Example b212h: Using Grid-based FEM with 3D BoxMG as the elliptic solver on a One-Element Domain

There are a few things to note about BoxMG. First, it can only be used for domains that can be mapped to a square in 2D or a cube in 3D. It was brought into CMISS for solving large scale cardiac tissue problems as it is ideally suited for such domains. We often say that such domains are logically rectangular. Second, there are many options when using BoxMG but I have hidden most of them from the unexperienced user. The most important option to be aware of is the relaxation (or smoothing) method. If the problem is highly anisotropric, either from conductivities or a stretched mesh, then you must use line relaxation in 2D and plane relaxation in 3D. Finally, it should be noted that no benefit will be gained until the number of unknowns begins approaching 500,000. For less than 250,000 unknowns it will probably be faster to use either LU or CG with ILU. These are not hard and fast rules but something to keep in mind.

References:

Solving the cardiac bidomain equations for discontinuous conductivities, IEEE Trans. Biomedical Engineering, 53, 7, pp. 1265-1272, 2006

Fast elliptic solvers for cardiac bioelectric modeling on structured meshes, submitted to Computers in Biology and Medicine in 2007

The comfile run by this example is as follows:

#
# Example b211h
#
# ------------

# -------------------------------------
# Set parameters and coors for problem
# -------------------------------------
fem define para;r;cube;example
fem define coor;r;cube;example

# -------------------------------------
# Define elements and fibres
# -------------------------------------
fem define node;r;cube;example
fem define base;r;cube;example
fem define elem;r;cube;example
fem define fibr;d
fem define elem;r;cube;example fibre

# -------------------------------------
# Define grids
# -------------------------------------
fem define grid;r;cube;example
fem update grid geometry
fem group grid external as boundary
fem group grid xi1 low as stimulus
fem group grid xi1 high as dirichlet

# -------------------------------------
# Define equations, materials, and cells
# -------------------------------------
fem define equa;r;cube;example class 1,2
fem define mate;r;cube;example class 1,2
fem define cell;r;cube;example class 1,2

# ---------------------------------------------
# Define initial and boundary conds and solver
# ---------------------------------------------
fem define init;r;cube;example class 1,2
fem define solv;r;pcg;example class 1
fem define solv;r;bmgpl;example class 2

#############################################
#
# With this example if you replace bmgpl in  
# the above line with bmtpt you will see the
# poor convergence as a result of the stretched
# mesh.  Note that the domain is
#
#      [0,10] X [0,1] X [0,1]
#
#############################################

# -------
#  SOLVE
# -------
fem solve to 1.0 class 1,2

Additional testing commands:

#Testing example b212h
fem li grid yq index v class 1

Files used by this example are:

Name               Modified     Size

example_b212h.com  27-Apr-2007  1.6k
bmgpl.ipsolv       27-Apr-2007  2.4k
bmgpt.ipsolv       27-Apr-2007  2.5k
cube.ipbase        27-Apr-2007  2.4k
cube.ipcell        27-Apr-2007  1.7k
cube.ipcoor        27-Apr-2007  570 
cube.ipelem        27-Apr-2007  404 
cube.ipelfb        27-Apr-2007  233 
cube.ipequa        27-Apr-2007  1.5k
cube.ipgrid        27-Apr-2007  600 
cube.ipinit        27-Apr-2007  905 
cube.ipmate        27-Apr-2007  1.7k
cube.ipnode        27-Apr-2007  1.8k
cube.ippara        27-Apr-2007  6.2k
cube.ipsolv        27-Apr-2007  1.8k
pcg.ipsolv         27-Apr-2007  2.1k
test_output.com    27-Apr-2007   54 

Download the entire example:

Name                                 Modified     Size

examples_b_b2_b21_b212_b212h.tar.gz  28-Apr-2007   10k

Testing status by version:

Testing status by file:

• signal
  

  rs6000-aix
  SIGSEGV	cm:	exit due to SIGSEGV signal.

  
  
• cmiss_test.out
  

  i686-linux
  Failure	cm:	ndiff test: significant differences with generic answer.
  Failure	cm-debug:	ndiff test: significant differences with generic answer.
  mips-irix
  Failure	cm:	ndiff test: significant differences with generic answer.
  Failure	cm-debug:	ndiff test: significant differences with generic answer.
  Failure	cm-debug-clear-malloc:	ndiff test: significant differences with generic answer.
  Failure	cm-debug-clear-malloc7:	ndiff test: significant differences with generic answer.
  Failure	cm64:	ndiff test: significant differences with generic answer.
  Failure	cm64-debug:	ndiff test: significant differences with generic answer.
  rs6000-aix
  Missing	cm:	output file not generated for ndiff; generic answer.
  Failure	cm-debug:	ndiff test: significant differences with generic answer.
  Failure	cm64:	ndiff test: significant differences with generic answer.
  Failure	cm64-debug:	ndiff test: significant differences with generic answer.
  x86_64-linux
  Failure	cm:	ndiff test: significant differences with generic answer.
  Failure	cm-debug:	ndiff test: significant differences with generic answer.

  
  

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Input last modified: Fri Apr 27 08:54:23 2007