GPU Acceleration of Partial Differential Equation Solvers

P. Iosifidis; P. Weit; P. Marlappan; R. Flanagan; I. Spence; P. Kilpatrick; J. Fitzsimons

doi:10.4203/ccp.107.45

GPU Acceleration of Partial Differential Equation Solvers

P. Iosifidis, P. Weit, P. Marlappan, R. Flanagan, I. Spence, P. Kilpatrick, J. Fitzsimons

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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Abstract

Differential equations are often directly solvable by analytical means only in their one dimensional version. Partial differential equations are generally not solvable by analytical means in two and three dimensions, with the exception of few special cases. In all other cases, numerical approximation methods need to be utilized. One of the most popular methods is the finite element method. The main areas of focus, here, are the Poisson heat equation and the plate bending equation. The purpose of this paper is to provide a quick walkthrough of the various approaches that the authors followed in pursuit of creating optimal solvers, accelerated with the use of graphical processing units, and comparing them in terms of accuracy and time efficiency with existing or self-made non-accelerated solvers.

Original language	English
Title of host publication	Proceedings of the Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering
Editors	P. Ivanyl, B.H.V. Topping
Publisher	Civil-Comp Press
Volume	107
ISBN (Print)	978-1-905088-62-1
DOIs	https://doi.org/10.4203/ccp.107.45
Publication status	Published - 2015
Event	Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering - Dubrovnik, Croatia Duration: 24 Mar 2015 → 27 Mar 2015

Conference

Conference	Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering
Country/Territory	Croatia
City	Dubrovnik
Period	24/03/2015 → 27/03/2015

Keywords

GPU acceleration
finite element
partial differential equations
Poisson
plates
plate bending

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10.4203/ccp.107.45

GPU Acceleration of Partial Differential Equation Solvers
Copyright 2015 Civil-Comp Press Final version was published in Proceedings of the Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, DOI: 10.4203/ccp.107.45
Accepted author manuscript, 530 KB

Cite this

Iosifidis, P., Weit, P., Marlappan, P., Flanagan, R., Spence, I., Kilpatrick, P., & Fitzsimons, J. (2015). GPU Acceleration of Partial Differential Equation Solvers. In P. Ivanyl, & B. H. V. Topping (Eds.), Proceedings of the Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering (Vol. 107). Article 45 Civil-Comp Press. https://doi.org/10.4203/ccp.107.45

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title = "GPU Acceleration of Partial Differential Equation Solvers",

abstract = "Differential equations are often directly solvable by analytical means only in their one dimensional version. Partial differential equations are generally not solvable by analytical means in two and three dimensions, with the exception of few special cases. In all other cases, numerical approximation methods need to be utilized. One of the most popular methods is the finite element method. The main areas of focus, here, are the Poisson heat equation and the plate bending equation. The purpose of this paper is to provide a quick walkthrough of the various approaches that the authors followed in pursuit of creating optimal solvers, accelerated with the use of graphical processing units, and comparing them in terms of accuracy and time efficiency with existing or self-made non-accelerated solvers.",

keywords = "GPU acceleration, finite element, partial differential equations, Poisson, plates, plate bending",

author = "P. Iosifidis and P. Weit and P. Marlappan and R. Flanagan and I. Spence and P. Kilpatrick and J. Fitzsimons",

year = "2015",

doi = "10.4203/ccp.107.45",

language = "English",

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editor = "P. Ivanyl and B.H.V. Topping",

booktitle = "Proceedings of the Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering",

publisher = "Civil-Comp Press",

note = "Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering ; Conference date: 24-03-2015 Through 27-03-2015",

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Iosifidis, P, Weit, P, Marlappan, P, Flanagan, R, Spence, I , Kilpatrick, P & Fitzsimons, J 2015, GPU Acceleration of Partial Differential Equation Solvers. in P Ivanyl & BHV Topping (eds), Proceedings of the Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering. vol. 107, 45, Civil-Comp Press, Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, Dubrovnik, Croatia, 24/03/2015. https://doi.org/10.4203/ccp.107.45

GPU Acceleration of Partial Differential Equation Solvers. / Iosifidis, P.; Weit, P.; Marlappan, P. et al.
Proceedings of the Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering. ed. / P. Ivanyl; B.H.V. Topping. Vol. 107 Civil-Comp Press, 2015. 45.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - GPU Acceleration of Partial Differential Equation Solvers

AU - Iosifidis, P.

AU - Weit, P.

AU - Marlappan, P.

AU - Flanagan, R.

AU - Spence, I.

AU - Kilpatrick, P.

AU - Fitzsimons, J.

PY - 2015

Y1 - 2015

N2 - Differential equations are often directly solvable by analytical means only in their one dimensional version. Partial differential equations are generally not solvable by analytical means in two and three dimensions, with the exception of few special cases. In all other cases, numerical approximation methods need to be utilized. One of the most popular methods is the finite element method. The main areas of focus, here, are the Poisson heat equation and the plate bending equation. The purpose of this paper is to provide a quick walkthrough of the various approaches that the authors followed in pursuit of creating optimal solvers, accelerated with the use of graphical processing units, and comparing them in terms of accuracy and time efficiency with existing or self-made non-accelerated solvers.

AB - Differential equations are often directly solvable by analytical means only in their one dimensional version. Partial differential equations are generally not solvable by analytical means in two and three dimensions, with the exception of few special cases. In all other cases, numerical approximation methods need to be utilized. One of the most popular methods is the finite element method. The main areas of focus, here, are the Poisson heat equation and the plate bending equation. The purpose of this paper is to provide a quick walkthrough of the various approaches that the authors followed in pursuit of creating optimal solvers, accelerated with the use of graphical processing units, and comparing them in terms of accuracy and time efficiency with existing or self-made non-accelerated solvers.

KW - GPU acceleration

KW - finite element

KW - partial differential equations

KW - Poisson

KW - plates

KW - plate bending

U2 - 10.4203/ccp.107.45

DO - 10.4203/ccp.107.45

M3 - Conference contribution

SN - 978-1-905088-62-1

VL - 107

BT - Proceedings of the Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering

A2 - Ivanyl, P.

A2 - Topping, B.H.V.

PB - Civil-Comp Press

T2 - Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering

Y2 - 24 March 2015 through 27 March 2015

ER -

GPU Acceleration of Partial Differential Equation Solvers

Abstract

Conference

Keywords

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