A GPU-Accelerated Tensorization Implementation of the Fast Sweeping Method for Solving Eikonal Equations

Summary The fast sweeping method (FSM) is a widely used numerical scheme for solving eikonal equations. It employs a local solver at each grid point and use Gauss-Seidel iteration to calculate the traveltime field. Due to the Gauss-Seidel iteration, the conventional programming of FSM is implemented by element-wise operations, making it difficult to leverage convenient GPU parallelization. This constraint hinders the potential for further improving the computational efficiency of the traveltime field, especially when dealing with large-scale models. In this paper, we adopt the Jacobi iteration instead and propose a tensorization implementation of FSM for factored eikonal equation with a first-order Lax-Friedrichs local solver. Particularly, it is very easy to carry out this implementation on computing device equipped with GPUs. Numerical experiments show that, although the number of iterations required for the algorithm to converge has increased a lot, tensor programming can greatly save computation time with almost no additional memory requirements.