A method for the Computational Frequency Sweep Analysis of Nonlinear ODEs using GPU Acceleration

ABSTRACT

Computational sweep analysis of nonlinear ODEs (ordinary differential equations) is of importance in engineering system analysis and design. Sweep analyses usually demand intense computational power according to the number of points and the number of system parameters. This paper presents an efficient parallel algorithm for the sweep analysis of nonlinear ODEs based on graphical processing unit acceleration. The developed method preserves the jump phenomenon characteristics intrinsic to nonlinear ODEs and reduces the effects of irregular computational load. Experiments were realized using Duffing equation by sweeping frequency, amplitude, and equation coefficients. Directly, data parallel implementation and proposed implementations are compared to show the efficiency of the proposed method. Experimental results show that the new method provides significant reductions in the computational durations when compared to sequential implementation.

KEYWORDS:

• Duffing equation
• Frequency response
• GPU computing
• Nonlinear systems
• Sweep analysis

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Devrim Akgün

Devrim Akgün has been working at the Department of Computer Engineering at Sakarya University. He received his PhD degree in 2008 from Sakarya University. His current research interests include Parallel Computing, Signal and Image Processing, and Machine Learning.

Corresponding author. E-mail: [email protected]

İlyas Çankaya

İlyas Çankaya has been working at the Department of Electrical and Electronics Engineering at Yıldırım Beyazıt University. He received his PhD degree in 1998 from The University of Sussex. His current research interests include Control Systems, Nonlinear Frequency Response Analysis, Signal and Image Processing.

E-mail: [email protected]

Sezgin Kaçar

Sezgin Kaçar has been working at the Department of Electrical and Electronics Engineering at Sakarya University. He received his PhD degree in 2014 from Sakarya University. His current research interests include Control Systems, Chaos, Signal and Image Processing.

E-mail: [email protected]