| This thesis introduces Adaptive Mesh Refinement (AMR) to the Fast Marching Method (FMM) that solves the eikonal equation. Although AMR can be applied to any FMM, in this thesis the Line-Of-Site (LOS) FMM is used mainly because it can be applied to any grid type, structured or unstructured, and also performs better on an adaptive mesh than some other FMMs such as the Generalized Fast Marching Method. It is shown that the line-of-site method achieves greater accuracy without sacrificing CPU cycles. In addition to AMR, the feasibility of parallelization of the LOS-AMR is investigated. The initial motivation for solving the eikonal equation is its application to detonation shock dynamics. This thesis also considers applying the LOS-FMM to optical waveguides that would involve a step function for the speed of propagation. |
