Basic HTML version of Foils prepared 15 March 1996

Foil 29 Mathematical Structure of Exemplar 16 by 16 Multigrid Solution

From Further PDE Solvers for the NAS Benchmarks CPSP713 Case studies in Computational Science -- Spring Semester 1996. by Geoffrey C. Fox
First Solve the 2 by 2 matrix A4 on the coarsest grid
Use A4 to precondition and solve grid 3 to get 4 by 4 matrix A3
Use A3 to precondition and solve grid 2 to get 8 by 8 matrix A2
Use A2 to precondition and solve grid 1 to get 16 by 16 matrix A1
Note both Domain Decomposition and Multigrid have Good Physical Motivation but they are quite different
  • Multigrid works from the bottom (fine scale) up
  • Domain Decomposition from the Macroscopic Structure down

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