Optimization: Running Time VS Desired Filling Ratio for Refinement Area

Jonathan and I were trying to do some optimization on the refinement patches, as the smaller the patches are the more resources (memory and computing time) it needs:

​https://clover.pas.rochester.edu/trac/astrobear/blog/bliu02272012

The current algorithm works as the following: if the filling ratio is less than the desired ratio, it cuts the refinement patch into smaller ones until the filling ratio is larger than the desired ratio according to the inflections of ErrFlags.

In Figure 1 filling ratio of the patch (big box) is 40%. When the desired filling ratio is larger than 40%, AMR goes to smaller patches. We can see the running time increases when Desired filling ratio goes beyond 40% in Figure 2.

Figure 1
http://www.pas.rochester.edu/~bliu/Optimization/patch1.png


Figure 2
http://www.pas.rochester.edu/~bliu/Optimization/timeVSfilling.png



For refinement patch in Figure 3, however, the current algorithm couldn't find smaller patches even when the filling ratio is less than the designed one.

Figure 3
http://www.pas.rochester.edu/~bliu/Optimization/patch2.png


Figure 4
http://www.pas.rochester.edu/~bliu/Optimization/timeVSfilling_2.png

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