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High-Order Factorization Based High-Order Hybrid Fast Sweeping Methods for Point-Source Eikonal Equations
SIAM Journal on Numerical Analysis
The solution for the eikonal equation with a point-source condition has an upwind singularity at the source point as the eikonal solution behaves like a distance function at and near the source. As such, the eikonal function is not differentiable at the source so that all formally high-order numerical schemes for the eikonal equation yield first-order convergence and relatively large errors. Therefore, it is a long standing challenge in computational geometrical optics how to compute adoi:10.1137/120901696 fatcat:42gj2pzlyba7rgpabevbt3qf7q