A new approach for solving evolution problems in time-parallel way

Nabil R. Nassif, Noha Makhoul Karam, Yeran Soukiassian

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

With the advent of massively parallel computers with thousands of processors, a large amount of work has been done during the last decades in order to enable a more effective use of a higher number of processors, by superposing parallelism in time-domain, even though it is known that time-integration is inherently sequential, to parallelism in the space-domain[8]. Consequently, many families of predictor-corrector methods have been proposed, allowing computing on several time-steps concurrently[5], [6]. The aim of our present work is to develop a new parallel-in-time algorithm for solving evolution problems, based on particularities of a rescaling method that has been developed for solving different types of partial and ordinary differential equations whose solutions have a finite existence time[9]. Such method leads to a sliced-time computing technique used to solve independently rescaled models of the differential equation. The determining factor for convergence of the iterative process are the predicted values at the start of each time slice. These are obtained using "ratio-based" formulae. In this paper we extend successfully this method to reaction diffusion problems of the form ut = Δum + aup, with their solutions having a global existence time when p ≤ m ≤ 1. The resulting algorithm RaPTI provides perfect parallelism, with convergence being reached after few iterations.

Original languageEnglish
Title of host publicationComputational Science - ICCS 2006
Subtitle of host publication6th International Conference, Proceedings
PublisherSpringer Verlag
Pages148-155
Number of pages8
ISBN (Print)3540343792, 9783540343790
DOIs
Publication statusPublished - 1 Jan 2006
Externally publishedYes
EventICCS 2006: 6th International Conference on Computational Science - Reading
Duration: 28 May 200631 May 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3991 LNCS - I
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

OtherICCS 2006: 6th International Conference on Computational Science
CityReading
Period28/5/0631/5/06

Fingerprint

Evolution Problems
Ordinary differential equations
Partial differential equations
Parallelism
Differential equations
Predictor-corrector Methods
Reaction-diffusion Problems
Computing
Rescaling
Iterative Process
Parallel Computers
Time Integration
Slice
Global Existence
Time Domain
Ordinary differential equation
Partial differential equation
Differential equation
Iteration

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Nassif, N. R., Karam, N. M., & Soukiassian, Y. (2006). A new approach for solving evolution problems in time-parallel way. In Computational Science - ICCS 2006: 6th International Conference, Proceedings (pp. 148-155). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3991 LNCS - I). Springer Verlag. https://doi.org/10.1007/11758501_24

A new approach for solving evolution problems in time-parallel way. / Nassif, Nabil R.; Karam, Noha Makhoul; Soukiassian, Yeran.

Computational Science - ICCS 2006: 6th International Conference, Proceedings. Springer Verlag, 2006. p. 148-155 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3991 LNCS - I).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Nassif, NR, Karam, NM & Soukiassian, Y 2006, A new approach for solving evolution problems in time-parallel way. in Computational Science - ICCS 2006: 6th International Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3991 LNCS - I, Springer Verlag, pp. 148-155, ICCS 2006: 6th International Conference on Computational Science, Reading, 28/5/06. https://doi.org/10.1007/11758501_24
Nassif NR, Karam NM, Soukiassian Y. A new approach for solving evolution problems in time-parallel way. In Computational Science - ICCS 2006: 6th International Conference, Proceedings. Springer Verlag. 2006. p. 148-155. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/11758501_24
Nassif, Nabil R. ; Karam, Noha Makhoul ; Soukiassian, Yeran. / A new approach for solving evolution problems in time-parallel way. Computational Science - ICCS 2006: 6th International Conference, Proceedings. Springer Verlag, 2006. pp. 148-155 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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