Example i25: Radial Dipole in a Sphere - Convergence

Computes the magnetic field due to a radial dipole in a sphere of radius 2 mm. The full magnetic field should be zero as the magnetic field from the dipole should exactly cancel that produced by the volume conductor. The magnetic fields are evaluated on the edges of a cube with vertices located at +/- 5 mm. Convergence plots for using different basis functions and element refinement are shown below:

The comfile run by this example is as follows:

# Example i25

if(!defined $example) 
{  
    $example='.' ;
    $OUT="output"; unless (-d $OUT) {mkdir $OUT};
} else{
    $OUT=".";
}


#$resolution = '16x16'
#$resolution = '4x4';
$resolution = '8x8'

#$interpolation = 'cubic';
$interpolation = 'linear';

fem define para;r;$example/torsotimedep;
fem define coor 3,1;
fem define regi;r;$example/two;
fem define base;r;$example/bi$interpolation;


if(0)
{
    fem def mesh;r;sphere_$resolution;
    fem def node;w;sphere_$resolution;
    fem def elem;w;sphere_$resolution;
    fem export node;$OUT/sphere as sphere;
    fem export elem;$OUT/sphere as sphere;
    quit;
} else
{
    fem define node;r;$example/sphere_$resolution reg 1;
    fem define elem;r;$example/sphere_$resolution reg 1;
    fem export node;$OUT/sphere as sphere;
    fem export elem;$OUT/sphere as sphere;
}

fem define node;r;$example/cube reg 2;
fem define elem;r;$example/cube reg 2;

#
# Export geometry
#
fem export node;$OUT/cube   as cube reg 2;
fem export elem;$OUT/cube   as cube reg 2;


fem define grid;r;$example/cube   reg 2;
fem update grid geometr            reg 2;
fem define equa;r;$example/laplace_bem_$interpolation reg 1 class 1 lock;
fem define mate;r;$example/laplace reg 1 class 1;
fem define sour;r;$example/dipole  reg 1 class 1;
fem de anal;r;$example/eccentricdipole reg 1 cl 1;
fem de init;g reg 1 cl 1;
fem define solv;r;$example/nosalu_$interpolation reg 1 class 1;
fem define equa;r;$example/laplace_grid reg 2 class 2 lock;

#
# Solve and export potential due to a dipole
#
fem solve reg 1 class 1;
fem export node;$OUT/sphere_pot as sphere field;
fem export elem;$OUT/sphere_pot as sphere field;


#
# Read in perl subroutine: WriteGradPhiExelem
#  which combines 3 scalar exelem files into a vector field
#
read com;$example/perl;


#
# Full magnetic field
#

fem li sour;
fem export source;$OUT/dipole as dipole;


for $TYPE ("dipole","volume","both")
{
    printf("\n");
    printf("*** Evalutating Magnetic Field from $TYPE\n");

    fem eval solu magnet grid elem 551 iy 1 $TYPE;

    $DXFILENAME="tmp_x";
    $DYFILENAME="tmp_y";
    $DZFILENAME="tmp_z";
    $OUTPUTNAME="$OUT/H_$TYPE";

    fem export elem;$DXFILENAME as cube field reg 2 class 2 iy 2 grid_numbers;
    fem export elem;$DYFILENAME as cube field reg 2 class 2 iy 3;
    fem export elem;$DZFILENAME as cube field reg 2 class 2 iy 4;

    #
    # Combine the 3 scalar field into a single vector field
    #
    
    &WriteGradPhiExelem($DXFILENAME,$DYFILENAME,$DZFILENAME,$OUTPUTNAME);
}

Files used by this example are:

Name                       Modified     Size


example_i25.com            27-Jan-2009  2.5k
README.txt                 27-Jan-2009  3.0k
bicubic.ipbase             27-Jan-2009  6.8k
bilinear.ipbase            27-Jan-2009  5.7k
cube.ipelem                27-Jan-2009  447 
cube.ipgrid                27-Jan-2009  601 
cube.ipnode                27-Jan-2009  2.1k
dipole.ipsour              27-Jan-2009  301 
draw.com                   27-Jan-2009  3.0k
eccentricdipole.ipanal     27-Jan-2009  720 
laplace.ipmate             27-Jan-2009   54 
laplace_bem_cubic.ipequa   27-Jan-2009  1.3k
laplace_bem_linear.ipequa  27-Jan-2009  1.3k
laplace_grid.ipequa        27-Jan-2009  1.2k
nosalu_cubic.ipsolv        27-Jan-2009  1.3k
nosalu_linear.ipsolv       27-Jan-2009  1.2k
perl.com                   27-Jan-2009  2.4k
sphere_16x16.ipelem        27-Jan-2009   84k
sphere_16x16.ipmesh        27-Jan-2009  985 
sphere_16x16.ipnode        27-Jan-2009  211k
sphere_4x4.ipelem          27-Jan-2009  5.7k
sphere_4x4.ipmesh          27-Jan-2009  983 
sphere_4x4.ipnode          27-Jan-2009   12k
sphere_8x8.ipelem          27-Jan-2009   21k
sphere_8x8.ipmesh          27-Jan-2009  983 
sphere_8x8.ipnode          27-Jan-2009   51k
torsotimedep.ippara        27-Jan-2009  5.9k
two.ipregi                 27-Jan-2009   93

Download the entire example:

Name                      Modified     Size


examples_i_i2_i25.tar.gz  31-Jan-2009   43k

Testing status by version:

StatusTestedReal time (s)
i686-linux
cmSuccessSun Mar 6 00:02:52 20161
cm-debugSuccessSat Mar 5 00:05:25 20161
rs6000-aix
cmSuccessMon Jan 17 11:33:19 20111
cm-debugSuccessTue Jan 18 10:56:24 20111
cm64SuccessMon Jan 17 11:32:41 20111
cm64-debugSuccessTue Jan 18 10:56:38 20111
x86_64-linux
cmSuccessSun Mar 6 00:01:08 20160
cm-debugSuccessSat Mar 5 00:01:39 20161

Testing status by file:

Html last generated: Sun Mar 6 05:51:38 2016

Input last modified: Fri Jan 30 12:10:09 2009

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