diff --git a/ElectrostaticsFloating/floating.pro b/ElectrostaticsFloating/floating.pro
index cb8224367b4298a79817c1fca0910aeb0cb2ee1d..4eb75fc217994f68c618dd4e8b474d143ffeee54 100644
--- a/ElectrostaticsFloating/floating.pro
+++ b/ElectrostaticsFloating/floating.pro
@@ -13,21 +13,23 @@
------------------------------------------------------------------- */
/*
- A thing GetDP is pretty good at is the management of global (non-local) basis functions.
- Finite element expansions typically associate basis functions to individual nodes
- or edges in the mesh. But consider the situation where a scalar field is set to be uniform
- over a region of the problem (Say a floating potential electrode
- in an Electrostatics problem, to fix the idea).
- By factorizing the identical nodal value "v_electrode",
+ A thing GetDP is pretty good at is the management of global (non-local) basis
+ functions. Finite element expansions typically associate basis functions to
+ individual nodes or edges in the mesh. But consider the situation
+ where a scalar field is set to be uniform over a region of the problem
+ (Say a floating potential electrode in an Electrostatics problem,
+ to fix the idea). By factorizing the identical nodal value "v_electrode",
a global (non-local) basis function "BF_electrode" is obtained as factor
- which is the sum of the shape functions of all the nodes in the electrode region.
- This basis function "BF_electrode"
- - is a continuous function
- - is equal to 1 at the nodes of the electrode region, and to 0 at all other nodes
- - decreases from 1 to 0 over the one element thick layer of outside finite elements
- immediately in contact with the electrode region.
- One such glabal basis function can be associated with each electrode in the system,
- so that the finite element expansion of the electric scalar potential reads:
+ which is the sum of the shape functions of all the nodes in the electrode
+ region. This basis function "BF_electrode"
+ - is a continuous function, scalar in this case,
+ - is equal to 1 at the nodes of the electrode region, and to 0
+ at all other nodes
+ - decreases from 1 to 0 over the one element thick layer of outside
+ finite elements immediately in contact with the electrode region.
+ One such glabal basis function can be associated with each electrode
+ in the system, so that the finite element expansion of the electric
+ scalar potential reads:
v = Sum_k sn_k vn_k + Sum_electrode v_electrode BF_electrode
@@ -36,10 +38,10 @@
- to reduce the number of unknowns
- to compute efficiently the electrode charges "Q_electrode",
which are precisely the energy duals of the global "v_electrode" quantities
- - to deal with floating potentials, which are the computed electrode potential
- when the electrode charge is imposed
- - to provide output quantities (charges, armature voltages, capacitances, ...)
- that can be immediately used in a external circuit.
+ - to deal with floating potentials, which are the computed electrode
+ potential when the electrode charge is imposed
+ - to provide output quantities (charges, armature voltages,
+ capacitances, ...) that can be immediately used in a external circuit.
*/
@@ -100,9 +102,10 @@ Constraint {
{ Name SetGlobalPotential; Type Assign;
Case {
- /* Define the imposed potential regionwise on the different parts of "Electrodes_Ele".
- No voltage imposed to the Microstrip electrode
- when the "Fixed charge" option is enabled ( MicrostripTypeBC = true ). */
+ /* Define the imposed potential regionwise on the different parts of
+ "Electrodes_Ele". No voltage imposed to the Microstrip electrode
+ when the "Fixed charge" option is enabled
+ ( MicrostripTypeBC = true ). */
{ Region Ground; Value 0; }
If( !MicrostripTypeBC )
{ Region Microstrip; Value MicrostripValueBC; }
@@ -128,15 +131,28 @@ Group{
FunctionSpace {
/* The magic in the treatment of global quantitities by GetDP is in the fact
- that nearly all the work is done at the level of the FunctionSpace definition.
-
- The finite element expansion is
+ that nearly all the work is done at the level of the FunctionSpace
+ definition. The finite element expansion of "v" is
v = Sum_k sn_k vn_k + Sum_electrode v_electrode BF_electrode
- The sum_k runs over all nodes except those of the electrode regions.
- "sf" stands for "BF_electrode"
- "vf" stands for "v_electrode"
+ with the the sum_k running over all nodes except those of the electrode
+ regions. This is exactly what one finds in the FunctionSpace definotion
+ below with "sf" standing for "BF_electrode" and "vf" for "v_electrode".
+ The global quantities are also be attributed a more explicit
+ and meaningful name. Moreover the "AssociatedWith" statement manifests
+ the fact that the global potential of an electrode is the (electrostatic)
+ energy dual of the electric charge carried by that electrode.
+ By checking the "Display global basis functions" checkbox and running
+ the model, you can take a look on how the two "BF_electrode" basis
+ functions in this model look like.
+ Constraints can then be set on either component of the FunctionSpace.
+ Besides the usual Dirichlet boundary condition conditions, which is
+ left here for the sake of completeness but is not used in this model,
+ there is the possibility to fix either the GlobalPotential or the
+ ArmatureCharge of each indidual electrode (not both, of course).
+ When the ArmatureCharge is fixed, the computed GlobalPotential computed
+ for that electrode is the so-called floating potential.
*/
{ Name Hgrad_v_Ele; Type Form0;
@@ -186,8 +202,9 @@ Integration {
Formulation {
/* Only minor changes in the formulation.
The global quantities are declared in the "Quantity{}" section,
- and a "GlobalTerm" is added that triggers the assembly of an additional equation
- per electrode in the system to compute the charge Q_electrode
+ and a "GlobalTerm" is added that triggers the assembly
+ of an additional equation per electrode in the system
+ to compute the charge Q_electrode accordint to:
Q_electrode = (-epsr[] Grad v, Grad BF_electrode)_Vol_Dielectric_Ele
*/
@@ -239,7 +256,7 @@ PostProcessing {
}
}
}
- // next lines only needed to display global basis functions in PostProcessing
+ // next lines only needed to display global BF in PostProcessing
{ Name BFGround; Value { Term { [ BF {vf} ]; In Dom_Hgrad_v_Ele;
SubRegion Ground; Jacobian Vol; } } }
{ Name BFMicrostrip; Value { Term { [ BF {vf} ]; In Dom_Hgrad_v_Ele;
@@ -249,12 +266,11 @@ PostProcessing {
}
}
-/* Various output results are generated.
- They are both displayed in the graphical user interface, and stored in disk files.
- In particular, global quantities related results are stored in the "output.txt" file.
- There is a user option to display the global basis functions of the two electrodes.
- Another option allows the user to chose to not overwrite
- the "output.txt" file when running a new simulation. */
+/* Various output results are generated, which are both displayed
+ in the graphical user interface, and stored in disk files.
+ In particular, global quantities related results are stored
+ in the "output.txt" file. A user option allows to chose
+ to not overwrite the "output.txt" file when running a new simulation. */
PostOperation {
{ Name Map; NameOfPostProcessing EleSta_v;
@@ -267,7 +283,8 @@ PostOperation {
"View[l].ShowElement = 1;"],
File "BFGround.opt", LastTimeStepOnly] ;
- Print[ BFMicrostrip, OnElementsOf Dom_Hgrad_v_Ele, File "BFMicrostrip.pos" ];
+ Print[ BFMicrostrip, OnElementsOf Dom_Hgrad_v_Ele,
+ File "BFMicrostrip.pos" ];
Echo[ StrCat["l=PostProcessing.NbViews-1;",
"View[l].IntervalsType = 1;",
"View[l].NbIso = 40;",
@@ -294,7 +311,8 @@ PostOperation {
Print[ C, OnRegion Microstrip, File > "output.txt", Color "AliceBlue",
Format Table, SendToServer "Output/Global/Capacitance [F]" ];
Echo[ "Electrostatic energy [J]:", Format Table, File > "output.txt"] ;
- Print[ energy, OnRegion Vol_Dielectric_Ele, File > "output.txt", Color "AliceBlue",
+ Print[ energy, OnRegion Vol_Dielectric_Ele, File > "output.txt",
+ Color "AliceBlue",
Format Table, SendToServer "Output/Global/Energy [J]" ];
}
}