A generalized front marching algorithm for the solution of the eikonal equation

A new front marching algorithm for solving the eikonal equation is presented. An important property of the algorithm is that it can be used on nodes that are located on highly distorted grids or on nodes that are randomly located. When the nodes are located on an orthogonal grid, the method is first-order accurate and is shown to be a generalization of the front marching algorithm in (Proc. Natl. Acad. Sci. 93 (4) (1996) 1591). The accuracy of the method is also shown to be dependent on the principle curvature of the wave front solution. Numerical results on a variety of node configurations as well as on shadow, nonconvex and nondifferentiable solutions are presented.