Using graphical processing units to solve the multidimensional Ginzburg-Landau equation

We demonstrate the use of ultrafast hardware, based on a graphical processing unit (GPU), to solve the complex Ginzburg-Landau equation. We implement an improved finite-difference time-domain method. We utilize parallel processing of our numerical procedure, resulting in tremendous acceleration in the execution of routines and substantial reduction of cost. Simulations are performed in two and three spatial dimensions with time as the marching variable. The numerical algorithm is also implemented on a CPU to make a comparison with the GPU. An acceleration of about 95 times is achieved. The benefits are discussed in detail and the results are presented visually to achieve the best solution strategy for the given problem. (paper)