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4209cc7b
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4209cc7b
authored
7 years ago
by
François Henrotte
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ElectrostaticsFloating/floating.pro
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ElectrostaticsFloating/floating.pro
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4209cc7b
...
@@ -3,7 +3,7 @@
...
@@ -3,7 +3,7 @@
Features:
Features:
- Global quantities and their special shape functions
- Global quantities and their special shape functions
-
Duality
-
Computation of the energy dual, i.e. of the armature charge of the electrode
- More on ONELAB parameters (flags, model options, check boxes, menus, ...)
- More on ONELAB parameters (flags, model options, check boxes, menus, ...)
To compute the solution interactively from the Gmsh GUI:
To compute the solution interactively from the Gmsh GUI:
...
@@ -13,19 +13,19 @@
...
@@ -13,19 +13,19 @@
------------------------------------------------------------------- */
------------------------------------------------------------------- */
/*
/*
A
T
hing GetDP is pretty good at is the management of global (non-local) basis functions.
A
t
hing GetDP is pretty good at is the management of global (non-local) basis functions.
Finite element expansions typically associate basis functions to individual nodes
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
or edges in the mesh. But consider the situation where a scalar field is set to be uniform
over a region of the problem (a floating potential electrode
in an Electrostatics problem,
over a region of the problem (
Say
a floating potential electrode
to fix the idea).
in an Electrostatics problem,
to fix the idea).
By factorizing the identical nodal value "v_electrode",
By factorizing the identical nodal value "v_electrode",
a global (non-local) basis function "BF_electrode" is obtained as factor
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.
which is the sum of the shape functions of all the nodes in the electrode region.
BF_electrode
This basis function "
BF_electrode
"
- is a continuous function
- is a continuous function
- is equal to 1 at the nodes of the electrode region, and to 0 at all other nodes
- 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
- decreases from 1 to 0 over the one element thick layer of outside finite elements
immediately in contact with the electrode region
immediately in contact with the electrode region
.
One such glabal basis function can be associated with each electrode in the system,
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:
so that the finite element expansion of the electric scalar potential reads:
...
@@ -34,9 +34,10 @@
...
@@ -34,9 +34,10 @@
We show in this tutorial how GetDP takes advantage of global quantities
We show in this tutorial how GetDP takes advantage of global quantities
and the associated global basis functions
and the associated global basis functions
- to reduce the number of unknowns
- to reduce the number of unknowns
- to deal with floating potentials
- to compute efficiently the electrode charges "Q_electrode",
- to compute efficiently the electrode charges "Q_electrode",
which are precisely the energy duals of the global "v_electrode" quantities
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, ...)
- to provide output quantities (charges, armature voltages, capacitances, ...)
that can be immediately used in a external circuit.
that can be immediately used in a external circuit.
*/
*/
...
@@ -58,9 +59,8 @@ Group {
...
@@ -58,9 +59,8 @@ Group {
Sur_Neu_Ele : Neumann bondary condition ( epsr[] n.Grad v = 0 )
Sur_Neu_Ele : Neumann bondary condition ( epsr[] n.Grad v = 0 )
Electrodes_Ele : electrode regions
Electrodes_Ele : electrode regions
No prefix (Vol_ or Sur_) for the region "Electrodes_Ele",
No prefix (Vol_ or Sur_) for the region "Electrodes_Ele",
which
can
contain both surface or volume regions.
which
may
contain both surface or volume regions.
There are two electrodes in this model: Ground and Microstrip
There are two electrodes in this model: Ground and Microstrip
*/
*/
...
@@ -92,7 +92,8 @@ Function {
...
@@ -92,7 +92,8 @@ Function {
Constraint
{
Constraint
{
/* Dirichlet boundary condition is no longer used.
/* Dirichlet boundary condition is no longer used.
The microstrip and the ground are now treated as electrodes */
The microstrip and the ground are now treated as electrodes,
whose voltage is imposed with the "SetGlobalPotential" constraint below. */
{
Name
Dirichlet_Ele
;
Type
Assign
;
{
Name
Dirichlet_Ele
;
Type
Assign
;
Case
{}
Case
{}
}
}
...
@@ -118,7 +119,7 @@ Constraint {
...
@@ -118,7 +119,7 @@ Constraint {
}
}
Group
{
Group
{
/* The domain of definition
of
lists all regions
/* The domain of definition lists all regions
on which the field "v" is defined.*/
on which the field "v" is defined.*/
Dom_Hgrad_v_Ele
=
Region
[
{
Vol_Dielectric_Ele
,
Dom_Hgrad_v_Ele
=
Region
[
{
Vol_Dielectric_Ele
,
Sur_Neu_Ele
,
Sur_Neu_Ele
,
...
@@ -183,10 +184,10 @@ Integration {
...
@@ -183,10 +184,10 @@ Integration {
}
}
Formulation
{
Formulation
{
/*
M
inor changes in the formulation.
/*
Only m
inor changes in the formulation.
G
lobal quantities are declared in the "Quantity{}" section
.
The g
lobal quantities are declared in the "Quantity{}" section
,
The
Global
t
erm triggers the creation of
the
addition equation
and a "
Global
T
erm
" is added that
triggers the creation of
an
addition
al
equation
in the system t
hat
compute
s
the charge Q_electrode
carried by each electrode
per electrode
in the system t
o
compute the charge Q_electrode
Q_electrode = (-epsr[] Grad v, Grad BF_electrode)_Vol_Dielectric_Ele
Q_electrode = (-epsr[] Grad v, Grad BF_electrode)_Vol_Dielectric_Ele
*/
*/
...
@@ -248,12 +249,11 @@ PostProcessing {
...
@@ -248,12 +249,11 @@ PostProcessing {
}
}
}
}
/* Various output results
associated with the global quantities
are generated.
/* Various output results are generated.
They are both displayed in the graphical user interface, and stored in disk files.
They are both displayed in the graphical user interface, and stored in disk files.
In particular, all global quantities related results
In particular, global quantities related results are stored in the "output.txt" file.
are stored in the "output.txt" file.
There is a user option to display the global basis functions of the two electrodes.
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
in the system. Another user option allow the user to chose to not overwrite
the "output.txt" file when running a new simulation. */
the "output.txt" file when running a new simulation. */
PostOperation
{
PostOperation
{
...
...
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