In the attached manuscript, we have coupled the extended finite element
method (X-FEM) to the fast marching method (FMM) for non-planar crack
growth simuations. Unlike the level set method, the FMM is
ideally-suited to advance a monotonically growing front. The FMM is a
single-pass algorithm (no iterations) without any time-step
restrictions. The perturbation crack solutions due to Gao and Rice
(IJF, 1987) and Lai, Movchan and Rodin (IJF, 2002) are used for the
purpose of comparisons. A few of the pertinent cited references can be
found off my X-FEM web page. The final version of the manuscript is now attached.