Solving the Eikonal equation on an adaptive mesh

A fast marching method (FMM) using the line-of-site calculation to solve the eikonal equation is applied to an adaptive mesh. The criteria for refinement are the curvature of the propagating front. It is shown empirically that for cases involving an initial front initiated from a single point in an open three dimensional domain and constant front propagating speed that the FMM with adaptive mesh refinement (AMR) uses roughly an order of magnitude less CPU time and an order of magnitude less CPU memory than the non-AMR FMM to attain a similar level of accuracy. It is also shown that the AMR-FMM refines when the curvature is caused by boundary irregularities and also non-constant front propagating speed.