Asynchronous waveform relaxation methods for ordinary differential equations on multiprocessors
Aslam, Sohail
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/22818
Description
Title
Asynchronous waveform relaxation methods for ordinary differential equations on multiprocessors
Author(s)
Aslam, Sohail
Issue Date
1990
Doctoral Committee Chair(s)
Gear, C.W.
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computer Science
Language
eng
Abstract
Multiprocessor architecture machines offer promising opportunities to achieve significant speedup in solving large systems of Ordinary Differential Equations (ODEs.) Often, large systems of ODEs have components that vary with different rates. If numerical solution is computed for the system as a whole, the step size will limited by the fastest component. Multirate methods avoid this restriction by partitioning the system of equations into smaller subsystems and integrating each separately. Step sizes are chosen for each subsystem and are synchronized among slow and fast subsystems. A partitioned system of ODEs can be integrated in parallel but synchronization of step sizes can severely limit speedup. The synchronization overhead can be avoided by using waveform relaxation methods that iteratively integrate subsystems. Asynchronous waveform relaxation methods are proposed in this study. By extending the results for synchronous waveform relaxation methods, the asynchronous waveform methods are shown to converge under certain conditions. The design and implementation issues of such methods on multiprocessors as a general purpose code are presented. The performance of the code in solving a variety of systems of ODEs is tested and the results presented. These results show significant speedup can be achieved over sequential waveform methods for the solution of ODEs.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
