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Author, Editor(s)

Author(s):

Göddeke, Dominik
Strzodka, Robert
Turek, Stefan

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dblp
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Not MPG Author(s):

Göddeke, Dominik
Turek, Stefan

BibTeX cite key*:

GoStTu07mixedPrec

Title

Title*:

Performance and accuracy of hardware-oriented native-, emulated- and mixed-precision solvers in FEM simulations

Journal

Journal Title*:

International Journal of Parallel, Emergent and Distributed Systems

Journal's URL:

http://www.tandf.co.uk/journals/titles/17445760.asp

Download URL
for the article:

http://www.informaworld.com/smpp/ftinterface~content=a779508744~fulltext=713240930

Language:

English

Publisher

Publisher's
Name:

Taylor \& Francis

Publisher's URL:


Publisher's
Address:


ISSN:


Vol, No, pp, Date

Volume*:

22

Number:

4

Publishing Date:

January 2007

Pages*:

221-256

Number of
VG Pages:


Page Start:


Page End:


Sequence Number:


DOI:


Note, Abstract, ©

Note:


(LaTeX) Abstract:

In this survey paper, we compare native double precision solvers with emulated- and mixed- precision solvers of linear systems of equations as they typically arise in finite element discretisations. The emulation utilises two single float numbers to achieve higher precision, while the mixed precision iterative refinement computes residuals and updates the solution vector in double precision but solves the residual systems in single precision. Both techniques have been known since the 1960s, but little attention has been devoted to their performance aspects. Motivated by changing paradigms in processor technology and the emergence of highly parallel devices with outstanding single float performance, we adapt the emulation and mixed precision techniques to coupled hardware configurations, where the parallel devices serve as scientific co-processors. The performance advantages are examined with respect to speedups over a native double precision implementation (time aspect) and reduced area requirements for a chip (space aspect). The paper begins with an overview of the theoretical background, algorithmic approaches and suitable hardware architectures. We then employ several conjugate gradient and multigrid solvers and study their behaviour for different parameter settings of the iterative refinement technique. Concrete speedup factors are evaluated on the coupled hardware configuration of a general-purpose CPU and a graphics processor. The dual performance aspect of potential area savings is assessed on a field programmable gate array. In the last part, we test the applicability of the proposed mixed precision schemes with ill-conditioned matrices. We conclude that the mixed precision approach works very well with the parallel co-processors gaining speedup factors of four to five, and area savings of three to four, while maintaining the same accuracy as a reference solver executing everything in double precision.

URL for the Abstract:


Categories,
Keywords:


HyperLinks / References / URLs:


Copyright Message:


Personal Comments:


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Access Level:

Public

Correlation

MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Computer Graphics Group

MPG Subsubunit:

Integrative Scientific Computing

Audience:

experts only

Appearance:

MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort


BibTeX Entry:

@ARTICLE{GoStTu07mixedPrec,
AUTHOR = {G{\"o}ddeke, Dominik and Strzodka, Robert and Turek, Stefan},
TITLE = {Performance and accuracy of hardware-oriented native-, emulated- and mixed-precision solvers in {FEM} simulations},
JOURNAL = {International Journal of Parallel, Emergent and Distributed Systems},
PUBLISHER = {Taylor \& Francis},
YEAR = {2007},
NUMBER = {4},
VOLUME = {22},
PAGES = {221--256},
MONTH = {January},
}


Entry last modified by Robert Strzodka, 02/28/2008
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Editor(s)
Robert Strzodka
Created
12/17/2007 06:11:43 PM
Revision
1.
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Editor
Robert Strzodka
Robert Strzodka


Edit Date
12/17/2007 08:34:03 PM
12/17/2007 06:11:43 PM


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