[Getdp] @D axisymmetric electrostatic problem
Gilles Quemener
quemener at lpsc.in2p3.fr
Wed Apr 6 11:59:54 CEST 2005
Patrick,
Thanks a lot for looking into this problem. Due to the cylindrical symmetry
around the vertical axis (Y), I am expecting to get the field component
along
the horizonthal X (the radial component) such that E_r(@r=0) = 0 ? But when
I look in the file "Er" which contains the radial field component within the
chamber, I obtain the following values for X = 0 :
# GetDP 1.0.0, binary
# PostData 'Er'
# Type Num X Y Z N1 N2 N3 Values <Values>...
15 66639 0 -0.04375 0 0 0 1 -23296.40465766675
15 70830 0 -0.04275 0 0 0 1 -23443.70018452443
15 64469 0 -0.04175 0 0 0 1 -23516.95331158148
15 64469 0 -0.04074999999999999 0 0 0 1 -23516.95331158148
15 65867 0 -0.03975 0 0 0 1 -21410.95426836388
15 65867 0 -0.03875 0 0 0 1 -21410.95426836388
15 62465 0 -0.03775 0 0 0 1 -19915.45461649752
15 62465 0 -0.03675 0 0 0 1 -19915.45461649752
15 58233 0 -0.03575 0 0 0 1 -16345.95241338546
15 58233 0 -0.03475 0 0 0 1 -16345.95241338546
15 67260 0 -0.03375 0 0 0 1 -21486.27224563957
15 67260 0 -0.03274999999999999 0 0 0 1 -21486.27224563957
15 59075 0 -0.03175 0 0 0 1 -20806.32373356267
15 59075 0 -0.03075 0 0 0 1 -20806.32373356267
15 69192 0 -0.02975 0 0 0 1 -17121.91130877584
15 69192 0 -0.02875 0 0 0 1 -17121.91130877584
15 69321 0 -0.02775 0 0 0 1 -13255.12227938629
15 69321 0 -0.02675 0 0 0 1 -13255.12227938629
15 62927 0 -0.02575 0 0 0 1 -13854.12868189462
15 62927 0 -0.02475 0 0 0 1 -13854.12868189462
15 55140 0 -0.02375 0 0 0 1 -14258.16683221585
15 65487 0 -0.02275 0 0 0 1 -11406.89200786646
15 65487 0 -0.02175 0 0 0 1 -11406.89200786646
15 69991 0 -0.02075 0 0 0 1 -9523.366909591761
15 69991 0 -0.01975 0 0 0 1 -9523.366909591761
15 71120 0 -0.01875 0 0 0 1 -9543.905133518228
15 71120 0 -0.01775 0 0 0 1 -9543.905133518228
15 59775 0 -0.01675 0 0 0 1 -8941.018697394928
15 59775 0 -0.01575 0 0 0 1 -8941.018697394928
.......................
etc....
This is a little puzzling for me !
Gilles
Patrick Dular wrote:
> Gilles,
>
> The solution I get for your problem looks correct regarding the
> distribution of the electric field.
>
> In which region do you have an undesirable nonzero radial component of
> the electric field?
>
> Patrick
>
> Gilles Quemener wrote:
>
>> Hello Gmsh/GetDP users,
>>
>> Currently I am trying to solve a simple 2D-axysymmetric electrostatic
>> problem.
>> In this problem, due to the symmetry, I should obtain a zero radial
>> component
>> of the elctric field, but this is not what I get. could someone help
>> me finding my
>> mistake(s) ?
>>
>> The problem is the following : I have a cylindrical chamber with a
>> top electrode
>> set at a voltage of -1.8e05 V and a bottom one which is grounded. The
>> cylindrical
>> wall is made of a dielectric (quartz). See the attached picture for a
>> detailled geometry
>> where only half of the chamber is drawn and should be rotated around
>> the left vertical
>> axis (corresponding to r=0) I also attached the .geo and different
>> .pro files that I took
>> from some 2D examples provided on the website.
>> Thanks a lot for any help,
>>
>> Gilles
>>
>>------------------------------------------------------------------------
>>
>>/* -------------------------------------------------------------------
>> File "mStrip.geo"
>>
>> This file is the geometrical description used by GMSH to produce
>> the file "mStrip.msh".
>> ------------------------------------------------------------------- */
>>
>>/*
>> Definition of some parameters for geometrical dimensions, i.e.
>> hd (height of 'Diel1'), td (thickness of dielectric 'Diel1')
>> wge (width of grounded electrode 'Elec0'), tge (thickness of 'Elec0')
>> wve (width of charged electrode 'ElecV'), tve (thickness of 'ElecV')
>> xBox (width of the air box) and yBox (height of the air box)
>>*/
>>cm = 1.e-02;
>>
>>/* ********************************************************** */
>>/* ********************************************************** */
>>/* ********************************************************** */
>>/* chamber quartz wall */
>>hd = 15.*cm ; td = 1.5*cm ; red = 25.*cm;
>>rid = red - td;
>>
>>/* +V electrode (1) */
>>wve = 35.5*cm; tve = 9.85*cm ;
>>epve = 3.*cm; hbve = 7.625*cm;
>>rcv = tve / 2. ;
>>
>>/* Grounded electrode */
>>wge = 37.0*cm; tge = 16.1*cm ; rtge = 3.35*cm;
>>epge = 3.*cm; hhge = 4.375*cm;
>>rcg = tge / 6. ;
>>retraitge = wge - wve;
>>rhge = wge - rcg - retraitge;
>>rbge = (rhge + red) / 2.;
>>
>>/* +V electrode (2) */
>>rbve = rhge;
>>rhve = rbge;
>>
>>/* curvature radius of all electrodes */
>>rcurv = td / 4.;
>>
>>/* profondeur des gorges */
>>pg = 1.5*cm;
>>
>>/* epaisseur alu */
>>epalu = 0.3*cm;
>>
>>/* External volume */
>>xBox = (wge + wve)/2. * 4.5 ; yBox = hd / 2. * 20. ;
>>
>>/* Definition of parameters for local mesh dimensions */
>>
>>s = 1. ;
>>p0 = hd / 10. * s ;
>>pGE = wge/2. / 10. * s ; pCE = wve/2. / 10. * s ;
>>pmiddle = (pCE + pGE) / 2. * 10.;
>>pGEcorner = wge/2. / 100. * s ; pCEcorner = wve/2. / 50. * s ;
>>pxBox = xBox / 10. * s ; pyBox = yBox / 8. * s ;
>>
>>/* ********************************************************** */
>>/* ********************************************************** */
>>/* ********************************************************** */
>>/* Definition of gemetrical points */
>>
>>/* external box */
>>Point(1) = { 0 , -yBox , 0, pyBox} ;
>>Point(2) = { xBox , -yBox , 0, pyBox} ;
>>Point(3) = { xBox , 0. , 0, pyBox} ;
>>Point(4) = { xBox , yBox , 0, pyBox} ;
>>Point(5) = { 0 , yBox , 0, pyBox} ;
>>Point(6) = { 0 , hbve + epve , 0, pCE} ;
>>Point(7) = { 0 , hbve , 0, pGEcorner} ;
>>Point(8) = { 0 , 0. , 0, pGEcorner} ;
>>Point(9) = { 0 , -hhge , 0, pGEcorner} ;
>>Point(10) = { 0 , -hhge - epge , 0, pGEcorner} ;
>>
>>/* grounded electrode (1) */
>>Point(11) = { rbge , -hhge - tge , 0, pGEcorner} ;
>>Point(12) = { wge - rcg , -hhge - tge , 0, pGEcorner} ;
>>Point(13) = { wge - rcg , -hhge - tge + rcg , 0, pGEcorner} ;
>>Point(14) = { wge , -hhge - tge + rcg , 0, pGEcorner} ;
>>Point(15) = { wge , -hhge - rcg , 0, pGEcorner} ;
>>Point(16) = { wge - rcg , -hhge - rcg , 0, pGEcorner} ;
>>Point(17) = { wge - rcg , -hhge , 0, pGEcorner} ;
>>Point(18) = { rhge , -hhge , 0, pGEcorner} ;
>>Point(19) = { red + rcurv , -hhge , 0, pGEcorner} ;
>>Point(20) = { red + rcurv , -hhge - rcurv, 0, pGEcorner} ;
>>Point(21) = { red , -hhge - rcurv, 0, pGEcorner} ;
>>Point(22) = { red , -hhge - pg , 0, pGEcorner} ;
>>Point(23) = { red - td , -hhge - pg , 0, pGEcorner} ;
>>Point(24) = { red - td , -hhge - rcurv, 0, pGEcorner} ;
>>Point(25) = { red - td - rcurv , -hhge - rcurv , 0, pGEcorner} ;
>>Point(26) = { red - td - rcurv , -hhge , 0, pGEcorner} ;
>>Point(27) = { (red +rtge)/2., -hhge , 0, pGEcorner} ;
>>Point(28) = { rtge + rcurv , -hhge , 0, pGEcorner} ;
>>Point(29) = { rtge + rcurv , -hhge - rcurv, 0, pGEcorner} ;
>>Point(30) = { rtge , -hhge - rcurv, 0, pGEcorner} ;
>>Point(31) = { rtge , -hhge - epge , 0, pGEcorner} ;
>>
>>/* chamber wall external middle point */
>>Point(32) = { red , 0 , 0, pGEcorner} ;
>>
>>/* +V electode (1/3) */
>>Point(33) = { red , hbve + rcurv, 0, pGEcorner} ;
>>Point(34) = { red , hbve + pg , 0, pGEcorner} ;
>>Point(35) = { red - td , hbve + pg , 0, pGEcorner} ;
>>Point(36) = { red - td , hbve + rcurv, 0, pGEcorner} ;
>>
>>/* chamber wall internal middle point */
>>Point(37) = { red - td , 0 , 0, pGEcorner} ;
>>
>>/* +V electode (2/3) */
>>Point(38) = { red - td - rcurv , hbve + rcurv, 0, pGEcorner} ;
>>Point(39) = { red - td - rcurv , hbve , 0, pGEcorner} ;
>>Point(40) = { (red - td)/2. , hbve , 0, pGEcorner} ;
>>Point(41) = { red + rcurv , hbve , 0, pGEcorner} ;
>>Point(42) = { red + rcurv , hbve + rcurv, 0, pGEcorner} ;
>>Point(43) = { rbve , hbve , 0, pGEcorner} ;
>>Point(44) = { rbve , hbve + rcv , 0, pGEcorner} ;
>>Point(45) = { rbve + rcv , hbve + rcv , 0, pGEcorner} ;
>>Point(46) = { rbve , hbve+ 2.*rcv, 0, pGEcorner} ;
>>Point(47) = { rhve , hbve+ epve , 0, pGEcorner} ;
>>
>>/* grounded electrode (2) */
>>Point(48) = { rbge , -hhge - epge , 0, pGEcorner} ;
>>Point(49) = { rhge , -hhge - epalu , 0, pGEcorner} ;
>>Point(50) = { wge - rcg , -hhge - epalu , 0, pGEcorner} ;
>>Point(51) = { wge - epalu , -hhge - rcg , 0, pGEcorner} ;
>>Point(52) = { wge - epalu , -hhge - tge + rcg , 0, pGEcorner} ;
>>Point(53) = { wge - rcg , -hhge - tge + epalu , 0, pGEcorner} ;
>>Point(54) = { rbge , -hhge - tge + epalu , 0, pGEcorner} ;
>>
>>/* +V electode (3/3) */
>>Point(55) = { rbve , hbve + epalu , 0, pGEcorner} ;
>>Point(56) = { rbve + rcv - epalu , hbve + rcv , 0, pGEcorner} ;
>>Point(57) = { rbve , hbve+ 2.*rcv - epalu, 0, pGEcorner} ;
>>
>>/* grounded valve */
>>Point(58) = { 1.5*rtge , -hhge - epge , 0, pGEcorner};
>>Point(59) = { 1.5*rtge , -hhge - 1.5*epge , 0, pGEcorner};
>>Point(60) = { 0. , -hhge - 1.5*epge , 0, pGEcorner};
>>
>>/* Additional points for meshing characteristic length */
>>Point(61) = { 0 , -hhge - 2.*epge , 0, pGEcorner} ;
>>Point(62) = { 0 , -hhge - 4.*epge , 0, pGEcorner} ;
>>Point(63) = { 0 , -hhge - 6.*epge , 0, pGEcorner} ;
>>
>>
>>/* ********************************************************** */
>>/* ********************************************************** */
>>/* ********************************************************** */
>>/* Definition of gemetrical lines */
>>
>>Line(1) = {1,2};
>>Line(2) = {2,3};
>>Line(3) = {3,4};
>>Line(4) = {4,5};
>>Line(5) = {5,6};
>>Line(7) = {7,8};
>>Line(8) = {8,9};
>>Line(9) = {9,10};
>>Line(10) = {60,61,63,1};
>>
>>Line(11) = {60,59};
>>Line(12) = {59,58};
>>Line(13) = {58,48};
>>Line(14) = {48,49};
>>Line(15) = {49,50};
>>Circle(16) = {50,16,51};
>>Line(17) = {51,52};
>>Circle(18) = {52,13,53};
>>Line(19) = {53,54};
>>Line(20) = {54,11};
>>Line(21) = {11,12};
>>Circle(22) = {12,13,14};
>>Line(23) = {14,15};
>>Circle(24) = {15,16,17};
>>Line(25) = {17,18};
>>Line(26) = {18,19};
>>Circle(27) = {19,20,21};
>>Line(28) = {21,22};
>>Line(29) = {22,23};
>>Line(30) = {23,24};
>>Circle(31) = {24,25,26};
>>Line(32) = {26,27};
>>Line(33) = {27,28};
>>Circle(34) = {28,29,30};
>>Line(35) = {30,31};
>>Line(36) = {31,10};
>>
>>Line(37) = {21,32};
>>Line(38) = {32,33};
>>Line(39) = {36,37};
>>Line(40) = {37,24};
>>
>>Line(41) = {6,47};
>>Line(42) = {47,55};
>>Circle(43) = {55,44,56};
>>Circle(44) = {56,44,57};
>>Line(45) = {57,46};
>>Circle(46) = {46,44,45};
>>Circle(47) = {45,44,43};
>>Line(48) = {43,41};
>>Circle(49) = {41,42,33};
>>Line(50) = {33,34};
>>Line(51) = {34,35};
>>Line(52) = {35,36};
>>Circle(53) = {36,38,39};
>>Line(54) = {39,40};
>>Line(55) = {40,7};
>>
>>
>>/* ********************************************************** */
>>/* ********************************************************** */
>>/* ********************************************************** */
>>/* Definition of geometrical surfaces */
>>
>>/* external vacuum */
>>Line Loop(30) = {1,2,3,4,5,41,42,43,44,45,46,47,48,49,-38,-37,-27,-26,-25,-24,-23,-22,-21,-20,-19,-18,-17,-16,-15,-14,-13,-12,-11,10};
>>Plane Surface(31) = {30};
>>
>>/* quartz wall */
>>Line Loop(32) = {37,38,50,51,52,39,40,-30,-29,-28};
>>Plane Surface(33) = {32};
>>
>>/* internal vacuum */
>>Line Loop(34) = {7,8,9,-36,-35,-34,-33,-32,-31,-40,-39,53,54,55};
>>Plane Surface(35) = {34};
>>
>>/* ********************************************************** */
>>/* ********************************************************** */
>>/* ********************************************************** */
>>/* Definition of Physical entities (surfaces, lines). The Physical
>> entities tell GMSH the elements and their associated region numbers
>> to save in the file 'mStrip.msh'. For example, the Region
>> 111 is made of elements of surface 13, while the Region 121 is
>> made of elements of lines 9, 10 and 11 */
>>
>>Physical Surface (101) = {31} ; /* External Vacuum */
>>Physical Surface (102) = {33} ; /* Quartz */
>>Physical Surface (103) = {35} ; /* Internal Vacuum */
>>
>>
>>Physical Line (120) = {11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36} ; /* Ground */
>>Physical Line (121) = {41,42,43,44,45,46,47,48,49,50,51,52,53,54,55} ; /* Elctrode V */
>>Physical Line (130) = {1,2,3,4} ; /* SurfInf */
>>
>>------------------------------------------------------------------------
>>
>>/* -------------------------------------------------------------------
>> File "mStrip.pro"
>>
>> This file defines the problem dependent data structures for the
>> microstrip problem.
>>
>> To compute the solution: getdp mStrip -solve EleSta_v
>> To compute post-results: getdp mStrip -pos Map
>> or getdp mStrip -pos Cut
>> ------------------------------------------------------------------- */
>>
>>Group {
>>
>> /* Let's start by defining the interface (i.e. elementary groups)
>> between the mesh file and GetDP (no mesh object is defined, so
>> the default mesh will be assumed to be in GMSH format and located
>> in "mChambre.msh") */
>>
>> EVacuum = Region[101] ; Quartz = Region[102] ; IVacuum = Region[103] ;
>> Ground = Region[120] ; ElectrodeV = Region[121];
>> SurfInf = Region[130];
>>
>> /* We can then define a global group (used in "EleSta_vl.pro",
>> the file containing the function spaces and formulations) */
>>
>> DomainCC_Ele = Region[{EVacuum, Quartz, IVacuum}] ;
>>
>>}
>>
>>Function {
>>
>> /* The relative permittivity (needed in the formulation) is piecewise
>> defined in elementary groups */
>>
>> epsr[EVacuum] = 1. ;
>> epsr[IVacuum] = 1. ;
>>/* epsr[Quartz] = 4.0 ;*/
>> epsr[Quartz] = 3.8 ;
>>/* epsr[Quartz] = 4.9 ;*/
>>
>>}
>>
>>Constraint {
>>
>> /* Now, some Dirichlet conditions are defined. The name
>> 'ElectricScalarPotential' refers to the constraint name given in
>> the function space */
>>
>> { Name ElectricScalarPotential ; Type Assign ;
>> Case {
>> { Region Region[{Ground, SurfInf}] ; Value 0. ; }
>> { Region ElectrodeV ; Value -1.8e05 ; }
>> }
>> }
>>
>>}
>>
>>/* The formulation used and its tools, considered as being
>> in a black box, can now be included */
>>
>>Include "Jacobian_Lib.pro"
>>Include "Integration_Lib.pro"
>>Include "EleSta_vl.pro"
>>
>>/* Finally, we can define some operations to output results */
>>
>>/* e = 1.e-7 ;*/
>>PostOperation {
>> { Name Map ; NameOfPostProcessing EleSta_v ;
>> Operation {
>> Print [ v, OnElementsOf DomainCC_Ele, File "mChambre_v.pos" ] ;
>> Print [ E, OnElementsOf DomainCC_Ele, File "mChambre_e.pos" ] ;
>> Print [ modE, OnElementsOf DomainCC_Ele, File "mChambre_mode.pos" ] ;
>> Print [ Er, OnElementsOf DomainCC_Ele, File "mChambre_ex.pos" ] ;
>> Print [ Ez, OnElementsOf DomainCC_Ele, File "mChambre_ey.pos" ] ;
>> Print [ th_EB, OnElementsOf DomainCC_Ele, File "mChambre_theb.pos" ] ;
>> }
>> }
>> { Name Cut ; NameOfPostProcessing EleSta_v ;
>> Operation {
>> Print [ E, OnLine {{0,0,0}{0.5,0,0}} {500}, File "Cut_e", Format Gnuplot ] ;
>> Print [ v, OnLine {{0.007,-0.5,0}{0.007,0.5,0}} {500}, File "Cut_v", Format Gnuplot ] ;
>> Print [ E, OnLine {{0.007,-0.5,0}{0.007,0.5,0}} {500}, File "Cut_e2", Format Gnuplot ] ;
>> Print [ Er, OnLine {{0.007,-0.5,0}{0.007,0.5,0}} {500}, File "Cut_Er", Format Gnuplot ] ;
>> Print [ Ez, OnLine {{0.007,-0.5,0}{0.007,0.5,0}} {500}, File "Cut_Ez", Format Gnuplot ] ;
>> Print [ Er, OnPlane {{0.,-0.04375,0}{0.235,-0.04375,0}{0.,0.07625,0}} {235,120}, File "Er", Format Gnuplot ] ;
>> Print [ Ez, OnPlane {{0.,-0.04375,0}{0.235,-0.04375,0}{0.,0.07625,0}} {235,120}, File "Ez", Format Gnuplot ] ;
>> Print [ th_EB, OnPlane {{0.,-0.04375,0}{0.235,-0.04375,0}{0.,0.07625,0}} {235,120}, File "th_EB", Format Gnuplot ] ;
>> }
>> }
>>
>>}
>>
>>
>>------------------------------------------------------------------------
>>
>>/* -------------------------------------------------------------------
>> File "EleSta_v.pro"
>>
>> Electrostatics - Electric scalar potential v formulation
>> -------------------------------------------------------------------
>>
>> I N P U T
>> ---------
>>
>> Global Groups : (Extension '_Ele' is for Electric problem)
>> -------------
>> Domain_Ele Whole electric domain (not used)
>> DomainCC_Ele Nonconducting regions
>> DomainC_Ele Conducting regions (not used)
>>
>> Function :
>> --------
>> epsr[] Relative permittivity
>>
>> Constraint :
>> ----------
>> ElectricScalarPotential Fixed electric scalar potential
>> (classical boundary condition)
>>
>> Physical constants :
>> ------------------ */
>>
>> eps0 = 8.854187818e-12 ;
>>
>>/* O U T P U T
>> -----------
>>
>> PostQuantities :
>> --------------
>> v : Electric scalar potential
>> e : Electric field
>> d : Electric flux density
>>
>>*/
>>
>>Group {
>> DefineGroup[ Domain_Ele, DomainCC_Ele, DomainC_Ele ] ;
>>}
>>
>>Function {
>> DefineFunction[ epsr ] ;
>>}
>>
>>FunctionSpace {
>> { Name Hgrad_v_Ele ; Type Form0 ;
>> BasisFunction {
>> // v = v s , for all nodes
>> // n n
>> { Name sn ; NameOfCoef vn ; Function BF_Node ;
>> Support DomainCC_Ele ; Entity NodesOf[ All ] ; }
>> }
>> Constraint {
>> { NameOfCoef vn ; EntityType NodesOf ;
>> NameOfConstraint ElectricScalarPotential ; }
>> }
>> }
>>}
>>
>>
>>Formulation {
>> { Name Electrostatics_v ; Type FemEquation ;
>> Quantity {
>> { Name v ; Type Local ; NameOfSpace Hgrad_v_Ele ; }
>> }
>> Equation {
>> Galerkin { [ epsr[] * Dof{d v} , {d v} ] ; In DomainCC_Ele ;
>> Jacobian VolAxi ; Integration GradGrad ; }
>> }
>> }
>>}
>>
>>
>>Resolution {
>> { Name EleSta_v ;
>> System {
>> { Name Sys_Ele ; NameOfFormulation Electrostatics_v ; }
>> }
>> Operation {
>> Generate Sys_Ele ; Solve Sys_Ele ; SaveSolution Sys_Ele ;
>> }
>> }
>>}
>>
>>
>>PostProcessing {
>> { Name EleSta_v ; NameOfFormulation Electrostatics_v ;
>> Quantity {
>> { Name v ;
>> Value {
>> Local { [ {v} ] ; In DomainCC_Ele ; Jacobian VolAxi ; }
>> }
>> }
>> { Name E ;
>> Value {
>> Local { [ -{d v} ] ; In DomainCC_Ele ; Jacobian VolAxi ; }
>> }
>> }
>> { Name Er ;
>> Value {
>> Local { [CompX[ -{d v} ]] ; In DomainCC_Ele ; Jacobian VolAxi ; }
>> }
>> }
>> { Name Ez ;
>> Value {
>> Local { [CompY[ -{d v} ]] ; In DomainCC_Ele ; Jacobian VolAxi ; }
>> }
>> }
>> { Name d ;
>> Value {
>> Local { [ -eps0*epsr[] * {d v} ] ; In DomainCC_Ele ; Jacobian VolAxi ; }
>> }
>> }
>> { Name th_EB ;
>> Value {
>> Local { [Atan2[CompX[ -{d v} ],CompY[ -{d v} ]]] ; In DomainCC_Ele ; Jacobian VolAxi ; }
>> }
>> }
>> { Name modE ;
>> Value {
>> Local { [Norm[ -{d v} ]] ; In DomainCC_Ele ; Jacobian VolAxi ; }
>> }
>> }
>>/*
>> { Name th_EB ;
>> Value {
>> Local { [Atan2[Fabs[CompX[ -{d v} ]],Fabs[CompY[ -{d v} ]]]] ; In DomainCC_Ele ; Jacobian VolAxi ; }
>> }
>> }
>>*/
>> }
>> }
>>}
>>
>>
>>------------------------------------------------------------------------
>>
>>/*
>> Jacobian methods
>> VolAxi
>>*/
>>
>>/* I N P U T
>> ---------
>>
>> GlobalGroup :
>> -----------
>> DomainInf Regions with Spherical Shell Transformation
>> DomainInfRectX Regions with Rectangular Transformation in X direction
>> DomainInfRectY Regions with Rectangular Transformation in Y direction
>> DomainInfRectZ Regions with Rectangular Transformation in Z direction
>>
>> Parameters :
>> ----------
>> Val_Rint, Val_Rext Inner and outer radius of the Spherical Shell
>> of DomainInf
>> Val_Xint, Val_Xext Inner and outer coordinates for
>> rectangular transformation with axis X
>> Val_Yint, Val_Yext idem axis Y
>> Val_Zint, Val_Zext idem axis Z
>>
>>*/
>>
>>/* --------------------------------------------------------------------------*/
>>
>>Group {
>> DefineGroup[ DomainInf ] ;
>> DefineVariable[ Val_Rint, Val_Rext ] ;
>> DefineGroup[ DomainInfRectX, DomainInfRectY, DomainInfRectZ ] ;
>> DefineVariable[ Val_Xint, Val_Xext, Val_Yint, Val_Yext, Val_Zint, Val_Zext ] ;
>>}
>>
>>/* --------------------------------------------------------------------------*/
>>
>>Jacobian {
>> {
>> Name VolAxi ;
>> Case {
>> { Region DomainInf ;
>> Jacobian VolAxiSphShell {Val_Rint, Val_Rext} ; }
>> { Region DomainInfRectX ;
>> Jacobian VolAxiRectShell {Val_Xint, Val_Xext, 1} ; }
>> { Region DomainInfRectY ;
>> Jacobian VolAxiRectShell {Val_Yint, Val_Yext, 2} ; }
>> { Region DomainInfRectZ ;
>> Jacobian VolAxiRectShell {Val_Zint, Val_Zext, 3} ; }
>> { Region All ; Jacobian VolAxi ; }
>> }
>> }
>> {
>> Name SurAxi ;
>> Case {
>> { Region All ; Jacobian SurAxi ; }
>> }
>> }
>>}
>>
>>/* --------------------------------------------------------------------------*/
>>
>>
>>------------------------------------------------------------------------
>>
>>/*
>> Integration method
>> GradGrad
>> CurlCurl
>>*/
>>
>>
>>Integration {
>> { Name GradGrad ;
>> Case { {Type Gauss ;
>> Case { { GeoElement Triangle ; NumberOfPoints 4 ; }
>> { GeoElement Quadrangle ; NumberOfPoints 4 ; }
>> { GeoElement Tetrahedron ; NumberOfPoints 4 ; }
>> { GeoElement Hexahedron ; NumberOfPoints 6 ; }
>> { GeoElement Prism ; NumberOfPoints 9 ; } }
>> }
>> }
>> }
>> { Name CurlCurl ;
>> Case { {Type Gauss ;
>> Case { { GeoElement Triangle ; NumberOfPoints 4 ; }
>> { GeoElement Quadrangle ; NumberOfPoints 4 ; }
>> { GeoElement Tetrahedron ; NumberOfPoints 4 ; }
>> { GeoElement Hexahedron ; NumberOfPoints 6 ; }
>> { GeoElement Prism ; NumberOfPoints 9 ; } }
>> }
>> }
>> }
>>
>> {
>> Name Sur ;
>> Case {
>> {
>> Type Gauss ;
>> Case {
>> { GeoElement Line ; NumberOfPoints 3 ; }
>> }
>> }
>> }
>> }
>>
>>}
>>
>>
>>/* --------------------------------------------------------------------------*/
>>/* --------------------------------------------------------------------------*/
>>
>>
>>------------------------------------------------------------------------
>>
>>_______________________________________________
>>getdp mailing list
>>getdp at geuz.org
>>http://www.geuz.org/mailman/listinfo/getdp
>>
>>
>
>--
>Patrick Dular, Dr. Ir., Research associate, F.N.R.S.
>Department of Electrical Engineering and Computer Science
>Unit of Applied Electricity
>University of Liege - Montefiore Institute - B28 - Parking P32
>B-4000 Liege - Belgium - Tel. +32-4 3663710 - Fax +32-4 3662910
>E-mail: Patrick.Dular at ulg.ac.be
>
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