Example 328: Heat conduction spherical BEM example

This problems solves Laplaces equation on a sphere of radius 1 with the Boundary Element Method (BEM). The sphere has 4 elements in the circumfrential direction and 4 elements in the azimuthal direction. The basis functions are cubic Hermite (including sector elements). The value of the dependent variable at each of the nodes is set according to x^2-y^2.The numerical results are compared to the known analytic formula for this problem.


The comfile run by this example is as follows:

#Sphere BEM test problem. Solves Laplaces equation on a 4x4 element
#sphere of radius 2 with cubic Hermite basis functions. The value of the 
# dependent variable at each of the nodes is set according to  x^2-y^2.
# Solution is checked against the analytic solution for this problem. 

fem define coord 3,1                  #Define 3d
fem define base;r;bemsphere;example   #Define a three basis functions.
#                                     !  a bicubic Hermite BEM basis
#                                     !  and two cubic Hermite sector
#                                     !  BEM basis functions.
fem define mesh;r;;example            #Define a spherical mesh with
#                                     !  4x4 elements, radius 2.
fem define equation;r;;example        #Define a standard Laplace 
#                                     !  equation for the BEM
fem define material;r;;example       #Define materials
#
fem define anal;r;;example             #Calculate the value of the dependent
#                                     !  variable at each of the nodes 
#                                     !  according to x^2+2xy-y^2
#                                     !  of the nodes
fem define initial;g                 #Generate the initial conditions 
#                                     !  as per the analytic equation
fem define solve;r;;example          #Define the solve parameters
fem solve                             #Solve the problem
fem check solution

Additional testing commands:

fem solve
fem check solution sphere

Files used by this example are:

Name              Modified     Size

example_328.com 08-Jun-2000 1.4k bemsphere.exelem 10-Apr-2000 12k bemsphere.exnode 10-Apr-2000 4.6k bemsphere.ipanal 10-Apr-2000 590 bemsphere.ipbase 10-Apr-2000 4.5k bemsphere.ipequa 26-May-2003 1.1k bemsphere.ipinit 10-Apr-2000 576 bemsphere.ipmate 10-Apr-2000 54 bemsphere.ipmesh 10-Apr-2000 981 bemsphere.ipsolv 13-Apr-2007 1.3k bemsphere.ipsour 10-Apr-2000 293 test.exelem 10-Apr-2000 12k test.exnode 10-Apr-2000 4.6k test_output.com 10-Apr-2000 36

Download the entire example:

Name                      Modified     Size

examples_3_32_328.tar.gz 14-Apr-2007 9.1k

Testing status by version:

StatusTestedReal time (s)
i686-linux
cmSuccessSun Mar 6 00:01:48 20160
cm-debugSuccessSat Mar 5 00:02:05 20161
mips-irix
cmSuccessSun Aug 19 01:25:28 20075
cm-debugSuccessWed Aug 15 01:25:23 20079
cm-debug-clear-mallocSuccessSat Aug 18 01:29:31 200713
cm-debug-clear-malloc7SuccessMon Aug 20 01:27:16 200712
cm64SuccessSun Aug 19 01:26:59 20073
cm64-debugSuccessTue Aug 21 01:24:17 20079
cm64-debug-clear-mallocSuccessThu Apr 1 10:13:19 20047
rs6000-aix
cmSuccessWed Mar 4 01:07:06 20091
cm-debugSuccessMon Mar 2 01:06:55 20092
cm64SuccessWed Mar 4 01:07:06 20091
cm64-debugSuccessTue Mar 3 01:12:07 20092
x86_64-linux
cmSuccessSun Mar 6 00:01:02 20161
cm-debugSuccessSat Mar 5 00:01:13 20161

Testing status by file:


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

Input last modified: Fri Apr 13 10:32:18 2007


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