Computational Science Technical Note CSTN-070

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Numerical Simulation of the Complex Ginzburg-Landau Equation on GPUs with CUDA

K. A. Hawick and D. P. Playne

Archived January 2009, Revised September 2010

Abstract

The Time Dependent Ginzburg Landau(TDGL) equation models a complex scalar field and is used to study a variety of different physical systems and exhibits phase transitional behaviours that necessitate study using numerical simulation methods. We employ fast data-parallel simulation algorithms on Graphical Processing Units (GPUs) and report on performance data and stability tradeoffs from using various implementations of both 32-bit and 64-bit complex numbers. Using NVIDIA's Compute Unified Device Architecture (CUDA) programming language running on a GTX480 GPU, we are able to simulate the TDGL with relatively large simulation system sizes of $256^3$ cells and we discuss the relative computational tradeoffs between numerical accuracy and stability using different methods as well as different data precisions.

Keywords: Ginzburg-Landau equation; PDE; complex numbers; numerical precision; CUDA, GPUs.

Full Document Text: PDF version.

Citation Information: BiBTeX database for CSTN Notes.

BiBTeX reference:

@INPROCEEDINGS{CSTN-070,
  author = {K. A. Hawick and D. P. Playne},
  title = {{Numerical Simulation of the Complex Ginzburg-Landau Equation on
	GPUs with CUDA}},
  booktitle = {Proc. IASTED International Conference on Parallel and Distributed
	Computing and Networks (PDCN)},
  year = {2011},
  number = {CSTN-070},
  pages = {39-45},
  address = {Innsbruck, Austria},
  month = {15-17 February},
  publisher = {IASTED},
  doi = {10.2316/P.2011.719-036},
  institution = {Massey University},
  timestamp = {2009.02.28}
}


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