Kenneth A. Hawick and Daniel P. Playne
Ginzburg-Landau equation, PDE, complex numbers, numerical precision
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-cubed 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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