GPU Acceleration of Solving Parabolic Partial Differential Equations Using Difference Equations

Parabolic partial differential equations are often used to model systems involving heat transfer, acoustics, and electrostatics. The need for more complex models with increasing precision drives greater computational demands from processors. Since solving these types of equations is inherently parallel, GPU computing offers an attractive solution for drastically decreasing time to completion, power usage, and increasing the computation per dollar. However, since GPU computing involves a much different programming paradigm than traditional processors, techniques for optimizing solvers must still be developed. This paper presents several optimization strategies for accelerating solvers using CUDA to implement difference equations and compares their performances to a standard processor. The results demonstrate that different strategies should be used for different GPU cards, such as the C1060 and GTX 480, resulting in up to 197 times and 257 times single-precision and up to 133 and 163 times doubleprecision speedups respectively.