Page 129 - Process Modelling and Simulation With Finite Element Methods

116 Process Modelling and Simulation with Finite Element Methods

output (j ,3) =I2;
output(j,4)=1.+11/12; %Last column is the Nusselt

end %closes the for-loop
dlmwrite('convect.dat',output,','); %writes comma-delimited ASCII
quit %stops MATLAB
The m-file freec0nv.m (see http:Neyrie.shef.ac.uWfemlab) has all these
alterations present. This m-file was executed under linux as a background job
using the following command:

matlab -nojvm <freeconv.m >err 2>err &
The -nojvm (no Java machine) flag stops the MATLAB GUI from loading,
although if you are in X-Windows, you will get a brief splash screen for
MATLAB. The command above generated the data in the file convect.dat used
in Figure 3.3 to plot the Nusselt vs. Rayleigh number dependence. The file err
contains the re-direction of the standard output (usually the screen) and the
standard err (usually the screen) units. When called with input re-direction from
an m-file, MATLAB does not launch the GUI, but evaluates the m-file
programme directly. This is the most efficient way to conduct MATLAB
computations, as the processor and memory are not tied up multitasking the GUI,
so can pay better attention to your computation. The parametric continuation in
Rayleigh number m-file generates a series of entries in the err file of the form:
Iter ErrEst Damping Stepsize nfun njac nfac nbsu
0 1 0 0 0
1 7.644421253e-07 1.0000000 0.1057807343 2 1 1 2
These entries all show error estimates of 0(10-7), which implies that the first
iteration on each new Rayleigh parameter value converges in one Newton
iteration step. Since the convergence is so good, we could probably take bigger
steps if the goal were only to reach the endpoint Rayleigh value. However,
adapting the stepsize in the continuation parameter would need to be automated
on the convergence performance, with substantial logic encoded for trapping
non-convergent continuation steps. The simple linear continuation conducted
here is easiest to code.
When using parametric continuation to arrive at the final parameter value,
running the MATLAB m-file as a background job does not help. The FEMLAB
GUI is not entered and will not be accessible with the solution results. FEMLAB
has its own MATLAB workspace, however, so if you wish, you can run your edited
m-files in the FEMLAB GUI. Just open the File Menu, Select Open (m-file) and
FEMLAl3 will evaluate all your commands sequentially. Even those commands
that execute non-FEMLAB functions in MATLAB. For instance, if you run
freec0nv.m in this way, you will eventually arrive at Ra=50, even though the for
command for looping is not a FEMLAB command.