March 25, 2005, 3:00 p.m. GWC 604
Using magnitudes of entries of differential systems in the analysis of convergence of waveform relaxation applied to the systems
Since magnitudes of elements of many differential systems that occur
in real life are distributed between very small and very large numbers,
it is worthwhile to establish the roles which are played by these elements
in waveform iterations.
It has been observed that convergence of waveform relaxation applied
systems with entries of smaller magnitudes is faster than the same
waveform relaxation scheme applied to systems with entries of larger
magnitudes. In this talk the influence of the elements of differential
systems on convergence of waveform relaxation is investigated
and new convergence theorems are presented.
It is also shown that for some stiff systems,
convergence of waveform relaxation depends on the order
in which the waveform iterations are performed.
Using the elements of the systems we formulate conditions
which order the waveform iterations in such a way that
the resulting iteration scheme converges with the fastest rate.
Our theoretical investigations are confirmed by numerical experiments.
To illustrate the advantage of waveform relaxation applied to nonlinear
problems, an example from atmospheric chemistry is presented.
For further information please contact: