diff --git a/Electrostatics/microstrip.pro b/Electrostatics/microstrip.pro
index e511520f1767ce00331bb1ad778c56ef71e201b3..7b152d65acb6b445a9ead1a20bb15163311ef063 100644
--- a/Electrostatics/microstrip.pro
+++ b/Electrostatics/microstrip.pro
@@ -52,19 +52,19 @@ Group {
/* We now define abstract regions to be used below in the definition of the
scalar electric potential formulation:
- Vol_Ele : volume where -Div(epsilon Grad v) = 0 is solved
- Sur_Neumann_Ele: surface where non homogeneous Neumann boundary conditions
- (on n.d == epsilon n.Grad v) are imposed
+ Vol_Ele : volume where -Div(epsilon Grad v) = 0 is solved
+ Sur_Neu_Ele: surface where non homogeneous Neumann boundary conditions
+ (on n.d == epsilon n.Grad v) are imposed
Vol_xxx groups contain only volume elements of the mesh (triangles here).
Sur_xxx groups contain only surface elements of the mesh (lines here).
Since there are no non-homogeneous Neumann conditions in the model,
- Sur_Neumann_Ele is defined as empty.
+ Sur_Neu_Ele is defined as empty.
*/
Vol_Ele = Region[ {Air, Diel1} ];
- Sur_Neumann_Ele = Region[ {} ];
+ Sur_Neu_Ele = Region[ {} ];
}
Function {
@@ -99,7 +99,7 @@ Group{
both volume and surface regions. Hence the use of the prefixes Vol_, Sur_
and Dom_ to avoid confusions.*/
- Dom_Hgrad_v_Ele = Region[ {Vol_Ele, Sur_Neumann_Ele} ];
+ Dom_Hgrad_v_Ele = Region[ {Vol_Ele, Sur_Neu_Ele} ];
}
FunctionSpace {
diff --git a/ElectrostaticsFloating/floating.pro b/ElectrostaticsFloating/floating.pro
index b099cffcc058d652c6f13b65c40f0f4010b9dc0f..5b668d5050011cb30216d21a6419234d2a707767 100644
--- a/ElectrostaticsFloating/floating.pro
+++ b/ElectrostaticsFloating/floating.pro
@@ -57,12 +57,12 @@ Group {
/* Abstract regions:
Vol_Ele : volume where -Div(epsilon Grad v) = 0 is solved
- Sur_Neumann_Ele : surface where non homogeneous Neumann boundary conditions
+ Sur_Neu_Ele : surface where non homogeneous Neumann boundary conditions
(on n.d == epsilon n.Grad v) are imposed
Sur_Electrodes_Ele : electrode regions */
Vol_Ele = Region[ {Air, Diel1} ];
- Sur_Neumann_Ele = Region[ {} ];
+ Sur_Neu_Ele = Region[ {} ];
Sur_Electrodes_Ele = Region [ {Ground, Microstrip} ];
}
@@ -117,7 +117,7 @@ Constraint {
Group{
/* The domain of definition lists all regions on which the field "v" is
defined.*/
- Dom_Hgrad_v_Ele = Region[ {Vol_Ele, Sur_Neumann_Ele, Sur_Electrodes_Ele} ];
+ Dom_Hgrad_v_Ele = Region[ {Vol_Ele, Sur_Neu_Ele, Sur_Electrodes_Ele} ];
}
FunctionSpace {
diff --git a/Magnetodynamics/Lib_MagStaDyn_av_2D_Cir.pro b/Magnetodynamics/Lib_MagStaDyn_av_2D_Cir.pro
index e0122eb1c43757fada989dfba4d3cf8d904e0f8d..145c95a2facbb957f2ed9655637d15d693c09e8c 100644
--- a/Magnetodynamics/Lib_MagStaDyn_av_2D_Cir.pro
+++ b/Magnetodynamics/Lib_MagStaDyn_av_2D_Cir.pro
@@ -16,24 +16,24 @@ DefineConstant[
TimeFinal = 1/50, // final time (for time-domain simulations)
DeltaTime = 1/500, // time step (for time-domain simulations)
InterpolationOrder = 1 // finite element order
- Val_Rint = 0, // interior radius of annulus shell transformation region (VolInf_Mag)
- Val_Rext = 0 // exterior radius of annulus shell transformation region (VolInf_Mag)
+ 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)
];
Group {
DefineGroup[
- VolCC_Mag, // the non-conducting part
- VolC_Mag, // the conducting part
- VolV_Mag, // a moving conducting part, with invariant mesh
- VolM_Mag, // permanent magnets
- VolS0_Mag, // current source domain with imposed current densities js0
- VolS_Mag, // current source domain with imposed current, imposed voltage or
- // circuit coupling
- VolInf_Mag, // annulus where a infinite shell transformation is applied
- SurFluxTube_Mag, // boundary with Neumann BC
- SurPerfect_Mag, // boundary of perfect conductors (i.e. non-meshed)
- SurImped_Mag // boundary of conductors approximated by a surface impedance
- // (i.e. non-meshed)
+ Vol_CC_Mag, // the non-conducting part
+ Vol_C_Mag, // the conducting part
+ Vol_V_Mag, // a moving conducting part, with invariant mesh
+ Vol_M_Mag, // permanent magnets
+ Vol_S0_Mag, // current source domain with imposed current densities js0
+ Vol_S_Mag, // current source domain with imposed current, imposed voltage or
+ // circuit coupling
+ Vol_Inf_Mag, // annulus where a infinite shell transformation is applied
+ Sur_FluxTube_Mag, // boundary with Neumann BC
+ Sur_Perfect_Mag, // boundary of perfect conductors (i.e. non-meshed)
+ Sur_Imped_Mag // boundary of conductors approximated by a surface impedance
+ // (i.e. non-meshed)
];
If(Flag_CircuitCoupling)
DefineGroup[
@@ -50,15 +50,15 @@ Group {
Function {
DefineFunction[
nu, // reluctivity (in Vol_Mag)
- sigma, // conductivity (in VolC_Mag and VolS_Mag)
- br, // remanent magnetic flux density (in VolM_Mag)
- js0, // source current density (in VolS0_Mag)
- nxh, // n x magnetic field (on SurFluxTube_Mag)
- Velocity, // velocity of moving part VolV_Moving
- Ns, // number of turns (in VolS_Mag)
- Sc, // cross-section of windings (in VolS_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)
+ nxh, // n x magnetic field (on Sur_FluxTube_Mag)
+ Velocity, // velocity of moving part 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
- Ysur // surface admittance (inverse of surface impedance Zsur) on SurImped_Mag
+ Ysur // surface admittance (inverse of surface impedance Zsur) on Sur_Imped_Mag
];
If(Flag_CircuitCoupling)
DefineFunction[
@@ -73,9 +73,9 @@ Function {
Group{
// all volumes
- Vol_Mag = Region[ {VolCC_Mag, VolC_Mag, VolV_Mag, VolM_Mag, VolS0_Mag, VolS_Mag} ];
+ Vol_Mag = Region[ {Vol_CC_Mag, Vol_C_Mag, Vol_V_Mag, Vol_M_Mag, Vol_S0_Mag, Vol_S_Mag} ];
// all volumes + surfaces on which integrals will be computed
- VolWithSur_Mag = Region[ {Vol_Mag, SurFluxTube_Mag, SurPerfect_Mag, SurImped_Mag} ];
+ 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} ];
@@ -89,7 +89,7 @@ Group{
Jacobian {
{ Name Vol;
Case {
- { Region VolInf_Mag ;
+ { Region Vol_Inf_Mag ;
Jacobian VolSphShell {Val_Rint, Val_Rext} ; }
{ Region All; Jacobian Vol; }
}
@@ -127,11 +127,11 @@ FunctionSpace {
// \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 VolWithSur_Mag; Entity NodesOf[All, Not SurPerfect_Mag]; }
+ 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 VolWithSur_Mag; Entity GroupsOfNodesOf[SurPerfect_Mag]; }
+ Support Dom_Mag; Entity GroupsOfNodesOf[Sur_Perfect_Mag]; }
// additional basis functions for 2nd order interpolation
If(InterpolationOrder == 2)
@@ -164,8 +164,8 @@ FunctionSpace {
BasisFunction {
{ Name sr; NameOfCoef ur; Function BF_RegionZ;
// constant vector (over the region) with nonzero z-component only
- Support Region[{VolC_Mag, SurImped_Mag}];
- Entity Region[{VolC_Mag, SurImped_Mag}]; }
+ Support Region[{Vol_C_Mag, Sur_Imped_Mag}];
+ Entity Region[{Vol_C_Mag, Sur_Imped_Mag}]; }
}
GlobalQuantity {
{ Name U; Type AliasOf; NameOfCoef ur; }
@@ -183,7 +183,7 @@ FunctionSpace {
{ Name Hregion_i_2D; Type Vector;
BasisFunction {
{ Name sr; NameOfCoef ir; Function BF_RegionZ;
- Support VolS_Mag; Entity VolS_Mag; }
+ Support Vol_S_Mag; Entity Vol_S_Mag; }
}
GlobalQuantity {
{ Name Is; Type AliasOf; NameOfCoef ir; }
@@ -233,16 +233,16 @@ Formulation {
In Vol_Mag; Jacobian Vol; Integration Gauss_v; }
Integral { [ -nu[] * br[] , {d a} ];
- In VolM_Mag; Jacobian Vol; Integration Gauss_v; }
+ In Vol_M_Mag; Jacobian Vol; Integration Gauss_v; }
Integral { [ -js0[] , {a} ];
- In VolS0_Mag; Jacobian Vol; Integration Gauss_v; }
+ In Vol_S0_Mag; Jacobian Vol; Integration Gauss_v; }
Integral { [ - (js0[]*Vector[0,0,1]) * Dof{ir} , {a} ];
- In VolS_Mag; Jacobian Vol; Integration Gauss_v; }
+ In Vol_S_Mag; Jacobian Vol; Integration Gauss_v; }
Integral { [ nxh[] , {a} ];
- In SurFluxTube_Mag; Jacobian Sur; Integration Gauss_v; }
+ In Sur_FluxTube_Mag; Jacobian Sur; Integration Gauss_v; }
}
}
}
@@ -272,55 +272,55 @@ Formulation {
Integral { [ nu[] * Dof{d a} , {d a} ];
In Vol_Mag; Jacobian Vol; Integration Gauss_v; }
Integral { [ -nu[] * br[] , {d a} ];
- In VolM_Mag; Jacobian Vol; Integration Gauss_v; }
+ In Vol_M_Mag; Jacobian Vol; Integration Gauss_v; }
// Electric field e = -Dt[{a}]-{ur},
- // with {ur} = Grad v constant in each region of VolC
+ // with {ur} = Grad v constant in each region of Vol_C_Mag
Integral { DtDof [ sigma[] * Dof{a} , {a} ];
- In VolC_Mag; Jacobian Vol; Integration Gauss_v; }
+ In Vol_C_Mag; Jacobian Vol; Integration Gauss_v; }
Integral { [ sigma[] * Dof{ur} / CoefGeos[] , {a} ];
- In VolC_Mag; Jacobian Vol; Integration Gauss_v; }
+ In Vol_C_Mag; Jacobian Vol; Integration Gauss_v; }
Integral { [ - sigma[] * (Velocity[] /\ Dof{d a}) , {a} ];
- In VolV_Mag; Jacobian Vol; Integration Gauss_v; }
+ In Vol_V_Mag; Jacobian Vol; Integration Gauss_v; }
Integral { [ -js0[] , {a} ];
- In VolS0_Mag; Jacobian Vol; Integration Gauss_v; }
+ In Vol_S0_Mag; Jacobian Vol; Integration Gauss_v; }
Integral { [ nxh[] , {a} ];
- In SurFluxTube_Mag; Jacobian Sur; Integration Gauss_v; }
+ In Sur_FluxTube_Mag; Jacobian Sur; Integration Gauss_v; }
Integral { DtDof [ Ysur[] * Dof{a} , {a} ];
- In SurImped_Mag; Jacobian Sur; Integration Gauss_v; }
+ In Sur_Imped_Mag; Jacobian Sur; Integration Gauss_v; }
Integral { [ Ysur[] * Dof{ur} / CoefGeos[] , {a} ];
- In SurImped_Mag; Jacobian Sur; Integration Gauss_v; }
+ 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 VolC
+ // relating the voltage and the current of each region in Vol_C_Mag
Integral { DtDof [ sigma[] * Dof{a} , {ur} ];
- In VolC_Mag; Jacobian Vol; Integration Gauss_v; }
+ In Vol_C_Mag; Jacobian Vol; Integration Gauss_v; }
Integral { [ sigma[] * Dof{ur} / CoefGeos[] , {ur} ];
- In VolC_Mag; Jacobian Vol; Integration Gauss_v; }
- GlobalTerm { [ Dof{I} *(CoefGeos[]/Fabs[CoefGeos[]]) , {U} ]; In VolC_Mag; }
+ 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 SurImped_Mag; Jacobian Sur; Integration Gauss_v; }
+ In Sur_Imped_Mag; Jacobian Sur; Integration Gauss_v; }
Integral { [ Ysur[] * Dof{ur} / CoefGeos[] , {ur} ];
- In SurImped_Mag; Jacobian Sur; Integration Gauss_v; }
- GlobalTerm { [ Dof{I} *(CoefGeos[]/Fabs[CoefGeos[]]) , {U} ]; In SurImped_Mag; }
+ 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 VolS_Mag; Jacobian Vol; Integration Gauss_v; }
+ In Vol_S_Mag; Jacobian Vol; Integration Gauss_v; }
Integral { DtDof [ Ns[]/Sc[] * Dof{a} , {ir} ];
- In VolS_Mag; Jacobian Vol; Integration Gauss_v; }
+ In Vol_S_Mag; Jacobian Vol; Integration Gauss_v; }
Integral { [ Ns[]/Sc[] / sigma[] * (js0[]*Vector[0,0,1]) * Dof{ir} , {ir} ];
- In VolS_Mag; Jacobian Vol; Integration Gauss_v; }
- GlobalTerm { [ Dof{Us} / CoefGeos[] , {Is} ]; In VolS_Mag; }
+ 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 SurPerfect_Mag; }
+ GlobalTerm { [ -Dof{I_perfect} , {A_floating} ]; In Sur_Perfect_Mag; }
If(Flag_CircuitCoupling)
GlobalTerm { NeverDt[ Dof{Uz} , {Iz} ]; In Resistance_Cir; }
@@ -339,8 +339,8 @@ Formulation {
GlobalEquation {
Type Network; NameOfConstraint ElectricalCircuit;
- { Node {I}; Loop {U}; Equation {I}; In VolC_Mag; }
- { Node {Is}; Loop {Us}; Equation {Us}; In VolS_Mag; }
+ { 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
@@ -392,45 +392,45 @@ PostProcessing {
{ Name b; Value { Term { [ {d a} ]; In Vol_Mag; Jacobian Vol; } } }
{ Name h; Value {
Term { [ nu[] * {d a} ]; In Vol_Mag; Jacobian Vol; }
- Term { [ -nu[] * br[] ]; In VolM_Mag; Jacobian Vol; }
+ Term { [ -nu[] * br[] ]; In Vol_M_Mag; Jacobian Vol; }
}
}
{ Name js; Value {
- Term { [ js0[] ]; In VolS0_Mag; Jacobian Vol; }
- Term { [ (js0[]*Vector[0,0,1])*{ir} ]; In VolS_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; } // to force a vector result out of sources
}
}
{ Name j;
// Only correct in MagDyn
Value {
- Term { [ -sigma[] * (Dt[{a}]+{ur}/CoefGeos[]) ]; In VolC_Mag; Jacobian Vol; }
- Term { [ js0[] ]; In VolS0_Mag; Jacobian Vol; }
- Term { [ (js0[]*Vector[0,0,1])*{ir} ]; In VolS_Mag; Jacobian Vol; }
+ 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 SurImped_Mag; Jacobian Sur; }
+ Term { [ -Ysur[] * (Dt[{a}]+{ur}/CoefGeos[]) ]; In Sur_Imped_Mag; Jacobian Sur; }
}
}
{ Name JouleLosses;
Value {
Integral { [ CoefPower * sigma[]*SquNorm[Dt[{a}]+{ur}/CoefGeos[]] ];
- In VolC_Mag; Jacobian Vol; Integration Gauss_v; }
+ In Vol_C_Mag; Jacobian Vol; Integration Gauss_v; }
Integral { [ CoefPower * 1./sigma[]*SquNorm[js0[]] ];
- In VolS0_Mag; Jacobian Vol; Integration Gauss_v; }
+ In Vol_S0_Mag; Jacobian Vol; Integration Gauss_v; }
Integral { [ CoefPower * 1./sigma[]*SquNorm[(js0[]*Vector[0,0,1])*{ir}] ];
- In VolS_Mag; Jacobian Vol; Integration Gauss_v; }
+ In Vol_S_Mag; Jacobian Vol; Integration Gauss_v; }
Integral { [ CoefPower * Ysur[]*SquNorm[Dt[{a}]+{ur}/CoefGeos[]] ];
- In SurImped_Mag; Jacobian Sur; Integration Gauss_v; }
+ In Sur_Imped_Mag; Jacobian Sur; Integration Gauss_v; }
}
}
{ Name U; Value {
- Term { [ {U} ]; In VolC_Mag; }
- Term { [ {Us} ]; In VolS_Mag; }
+ Term { [ {U} ]; In Vol_C_Mag; }
+ Term { [ {Us} ]; In Vol_S_Mag; }
If(Flag_CircuitCoupling)
Term { [ {Uz} ]; In Domain_Cir; }
EndIf
@@ -438,8 +438,8 @@ PostProcessing {
}
{ Name I; Value {
- Term { [ {I} ]; In VolC_Mag; }
- Term { [ {Is} ]; In VolS_Mag; }
+ Term { [ {I} ]; In Vol_C_Mag; }
+ Term { [ {Is} ]; In Vol_S_Mag; }
If(Flag_CircuitCoupling)
Term { [ {Iz} ]; In Domain_Cir; }
EndIf
@@ -459,7 +459,8 @@ PostProcessing {
{ Name h; Value { Term { [ nu[] * {d a} ]; In Vol_Mag; Jacobian Vol; } } }
{ Name j;
Value {
- Term { [ js0[] ]; In VolS0_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; }
}
}
diff --git a/Magnetodynamics/electromagnet.pro b/Magnetodynamics/electromagnet.pro
index 1daf5af9e96f2708a84fcd894622a47bc62435d9..351d0cce2a1229242b101da3dde96aba86518bdb 100644
--- a/Magnetodynamics/electromagnet.pro
+++ b/Magnetodynamics/electromagnet.pro
@@ -29,10 +29,10 @@ Group {
// Abstract regions used in the "Lib_MagStaDyn_av_2D_Cir.pro" template file
// that is included below:
- VolCC_Mag = Region[{Air, AirInf}]; // Non-conducting regions
- VolC_Mag = Region[{Core}]; // Massive conducting regions
- VolS_Mag = Region[{Ind}]; // Stranded conductors, i.e., coils
- VolInf_Mag = Region[{AirInf}]; // Annulus for infinite shell transformation
+ Vol_CC_Mag = Region[{Air, AirInf}]; // Non-conducting regions
+ Vol_C_Mag = Region[{Core}]; // Massive conducting regions
+ Vol_S_Mag = Region[{Ind}]; // Stranded conductors, i.e., coils
+ Vol_Inf_Mag = Region[{AirInf}]; // Annulus for infinite shell transformation
Val_Rint = rInt; Val_Rext = rExt; // Interior and exterior radii of annulus
}
diff --git a/Magnetodynamics/transfo.pro b/Magnetodynamics/transfo.pro
index 88f0dba59bba74195588d44d190dea40f8e1ba23..0feabec89c9cd9b5a3cc85862a2184ac4924f46c 100644
--- a/Magnetodynamics/transfo.pro
+++ b/Magnetodynamics/transfo.pro
@@ -32,20 +32,20 @@ Group {
template file included below; the regions are first intialized as empty,
before being filled with physical groups */
- VolCC_Mag = Region[{}]; // Non-conducting regions
- VolC_Mag = Region[{}]; // Massive conductors
- VolS_Mag = Region[{}]; // Stranded conductors, i.e., coils
+ Vol_CC_Mag = Region[{}]; // Non-conducting regions
+ Vol_C_Mag = Region[{}]; // Massive conductors
+ Vol_S_Mag = Region[{}]; // Stranded conductors, i.e., coils
// air physical groups
Air = Region[{AIR_WINDOW, AIR_EXT}];
- VolCC_Mag += Region[Air];
+ Vol_CC_Mag += Region[Air];
// exterior boundary
Sur_Air_Ext = Region[{SUR_AIR_EXT}];
// magnetic core of the transformer, assumed to be non-conducting
Core = Region[CORE];
- VolCC_Mag += Region[Core];
+ Vol_CC_Mag += Region[Core];
Coil_1_P = Region[COIL_1_PLUS];
Coil_1_M = Region[COIL_1_MINUS];
@@ -58,10 +58,10 @@ Group {
Coils = Region[{Coil_1, Coil_2}];
If (type_Conds == 1)
- VolC_Mag += Region[{Coils}];
+ Vol_C_Mag += Region[{Coils}];
ElseIf (type_Conds == 2)
- VolS_Mag += Region[{Coils}];
- VolCC_Mag += Region[{Coils}];
+ Vol_S_Mag += Region[{Coils}];
+ Vol_CC_Mag += Region[{Coils}];
EndIf
}
@@ -219,7 +219,7 @@ Include "Lib_MagStaDyn_av_2D_Cir.pro";
PostOperation {
{ Name Map_a; NameOfPostProcessing MagDyn_a_2D;
Operation {
- Print[ j, OnElementsOf Region[{VolC_Mag, VolS_Mag}], Format Gmsh, File "j.pos" ];
+ Print[ j, OnElementsOf Region[{Vol_C_Mag, Vol_S_Mag}], Format Gmsh, File "j.pos" ];
Print[ b, OnElementsOf Vol_Mag, Format Gmsh, File "b.pos" ];
Print[ az, OnElementsOf Vol_Mag, Format Gmsh, File "az.pos" ];
diff --git a/Magnetostatics/electromagnet.pro b/Magnetostatics/electromagnet.pro
index 1e1c1c4348eba7d9fb4621b0c9d7fe4d69c121d2..37293eeac3c5c834919a7464d5f62e4f377afcf2 100644
--- a/Magnetostatics/electromagnet.pro
+++ b/Magnetostatics/electromagnet.pro
@@ -3,7 +3,7 @@
Features:
- Infinite ring geometrical transformation
- - Parameters shared by Gmsh and GetDp, and Onelab parameters
+ - Parameters shared by Gmsh and GetDP, and ONELAB parameters
- FunctionSpaces for the 2D vector potential formulation
To compute the solution in a terminal:
@@ -15,35 +15,43 @@
Run (button at the bottom of the left panel)
------------------------------------------------------------------- */
-/* Electromagnetic fields expand to infinity.
- The corresponding boundary condition can be imposed rigorously
- by means of a gometrical transformation that maps a ring (or shell) of finite elements
- to the complementary of its interior.
- As this is a mere geometric transformation,
- it is enough in the model description to attribute a special jacobian
- to the ring region ("AirInf"). See Jacobian{} section below.
- With this information, GetDP is able to deal with the correct transformation
- of all quantities involved in the model.
-
- The special jacobian "VolSphShell" has parameters.
- There are 2 parameters in this case, "Val_Rint" and "Val_Rext",
- which represent the inner and outer radii of the transformed ring region
- and whose value must match those used
- in the geometrical description of the model (.geo file).
- This is a typical case where Gmsh and GetDP must consistently share parameter values.
- To ensure consistency in all cases, common parameters are defined
- is a specific file "electromagnet_common.pro",
- which is included in both the .geo and .pro file of the model.
-
- Besides sharing parameters between Gmsh and GetDP,
- it is also useful to share some parameters (not all) with the user of the model,
- i.e., to make them editable in the GUI before running the model.
- Such variables are called Onelab variables (because the sharing mechanism
- between the model and the GUI uses the Onelab interface).
- Onelab parameters are defined with a "DefineNumber" statement,
- which can be invoked in the .geo, .pro, or _common.pro files.
- */
-
+/* Electromagnetic fields expand to infinity. The corresponding boundary
+ condition can be imposed rigorously by means of a gometrical transformation
+ that maps a ring (or shell) of finite elements to the complementary of its
+ interior. As this is a mere geometric transformation, it is enough in the
+ model description to attribute a special Jacobian to the ring region
+ ("AirInf") - see the "Jacobian" section below. With this information, GetDP
+ is able to deal with the correct transformation of all quantities involved in
+ the model.
+
+ The special Jacobian "VolSphShell" takes 2 parameters in this case,
+ "Val_Rint" and "Val_Rext", which represent the inner and outer radii of the
+ transformed ring region and whose value must match those used in the
+ geometrical description of the model (.geo file). This is a typical case
+ where Gmsh and GetDP must consistently share parameter values. To ensure
+ consistency in all cases, common parameters are defined is a specific file
+ "electromagnet_common.pro", which is included in both the .geo and .pro file
+ of the model.
+
+ Besides sharing parameters between Gmsh and GetDP, it is also useful to share
+ some parameters (not all) with the user of the model, i.e., to make them
+ editable in the GUI before running the model. Such variables are called
+ ONELAB variables (because the sharing mechanism between the model and the GUI
+ uses the ONELAB interface). ONELAB parameters are defined with a
+ "DefineNumber" statement, which can be invoked in the .geo and .pro files.
+
+ This model computes the static magnetic field produced by a DC current. This
+ corresponds to a "magnetostatic" physical model, obtained by combining the
+ time-invariant Maxwell-Ampere equation (Curl h = js, with h the magnetic
+ field and js the source current density) with Gauss' law (Div b = 0, with b
+ the magnetic flux density) and the magnetic constitutive law (b = mu h, with
+ mu the magnetic permeability).
+
+ Since Div b = 0, b can be derived from a vector magnetic potential a, such
+ that b = Curl a. Plugging this potential in Maxwell-Ampere's law and using
+ the constitutive law leads to a vector Poisson equation in terms of the
+ magnetic vector potential: Curl(nu Curl a) = js, where nu = 1/mu is
+ the reluctivity. */
Group {
// Physical regions:
@@ -54,25 +62,24 @@ Group {
Surface_bn0 = Region[ 1101 ];
Surface_Inf = Region[ 1102 ];
-
/* Abstract regions :
- The purpose of abstract regions is to allow a generic definition of
- the FunctionSpace, Formulation and PostProcessing fields
- with no reference to model-specific Physical regions.
- We will show in a later tutorial how abstract formulations can then be isolated
- in geometry independent template files, thanks to an appropriate declaration mechanism
- (using DefineConstant[], DefineGroup[] and DefineFunction[]).
+ The purpose of abstract regions is to allow a generic definition of the
+ FunctionSpace, Formulation and PostProcessing fields with no reference to
+ model-specific Physical regions. We will show in a later tutorial how
+ abstract formulations can then be isolated in geometry independent template
+ files, thanks to an appropriate declaration mechanism (using
+ DefineConstant[], DefineGroup[] and DefineFunction[]).
The abstract regions in this model have the following interpretation:
- - Vol_Nu_Mag = region where the term [ nu[] * Dof{d a} , {d a} ] is assembled
- - Vol_Js_Mag = region where the term [ - Dof{js} , {a} ] is assembled
- - Vol_Inf_Mag = region where the infinite ring geometric transformation is applied
- - Sur_Dir_Mag = Homogeneous Dirichlet part of the model's boundary;
- - Sur_Neu_Mag = Homogeneous Neumann part of the model's boundary;
+ - Vol_Mag : full volume domain
+ - Vol_S_Mag : region where the current source js is defined
+ - Vol_Inf_Mag : region where the infinite ring geometric transformation is applied
+ - Sur_Dir_Mag : homogeneous Dirichlet part of the model boundary
+ - Sur_Neu_Mag : homogeneous Neumann part of the model boundary
*/
- Vol_Nu_Mag = Region[ {Air, AirInf, Core, Ind} ];
- Vol_Js_Mag = Region[ Ind ];
- Vol_Inf_Mag = Region[ {AirInf} ];
+ Vol_Mag = Region[ {Air, AirInf, Core, Ind} ];
+ Vol_S_Mag = Region[ Ind ];
+ Vol_Inf_Mag = Region[ AirInf ];
Sur_Dir_Mag = Region[ {Surface_bn0, Surface_Inf} ];
Sur_Neu_Mag = Region[ {Surface_ht0} ];
}
@@ -88,7 +95,7 @@ Function {
NbTurns = 1000 ;
Current = DefineNumber[0.01, Name "Model parameters/Current",
Help "Current injected in coil [A]"];
- Js_fct[ Ind ] = -NbTurns*Current/SurfaceArea[];
+ js_fct[ Ind ] = -NbTurns*Current/SurfaceArea[];
/* The minus sign is to have the current in -e_z direction,
so that the magnetic induction field is in +e_y direction */
}
@@ -104,22 +111,22 @@ Function {
"Hcurl_a_Mag_2D" and "Hregion_j_Mag_2D" as they are defined below.
The function space "Hregion_j_Mag_2D" provides one basis function,
- and hence one degree of freedom, per physical region in the abstract region "Vol_Js_Mag".
+ and hence one degree of freedom, per physical region in the abstract region "Vol_S_Mag".
The constraint "SourceCurrentDensityZ" fixes all these dofs,
so the FunctionSpace "Hregion_j_Mag_2D" is fully fixed and has no FE unknowns.
One could thus have replaced it by a simple function
and the Integral term would have been
- Integral { [ Vector[ 0,0,-Js_fct[] ] , {a} ]; In Vol_Js_Mag;
+ Integral { [ Vector[ 0,0,-js_fct[] ] , {a} ]; In Vol_S_Mag;
Jacobian Vol; Integration Int; }
instead of
- Integral { [ - Dof{js} , {a} ]; In Vol_Js_Mag;
+ Integral { [ - Dof{js} , {a} ]; In Vol_S_Mag;
Jacobian Vol; Integration Int; }
Thechosen implementation below is however more effeicient
- as it avoids evaluating repeatedly the function Js_fct[] during assembly.
+ as it avoids evaluating repeatedly the function js_fct[] during assembly.
*/
@@ -131,13 +138,13 @@ Constraint {
}
{ Name SourceCurrentDensityZ;
Case {
- { Region Vol_Js_Mag ; Value Js_fct[]; }
+ { Region Vol_S_Mag ; Value js_fct[]; }
}
}
}
Group {
- Dom_Hcurl_a_Mag_2D = Region[ {Vol_Nu_Mag, Sur_Neu_Mag} ];
+ Dom_Hcurl_a_Mag_2D = Region[ {Vol_Mag, Sur_Neu_Mag} ];
}
FunctionSpace {
{ Name Hcurl_a_Mag_2D; Type Form1P; // Magnetic vector potential A
@@ -154,7 +161,7 @@ FunctionSpace {
{ Name Hregion_j_Mag_2D; Type Vector; // Electric current density Js
BasisFunction {
{ Name sr; NameOfCoef jsr; Function BF_RegionZ;
- Support Vol_Js_Mag; Entity Vol_Js_Mag; }
+ Support Vol_S_Mag; Entity Vol_S_Mag; }
}
Constraint {
{ NameOfCoef jsr; EntityType Region;
@@ -193,9 +200,9 @@ Formulation {
{ Name js; Type Local; NameOfSpace Hregion_j_Mag_2D; }
}
Equation {
- Integral { [ nu[] * Dof{d a} , {d a} ]; In Vol_Nu_Mag;
+ Integral { [ nu[] * Dof{d a} , {d a} ]; In Vol_Mag;
Jacobian Vol; Integration Int; }
- Integral { [ -Dof{js} , {a} ]; In Vol_Js_Mag;
+ Integral { [ -Dof{js} , {a} ]; In Vol_S_Mag;
Jacobian Vol; Integration Int; }
}
}