Rarefaction fans are common phenomena known to degrade the rate of convergence of numerical methods. The factored Eikonal equation was developed to address rarefaction fans caused by point sources, but not other more complicated cases. For example, in the following "maze navigation" task, around several "bad" corners(with white line segment), rarefaction fans cause numerical artifacts(in the first figure, whereas resolved in the second).
In this project, we developed a "just-in-time factoring" technique, which factors the 2D rarefactions arising from either non-smoothness of the boundary or discontinuities in PDE coefficients. Joint work with Professor Alexander Vladimirsky.