parallel iterative methods for linear systems
We continued our discussion of the parallel Jacobi method
to solve linear systems. Note that the MPI documentation
uses this method to motivate and illustrate non-blocking
communications. We analyzed the speedup.
A simple Maple
worksheet illustrates that the optimal number of processors
depends on the size of the problem.
Click to download
the Maple worksheet.
Using the Laplace equation, we introduced the Red/Black Ordering
to derive another synchronous iteration method.
Bibliography
- Marc Snir, Steve Otto, Steven Huss-Lederman, David Walker,
and Jack Dongarra:
"MPI - The Complete Reference Volume 1, The MPI Core"
second edition, Massachusetts Institute of Technology, 1998.
Online documentation:
The Message Passing Interface (MPI) standard