[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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