , {e} ]; In Region[{Sur_SIBC_B}];
                 Jacobian JSur; Integration I1; }	
      Galerkin { [ 1.0/(Complex[1,1]* Sqrt[3.14*Freq/(nu_nu0[]*sigma[])]) * Dof{e} , {e} ]; In Region[{Sur_SIBC_B}];
                 Jacobian JSur; Integration I1; }
				 
	   Galerkin { [ nu_nu0[Norm[{d a}]] * Dof{d a} , {d a} ] ;
        In Region[{non_conducting_domain, conducting_domain, source_domain, stranded_source_domain}] ; Jacobian JVol ; Integration I1 ; }
		
  //    Galerkin { [ - nu_nu0[Norm[{d a}]] * br[] * Complex[ Vector[ orientx[], orienty[], orientz[]], Vector[ -Sign[direction[]]*orienty[], Sign[direction[]]*orientx[], orientz[]] ] , {d a} ]; In Region[{magnet_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 { DtDof[ sigma[] * Dof{a} , {a} ] ;
        In Region[{conducting_domain, source_domain}] ; Jacobian JVol ; Integration I1 ; }
		
      Galerkin { [ sigma[] * Dof{e} , {a} ] ;
        In Region[{conducting_domain, source_domain}] ; Jacobian JVol ; Integration I1 ; }

      Galerkin { DtDof[ sigma[] * Dof{a} , {e} ] ;
        In Region[{conducting_domain, source_domain}] ; Jacobian JVol ; Integration I1 ; }
		
      Galerkin { [ sigma[] * Dof{e} , {e} ] ;
        In Region[{conducting_domain, source_domain}] ; Jacobian JVol ; Integration I1 ; }		

	  EndIf
	    
		// surface contact resistance
	  If (#Sur_RESISTANCE_B_List())
		Galerkin { [ 1/resistance_electric[] * Dof{dInv eResistance} , {dInv eResistance} ] ;
			In Region[{Sur_RESISTANCE_B}] ; Jacobian JSur ; Integration I1 ; }
	  EndIf
		
		// This part is for calculation of stranded coil in 3D. e0 calculated in stranded_sigma_formulation
		// is used to determine the effective sigma
		
	  Galerkin { [ Nc[]^(1-a_litz[]) * I_str[$Time]/cross_section_area[]/(Norm[{e0}])* {e0}, {a} ] ;
        In Region[{stranded_source_domain}] ; Jacobian JVol ; Integration I1 ; }

	  Galerkin { [ -Nc[]^(1-a_litz[])*I_str[$Time]/cross_section_area[]/(Norm[{e0}])* {e0}, {e} ] ;
        In Region[{stranded_source_domain}] ; Jacobian JVol ; Integration I1 ; }

	If(Flag_MagTherm==3)
	
	   Galerkin { [ FillFactor[]/Fs[Sqrt[cross_section_area[]*4/3.14]*Sqrt[3.14*Freq*sigma[<T>[{T}]]/(2*nu_nu0[{d a}, <T>[{T}]])]] *sigma[<T>[{T}]]* Dof{e}, {e} ] ;
        In Region[{stranded_source_domain}] ; Jacobian JVol ; Integration I1 ; } 
		
		// This part if for calculation of induced EMF (estr, and global variable Ustr_ind)
		
      Galerkin { DtDof[ sigma[<T>[{T}]] * Dof{a} , {estr} ] ;
        In Region[{stranded_source_domain}] ; Jacobian JVol ; Integration I1 ; }
		
      Galerkin { [ sigma[<T>[{T}]]/(Nc[]^(1-a_litz[])) * Dof{estr} , {estr} ] ;
        In Region[{stranded_source_domain}] ; Jacobian JVol ; Integration I1 ; }	
		
	Else
	
	   Galerkin { [ FillFactor[]/Fs[Sqrt[cross_section_area[]*4/3.14]*Sqrt[3.14*Freq*sigma[]/(2*nu_nu0[])]] *sigma[]* Dof{e}, {e} ] ;
        In Region[{stranded_source_domain}] ; Jacobian JVol ; Integration I1 ; } 
		
		// This part if for calculation of induced EMF (estr, and global variable Ustr_ind)
		
      Galerkin { DtDof[ sigma[] * Dof{a} , {estr} ] ;
        In Region[{stranded_source_domain}] ; Jacobian JVol ; Integration I1 ; }
		
      Galerkin { [ sigma[]/(Nc[]^(1-a_litz[])) * Dof{estr} , {estr} ] ;
        In Region[{stranded_source_domain}] ; Jacobian JVol ; Integration I1 ; }	
		
	EndIf
	

									
      GlobalTerm {  [ - Dof{I}, {U} ] ; In Region[{Sur_CURRENT_B_CH, Sur_POWER_B_CH, Sur_VOLTAGE_B_CH}]; } 
	  GlobalTerm { [  Dof{I_post},	{I_post} ];	        In Region[{Sur_CURRENT_B_CH, Sur_POWER_B_CH, Sur_VOLTAGE_B_CH}]; }
	  GlobalTerm { [  -{I},	{I_post} ];	        In Region[{Sur_CURRENT_B_CH, Sur_POWER_B_CH, Sur_VOLTAGE_B_CH}]; }
	  
	  Integral { [ 0 * Dof{ln} , {ln} ] ;
          In Region[{non_conducting_domain, conducting_domain, source_domain, stranded_source_domain}] ; Jacobian JVol ; Integration I1 ; }
    }
  }
}