Parallel Methods for PDE Eigenvalue Problems |
This page is devoted to the research project
Parallel Methods for PDE Eigenvalue Problems
which was supported by EPSRC grant GR/M59075. The investigators were Alastair Spence (PI) and Ivan Graham .
From the grant we employed Eero Vainikko as a
Postdoctoral Research Assistant and Joerg Berns-Mueller
as a PhD student.
Our industrial collaborator was Andrew Cliffe of Serco Assurance
The project was concerned with the computation of eigenavalue problems in PDE, using Arnoldi and inverse iteration strategies with variable shifts. The project involves both the analysis of shift-invert eigenvalue solvers with inexact inner solves and the parallel implementation of such algorithms on bifurcation problems in fluid dynamics.
The eigenvalue solvers demand repeated solves of algebraic systems arising from discretisations of shifted systems of PDEs. For this we have developed the DOUG package as a fast parallel solver. In this part of the project most of the effort has been in extending the DOUG code to the case of systems of PDEs and the design and implementation of parallel preconditioners, especially for the incompressible Navier-Stokes equations.
Here is the final
report for the grant (March 31st 2003). The work
is continuing
and further updates will be posted here in due course.
Currently there are four papers: