Basic HTML version of Foils prepared March 15 00

Foil 16 Multigrid Methods

From Collection of Extra Foils for CPS615 PDE Iterative Solution Discussion CPS615 Spring Semester 00 -- March 00. by Geoffrey C. Fox


1 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
2 Then in simple methods one needs of order N2 iterations to get good results
3 Ironically one goes to large N to get detail as if all you wanted was coarse structure, a smaller mesh would be fine
4 Basic idea in multigrid is key in many areas of science
  • Solve a problem at multiple scales
5 We get coarse structure from small N and fine detail from large N
  • Good qualitative idea but how do we implement?
6 Material taken from http://www.mgnet.org/mgnet/www/mgnet/www/mgnet/www/mgnet/www/ Tutorial by Ulrich Ruede

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