Multigrid Methods
We remarked that key problem with iterative methods is that got detail (short wavelength) correct but that convergence was controlled by coarse (long wavelength) structure
Then in simple methods one needs of order N2 iterations to get good results
Ironically one goes to large N to get detail as if all you wanted was coarse structure, a smaller mesh would be fine
Basic idea in multigrid is key in many areas of science
- Solve a problem at multiple scales
We get coarse structure from small N and fine detail from large N
- Good qualitative idea but how do we implement?
Material taken from http://www.mgnet.org/mgnet/www/mgnet/www/mgnet/www/mgnet/www/ Tutorial by Ulrich Ruede