explain both frequency- and time-domain simulation

Magnetodynamics/electromagnet.pro

@@ -4,14 +4,18 @@
    Features:
    - Use of a template formulation library
    - Identical to Tutorial 2 for a static current source
-   - Frequency-domain solution (phasor) for a dynamic current source
+   - Frequency-domain or time-domain solution for a time-dependent
+     current source
 
    To compute the static solution in a terminal:
        getdp electromagnet -solve Magnetostatics2D_a -pos Map_a
 
-   To compute the time-harmonic dynamic solution in a terminal:
+   To compute the frequency-domain solution in a terminal:
        getdp electromagnet -solve Magnetodynamics2D_av -pos Map_a
 
+   To compute the time-dependent dynamic solution in a terminal:
+       getdp electromagnet -setnumber TimeDomain 1 -solve Magnetodynamics2D_av -pos Map_a
+
    To compute the solution interactively from the Gmsh GUI:
        File > Open > electromagnet.pro
        You may choose the Resolution in the left panel:
@@ -42,10 +46,27 @@ Function {
   DefineConstant[
     murCore = {100, Name "Model parameters/Mur core"},
     Current = {0.01, Name "Model parameters/Current"},
-    frequency = {1, Name "Model parameters/Frequency"}
+    TimeDomain = {0, Choices{0 = "Frequency-domain", 1 = "Time-domain"},
+      Name "Model parameters/03Analysis type"}
+    frequency = {50, Visible !TimeDomain,
+      Name "Model parameters/Frequency" }
   ];
 
-  Freq = frequency;
+  If(TimeDomain)
+    // Fix parameters from the "Lib_Magnetodynamics2D_av_Cir.pro" template:
+    Flag_FrequencyDomain = 0;
+    TimeInit = 0; // start simulation at time = 0s
+    TimeFinal = 20e-3; // stop simulation at time = 20 ms
+    DeltaTime = 1e-3; // use time steps equal to 1 ms
+    // Define the time modulation of the current source, i.e. a linear ramp from
+    // 0 to 1 until 10 ms, then a constant value of 1:
+    myModulation[] = ($Time < TimeFinal / 2) ? (2 / TimeFinal * $Time) : 1;
+  Else
+    // Fix parameters from the "Lib_Magnetodynamics2D_av_Cir.pro" template:
+    Flag_FrequencyDomain = 1;
+    Freq = frequency;
+  EndIf
+
   mu0 = 4.e-7 * Pi;
   nu[ Region[{Air, Ind, AirInf}] ]  = 1. / mu0;
   nu[ Core ]  = 1. / (murCore * mu0);
@@ -55,10 +76,13 @@ Function {
 
   Ns[ Ind ] = 1000 ; // number of turns in coil
   Sc[ Ind ] = SurfaceArea[] ; // area of coil cross section
+
   // Current density in each coil portion for a unit current (will be multiplied
   // by the actual total current in the coil)
-  js0[ Ind ] = Ns[]/Sc[] * Vector[0,0,-1];
-  CoefGeos[] = 1;
+  js0[ Ind ] = Ns[] / Sc[] * Vector[0, 0, -1];
+
+  // For a correct definition of the voltage:
+  CoefGeos[] = 1; // planar model, 1 meter thick
 }
 
 Constraint {
@@ -70,8 +94,13 @@ Constraint {
   }
   { Name Current_2D;
     Case {
-      // represents the phasor amplitude (peak to peak value) for a dynamic analysis
-      { Region Ind; Value Current; }
+      If(Flag_FrequencyDomain)
+        // Amplitude of the phasor is set to "Current"
+        { Region Ind; Value Current; }
+      Else
+        // Time-dependent value is set to "Current * myModulation[]"
+        { Region Ind; Value Current; TimeFunction myModulation[]; }
+      EndIf
     }
   }
   { Name Voltage_2D;
@@ -87,8 +116,8 @@ PostOperation {
   { Name Map_a; NameOfPostProcessing Magnetodynamics2D_av;
     Operation {
       Print[ a, OnElementsOf Vol_Mag, File "a.pos" ];
-      Print[ b, OnElementsOf Vol_Mag, File "b.pos" , HarmonicToTime 20];
-      Print[ j, OnElementsOf Vol_Mag, File "j.pos", HarmonicToTime 20];
+      Print[ b, OnElementsOf Vol_Mag, File "b.pos" ];
+      Print[ j, OnElementsOf Vol_Mag, File "j.pos" ];
     }
   }
 }