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

K.A. Hawick and D.P. Playne
Computer Science, Institute for Information and Mathematical Sciences, Massey University, North Shore 102-904, Auckland, New Zealand
Technical Report CSTN-070, Massey University, 2010


   title={Numerical Simulation of the Complex Ginzburg-Landau Equation on GPUs with CUDA},

   author={Hawick, KA and Playne, DP},


   organization={Massey University, Tech. Rep. CSTN-070, January 2010, to appear in Proc. IASTED International Conference on Parallel and Distributed Computing and Networks (PDCN), 14-16 Feb. 2011, in Innsbruck, Austria}


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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.
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