Mitigating the Curse of Dimensionality: A Parallel Fast Sweeping Method for the Eikonal Equation

The “Curse of Dimensionality” refers to the prohibitive cost of computing numerical solutions to problems of high dimensionality. We provide a method for solving the Eikonal Equation in parallel that efficiently uses all available processors. The advantages of our approach are that (1) the efficiency does not plateau for a large number of threads, i.e. we can use any number of processors and (2) the algorithmic complexity is the same as the serial implementation. We compare to the current state-of-the-art method for a number of test problems