Insights from the parallel implementation of efficient algorithms for the fractional calculus

Hdl Handle:
http://hdl.handle.net/10034/613841
Title:
Insights from the parallel implementation of efficient algorithms for the fractional calculus
Authors:
Banks, Nicola E.
Abstract:
This thesis concerns the development of parallel algorithms to solve fractional differential equations using a numerical approach. The methodology adopted is to adapt existing numerical schemes and to develop prototype parallel programs using the MatLab Parallel Computing Toolbox (MPCT). The approach is to build on existing insights from parallel implementation of ordinary differential equations methods and to test a range of potential candidates for parallel implementation in the fractional case. As a consequence of the work, new insights on the use of MPCT for prototyping are presented, alongside conclusions and algorithms for the effective implementation of parallel methods for the fractional calculus. The principal parallel approaches considered in the work include: - A Runge-Kutta Method for Ordinary Differential Equations including the application of an adapted Richardson Extrapolation Scheme - An implementation of the Diethelm-Chern Algorithm for Fractional Differential Equations - A parallel version of the well-established Fractional Adams Method for Fractional Differential Equations - The adaptation for parallel implementation of Lubich's Fractional Multistep Method for Fractional Differential Equations An important aspect of the work is an improved understanding of the comparative diffi culty of using MPCT for obtaining fair comparisons of parallel implementation. We present details of experimental results which are not satisfactory, and we explain how the problems may be overcome to give meaningful experimental results. Therefore, an important aspect of the conclusions of this work is the advice for other users of MPCT who may be planning to use the package as a prototyping tool for parallel algorithm development: by understanding how implicit multithreading operates, controls can be put in place to allow like-for-like performance comparisons between sequential and parallel programs.
Citation:
Banks, N. E. (2015). Insights from the parallel implementation of efficient algorithms for the fractional calculus. (Doctoral dissertation). University of Chester, United Kingdom.
Publisher:
University of Chester
Publication Date:
Jul-2015
URI:
http://hdl.handle.net/10034/613841
Type:
Thesis or dissertation
Language:
en
Appears in Collections:
Theses

Full metadata record

DC FieldValue Language
dc.contributor.authorBanks, Nicola E.en
dc.date.accessioned2016-06-21T09:36:14Zen
dc.date.available2016-06-21T09:36:14Zen
dc.date.issued2015-07en
dc.identifier.citationBanks, N. E. (2015). Insights from the parallel implementation of efficient algorithms for the fractional calculus. (Doctoral dissertation). University of Chester, United Kingdom.en
dc.identifier.urihttp://hdl.handle.net/10034/613841en
dc.description.abstractThis thesis concerns the development of parallel algorithms to solve fractional differential equations using a numerical approach. The methodology adopted is to adapt existing numerical schemes and to develop prototype parallel programs using the MatLab Parallel Computing Toolbox (MPCT). The approach is to build on existing insights from parallel implementation of ordinary differential equations methods and to test a range of potential candidates for parallel implementation in the fractional case. As a consequence of the work, new insights on the use of MPCT for prototyping are presented, alongside conclusions and algorithms for the effective implementation of parallel methods for the fractional calculus. The principal parallel approaches considered in the work include: - A Runge-Kutta Method for Ordinary Differential Equations including the application of an adapted Richardson Extrapolation Scheme - An implementation of the Diethelm-Chern Algorithm for Fractional Differential Equations - A parallel version of the well-established Fractional Adams Method for Fractional Differential Equations - The adaptation for parallel implementation of Lubich's Fractional Multistep Method for Fractional Differential Equations An important aspect of the work is an improved understanding of the comparative diffi culty of using MPCT for obtaining fair comparisons of parallel implementation. We present details of experimental results which are not satisfactory, and we explain how the problems may be overcome to give meaningful experimental results. Therefore, an important aspect of the conclusions of this work is the advice for other users of MPCT who may be planning to use the package as a prototyping tool for parallel algorithm development: by understanding how implicit multithreading operates, controls can be put in place to allow like-for-like performance comparisons between sequential and parallel programs.en
dc.language.isoenen
dc.publisherUniversity of Chesteren
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectparallel algorithmsen
dc.subjectfractional differential equationsen
dc.subjectnumerical approachen
dc.titleInsights from the parallel implementation of efficient algorithms for the fractional calculusen
dc.typeThesis or dissertationen
dc.type.qualificationnamePhDen
dc.type.qualificationlevelDoctoralen
dc.description.advisorFord, Nevilleen
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