EIKONAL EQUATIONS: NEW TWO-SCALE ALGORITHMS AND ERROR ANALYSIS

Hamilton-Jacobi equations arise in a number of seemingly disparate applications, from front propagation to photolithography to robotic navigation. Eikonal equations fall into an important subset representing isotropic optimal control and often are used as a first benchmark for numerical methods. Many of the interesting geometrical properties of Eikonal and related equations are exploited in two families of popular algorithms: the single-pass Fast Marching Methods and the iterative Fast Sweeping Methods. We start by developing a class of two-scale hybrid algorithms that combine the ideas of these prior methods on different scales. These hybrid methods are shown to have a clear advantage compared to other serial algorithms, but more importantly, one of them (“HCM”) is very suitable for parallelization on a shared memory archi-tecture. Our extensive numerical experiments benchmark this parallel HCM against current serial methods and another parallel state-of-the-art solver for the same com-puter architecture. We demonstrate the robustness of the parallel HCM on a wide range of problems, its good scaling in the number of processors, and its efficiency in solving a problem from exploratory geophysics. In the last part, we focus on estimat