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:

Testing status by file:

• cmiss_test.log
  

  i686-linux
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.
  mips-irix
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.
  Success	cm-debug-clear-malloc:	cmiss_test.log.retain.
  Success	cm-debug-clear-malloc7:	cmiss_test.log.retain.
  Success	cm64:	cmiss_test.log.retain.
  Success	cm64-debug:	cmiss_test.log.retain.
  Success	cm64-debug-clear-malloc:	cmiss_test.log.retain.
  rs6000-aix
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.
  Success	cm64:	cmiss_test.log.retain.
  Success	cm64-debug:	cmiss_test.log.retain.
  x86_64-linux
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.

  
  
• cmiss_test.out
  

  i686-linux
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.
  mips-irix
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.
  Success	cm-debug-clear-malloc:	ndiff test: no significant differences with generic answer.
  Success	cm-debug-clear-malloc7:	ndiff test: no significant differences with generic answer.
  Success	cm64:	ndiff test: no significant differences with generic answer.
  Success	cm64-debug:	ndiff test: no significant differences with generic answer.
  Success	cm64-debug-clear-malloc:	ndiff test: no significant differences with generic answer.
  rs6000-aix
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.
  Success	cm64:	ndiff test: no significant differences with generic answer.
  Success	cm64-debug:	ndiff test: no significant differences with generic answer.
  x86_64-linux
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.

  
  

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

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