Solving large-scale three-dimensional heat equations on CUDA

Heat equation is the model of many real-world simulation problems. This paper presents a method for solving large-scale three-dimensional heat equation on CUDA. The implicit differential method is used to discretize the equation and the preconditioned Conjugate Gradient algorithm is applied to solve the discretized equation. The implementing methods for the sparse matrix-vector multiplication and the vector inner product on CUDA are given. And the experimental results show that GPUs can speed up the heat equation solving process greatly.