| 1 |
This is a particular example of multi-scale or multi-resolution approach which we also find in CPS713 with cluster algorithms in statistical physics
|
| 2 |
All Physical Systems have different effects going on at different physical length scales
|
| 3 |
The best algorithms build in this in and tailor algorithm for features at each scale
|
| 4 |
In Iterative solvers, we saw in eigenvalue analysis that
-
Short wavelength features converge fast
-
Slow convergence corresponded to long wavelength effects
|
| 5 |
In Multigrid, you precondition matrix to remove long wavelength effects so local iterative solver only has to address short wavelengths
|
| 6 |
This is done recursively so you successively remove effects at wavelengths that increase at each step by a factor of two
|
