Example 329: Analytic Concentric Spheres with a Static Dipole

Calculates the potential generated due a dipole in concentric spheres with bilinear basis functions. The inner sphere has unit radius and the outer sphere a radius of 2. There is a conductivity of 0.3 in the inner sphere and 0.2 in the outer sphere.

The numerical solution is compared to the analytic solution.

The output for the mesh with discretisation 16x16 is also given and can be visualised using draw.com. The potential field on the inner and outer spheres is shown below.

innersphere outersphere

The comfile run by this example is as follows:

#Example 329
# Dipole in bilinear concentric spheres with a static dipole.

$size= "8x8"
$size= "16x16"
$size= "32x32"
$size= "4x4"                                 #choose a mesh resolution

fem def para;r;bemsphere;example
fem def coord 3,1
fem def base;r;bilinear;example              #bilinear basis function
fem def mesh;r;bemsphere_$size;example

fem export node;sphere as sphere reg all     #export geometry
fem export elem;inner as inner reg 1 
fem export elem;outer as outer reg 2 

fem def equa;r;bemsphere;example region all  #gen. laplaces equation
fem def mate;r;bemsphere;example region all
fem def sour;r;bemsphere;example region 1    #static dipole
fem def anal;r;bemsphere_$size;example region all
fem def init;g region all

fem def coup;r;bemsphere;example
fem def solv;r;bemsphere;example coupled region all

Additional testing commands:

#Testing example 329

fem solve coupled
fem check solution sphere region 2

# Export the solution field
fem export node;soln as soln reg all field 
fem export elem;soln_inner field as soln_inner reg 1 
fem export elem;soln_outer field as soln_outer reg 2 

Files used by this example are:

Name                    Modified     Size

example_329.com 24-Oct-2000 834 bemsphere.ipcoup 21-Aug-2002 437 bemsphere.ipcoup.old 24-Oct-2000 386 bemsphere.ippara 12-Nov-2002 5.9k bemsphere.ipsour 24-Oct-2000 299 bemsphere.irequa 26-May-2003 1.9k bemsphere.irmate 24-Oct-2000 1.7k bemsphere.irsolv 13-Apr-2007 1.3k bemsphere_16x16.ipmesh 24-Oct-2000 1.3k bemsphere_16x16.iranal 24-Oct-2000 1.3k bemsphere_32x32.ipmesh 24-Oct-2000 1.3k bemsphere_32x32.iranal 24-Oct-2000 1.3k bemsphere_4x4.ipmesh 24-Oct-2000 1.3k bemsphere_4x4.iranal 24-Oct-2000 1.3k bemsphere_8x8.ipmesh 24-Oct-2000 1.3k bemsphere_8x8.iranal 24-Oct-2000 1.3k bilinear.ipbase 24-Oct-2000 3.4k test_output.com 24-Oct-2000 263

Download the entire example:

Name                      Modified     Size

examples_3_32_329.tar.gz 14-Apr-2007 117k

Testing status by version:

StatusTestedReal time (s)
cmSuccessSun Mar 6 00:01:49 20161
cm-debugSuccessSat Mar 5 00:02:06 20161
cmSuccessSun Aug 19 01:31:20 20075
cm-debugSuccessWed Aug 15 01:30:54 200715
cm-debug-clear-mallocSuccessSat Aug 18 01:41:19 200729
cm-debug-clear-malloc7SuccessMon Aug 20 01:37:09 200727
cm64SuccessSun Aug 19 01:30:31 20075
cm64-debugSuccessTue Aug 21 01:29:31 200716
cm64-debug-clear-mallocSuccessThu Apr 1 10:13:24 200410
cmSuccessWed Mar 4 01:08:02 20091
cm-debugSuccessMon Mar 2 01:07:55 20093
cm64SuccessWed Mar 4 01:08:02 20091
cm64-debugSuccessTue Mar 3 01:13:13 20093
cmSuccessSun Mar 6 00:01:02 20161
cm-debugSuccessSat Mar 5 00:01:13 20161

Testing status by file:

Graphical output from this problem is given here.

Html last generated: Sun Mar 6 05:50:17 2016

Input last modified: Fri Apr 13 10:32:20 2007

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