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.

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:

• example_329.com
• bemsphere.ipcoup
• bemsphere.ippara
• bemsphere.ipsour
• bemsphere.irequa
• bemsphere.irmate
• bemsphere.irsolv
• bemsphere_16x16.ipmesh
• bemsphere_16x16.iranal
• bemsphere_32x32.ipmesh
• bemsphere_32x32.iranal
• bemsphere_4x4.ipmesh
• bemsphere_4x4.iranal
• bemsphere_8x8.ipmesh
• bemsphere_8x8.iranal
• bilinear.ipbase
• test_output.com

Testing status by version:

Testing status by file:

• cmiss_test.log
  

  Success	cmo_irix:	cmiss_test.log.retain.
  Success	cmo_linux:	cmiss_test.log.retain.

  
  
• cmiss_test.out
  

  Success	cmo_irix:	ndiff test: no significant differences with generic answer.
  Success	cmo_linux:	ndiff test: no significant differences with generic answer.

  
  

Graphical output from this problem is given here.

Html last generated: Thu May 15 16:25:06 2003

Input last modified: Mon Jan 20 23:36:19 2003