Red Black Parallel Gauss Seidel IV
Fortunately very irregular problems like power systems tend not to be huge.
- 100’s or 10,000’s not billions of points
- Thus can use very difficult optimized “full matrix exploiting zero structure” algorithms
In PDE case, one can show for some elliptic problems that red black can be better than original ordering
For some hyperbolic equations used in computational fluid dynamics, this is not so clear and SOR methods are used
If one has more complex differencing schemes e.g. fourth order differencing, then red-black does not work but a scheme with more colors (and more update phases) can be devised
- Difficulty is irregular graphs not complex stencils