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Parallel Low-Storage Runge-Kutta Solvers for ODE Systems with Limited Access Distance

URN to cite this document: urn:nbn:de:bvb:703-opus-7136

Title data

Korch, Matthias ; Rauber, Thomas:
Parallel Low-Storage Runge-Kutta Solvers for ODE Systems with Limited Access Distance.
Bayreuth , 2010 . - (Bayreuth Reports on Parallel and Distributed Systems ; 1 )

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Abstract

We consider the solution of initial value problems (IVPs) of large systems of ordinary differential equations (ODEs) for which memory space requirements determine the choice of the integration method. In particular, we discuss the space-efficient sequential and parallel implementation of embedded Runge-Kutta (RK) methods. We focus on the exploitation of a special structure of commonly appearing ODE systems, referred to as "limited access distance", to improve scalability and memory usage. Such systems may arise, for example, from the semi-discretization of partial differential equations (PDEs). The storage space required by classical RK methods is directly proportional to the dimension n of the ODE system and the number of stages s of the method. We propose an implementation strategy based on a pipelined processing of the stages of the RK method and show how the memory usage of this computation scheme can be reduced to less than three storage registers by an overlapping of vectors without compromising the choice of method coefficients or the potential for efficient stepsize control. We analyze and compare the scalability of different parallel implementation strategies in detailed runtime experiments on different parallel architectures.

Further data

Item Type: Project report, research report, survey
Keywords: Gewöhnliche Differentialgleichung; Runge-Kutta-Verfahren; Parallelverarbeitung; Lokalität <Informatik>; Speicherbedarf; Ordinary Differential Equations; Runge-Kutta Methods; Parallel Computing; Locality; Storage Space
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Computer Science
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-opus-7136
Date Deposited: 25 Apr 2014 09:36
Last Modified: 25 Apr 2014 09:36
URI: https://epub.uni-bayreuth.de/id/eprint/428

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