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GPU-Accelerated LOBPCG Method with Inexact Null-Space Filtering for Solving Generalized Eigenvalue Problems in Computational Electromagnetics Analysis with Higher-Order FEM

Part of: Partial differential equations, boundary value problems Numerical methods Numerical linear algebra Computer aspects of numerical algorithms Algorithms - Computer Science

Published online by Cambridge University Press:  28 July 2017

A. Dziekonski ,
M. Rewienski ,
P. Sypek ,
A. Lamecki  and
M. Mrozowski
A. Dziekonski*
Affiliation:
Department of Microwave and Antenna Engineering, Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, Gdansk 80-23, Poland; CUDA Research Center for Computational Electromagnetics atGdansk University of Technology (2012-2016)
M. Rewienski*
Affiliation:
Department of Microwave and Antenna Engineering, Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, Gdansk 80-23, Poland; CUDA Research Center for Computational Electromagnetics atGdansk University of Technology (2012-2016)
P. Sypek*
Affiliation:
Department of Microwave and Antenna Engineering, Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, Gdansk 80-23, Poland; CUDA Research Center for Computational Electromagnetics atGdansk University of Technology (2012-2016)
A. Lamecki*
Affiliation:
Department of Microwave and Antenna Engineering, Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, Gdansk 80-23, Poland; CUDA Research Center for Computational Electromagnetics atGdansk University of Technology (2012-2016)
M. Mrozowski*
Affiliation:
Department of Microwave and Antenna Engineering, Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, Gdansk 80-23, Poland; CUDA Research Center for Computational Electromagnetics atGdansk University of Technology (2012-2016)
*
*Corresponding author. Email addresses:adziek@eti.pg.gda.pl (A. Dziekonski), mrewiens@eti.pg.gda.pl (M. Rewienski), psypek@eti.pg.gda.pl (P. Sypek), adam.lamecki@ieee.org (A. Lamecki), m.mrozowski@ieee.org (M. Mrozowski)
*Corresponding author. Email addresses:adziek@eti.pg.gda.pl (A. Dziekonski), mrewiens@eti.pg.gda.pl (M. Rewienski), psypek@eti.pg.gda.pl (P. Sypek), adam.lamecki@ieee.org (A. Lamecki), m.mrozowski@ieee.org (M. Mrozowski)
*Corresponding author. Email addresses:adziek@eti.pg.gda.pl (A. Dziekonski), mrewiens@eti.pg.gda.pl (M. Rewienski), psypek@eti.pg.gda.pl (P. Sypek), adam.lamecki@ieee.org (A. Lamecki), m.mrozowski@ieee.org (M. Mrozowski)
*Corresponding author. Email addresses:adziek@eti.pg.gda.pl (A. Dziekonski), mrewiens@eti.pg.gda.pl (M. Rewienski), psypek@eti.pg.gda.pl (P. Sypek), adam.lamecki@ieee.org (A. Lamecki), m.mrozowski@ieee.org (M. Mrozowski)
*Corresponding author. Email addresses:adziek@eti.pg.gda.pl (A. Dziekonski), mrewiens@eti.pg.gda.pl (M. Rewienski), psypek@eti.pg.gda.pl (P. Sypek), adam.lamecki@ieee.org (A. Lamecki), m.mrozowski@ieee.org (M. Mrozowski)
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Abstract

This paper presents a GPU-accelerated implementation of the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method with an inexact nullspace filtering approach to find eigenvalues in electromagnetics analysis with higher-order FEM. The performance of the proposed approach is verified using the Kepler (Tesla K40c) graphics accelerator, and is compared to the performance of the implementation based on functions from the Intel MKL on the Intel Xeon (E5-2680 v3, 12 threads) central processing unit (CPU) executed in parallel mode. Compared to the CPU reference implementation based on the Intel MKL functions, the proposed GPU-based LOBPCG method with inexact nullspace filtering allowed us to achieve up to 2.9-fold acceleration.

Keywords

LOBPCGinexact nullspace filteringmultilevel preconditioningFEMGPUparallel computing

MSC classification

Secondary: 65N25: Eigenvalue problems 68W10: Parallel algorithms 65Y05: Parallel computation 65F08: Preconditioners for iterative methods 65F10: Iterative methods for linear systems 74S05: Finite element methods
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 4 , October 2017 , pp. 997 - 1014
Copyright
Copyright © Global-Science Press 2017 

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