Example 322: Circular BEM example

This problems solves Laplaces equation on a circle of radius 1 with the Boundary Element Method (BEM). The circle has 16 nodes and 16 elements around the circumference and the basis functions used are cubic Hermite. A Dirichlet boundary condition of x^2 + 2xy -y^2 is set and the normal derivative is solved for. The numerical results are compared to the known analytic formula for this problem.


The comfile run by this example is as follows:

#Circular BEM test problem. Solves Laplaces equation on a 16 node circle
#of radius 1 with cubic Hermite basis functions. Solution is checked 
#against the analytic solution for a Dirichlet problem. 

fem define base;r;bemcircle;example   #Define a cubic Hermite BEM basis
fem define mesh;r;;example             #Define a circlar mesh with 16
#                                     !  nodes and 16 elements
fem define equa;r;;example             #Define a standard Laplace 
#                                     !  equation for the BEM
fem define mate;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
fem define init;g                     #Generate the initial conditions 
#                                     !  as per the analytic equation
fem define solv;r;;example             #Define the solve parameters
fem solve                             #Solve the problem

Additional testing commands:

fem solve
fem check solution

Files used by this example are:

Name               Modified     Size

example_322.com 08-Jun-2000 1.0k bemcircle.changes 10-Apr-2000 0 bemcircle.ipanal 10-Apr-2000 492 bemcircle.ipbase 10-Apr-2000 1.2k bemcircle.ipelem 10-Apr-2000 1.3k bemcircle.ipequa 26-May-2003 1.0k bemcircle.ipinit 10-Apr-2000 107 bemcircle.ipmate 10-Apr-2000 54 bemcircle.ipmesh 10-Apr-2000 736 bemcircle.ipnode 10-Apr-2000 3.0k bemcircle.ippara 17-Dec-2002 5.0k bemcircle.ipsolv 13-Apr-2007 1.4k bemcircle.out 10-Apr-2000 6.0k test_output.com 10-Apr-2000 29

Download the entire example:

Name                      Modified     Size

examples_3_32_322.tar.gz 14-Apr-2007 8.2k

Testing status by version:

StatusTestedReal time (s)
i686-linux
cmSuccessSun Mar 6 00:01:46 20160
cm-debugSuccessSat Mar 5 00:02:02 20160
mips-irix
cmSuccessSun Aug 19 01:24:14 20073
cm-debugSuccessWed Aug 15 01:20:10 20074
cm-debug-clear-mallocSuccessSat Aug 18 01:30:42 20079
cm-debug-clear-malloc7SuccessMon Aug 20 01:23:24 20079
cm64SuccessSun Aug 19 01:22:04 20074
cm64-debugSuccessTue Aug 21 01:19:30 20075
cm64-debug-clear-mallocSuccessThu Apr 1 10:12:58 20044
rs6000-aix
cmSuccessWed Mar 4 01:07:03 20091
cm-debugSuccessMon Mar 2 01:06:16 20091
cm64SuccessWed Mar 4 01:07:03 20091
cm64-debugSuccessTue Mar 3 01:11:52 20090
x86_64-linux
cmSuccessSun Mar 6 00:01:01 20160
cm-debugSuccessSat Mar 5 00:01:12 20160

Testing status by file:


Html last generated: Sun Mar 6 05:50:16 2016

Input last modified: Fri Apr 13 10:32:06 2007


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