CUDA acceleration for solving three-dimension time-dependent parabolic partial differential equation

In this paper, we propose a detailed description of programming the time-dependent three-dimensional (3D) parabolic partial differential equation on graphics processing units (GPU). To this end, we frame the problem as the progression stencil on a 3D surface. We adopt finite-different time-domain (FDTD) method to obtain the stencil corresponding to the partial differential equation, which is then programmed according to CUDA (compute unified device architecture) parallel programming model using GPU's shared memory. Experimental results show that comparing with the program that runs on a single CPU (central processing unit), the current GPU version can greatly reduce the run time so as to improve the performance, accelerate the computation speed, and enable the large-scale simulation.