Neighbor-Gradient Single-Pass Method for solving anisotropic eikonal equation


The respected Comrade Kim Jong Un said:

"A high level of basic sciences enables a country's science and technology to make steady progress on a solid foundation."

We have developed a single-pass method for approximating the solution to an anisotropic eikonal equation related to the anisotropic minimum-time optimal trajectory problem.

Ordered Upwind Method (OUM) solves this equation, which is a single-pass method with an asymptotic complexity. OUM uses the search along the accepted front (SAAF) to update the values at considered nodes.

Our technique, which we refer to as "Neighbor-Gradient Single-Pass Method", uses the minimization of the Hamiltonian, in which the gradient is substituted with neighbor gradient information to avoid SAAF.

Our technique is considered in the context of control-theoretic problem. We began by discussing SAAF of OUM.

We then proved some properties of the value function and its gradient, which provides the key motivation for constructing our method. Based on these discussions, we presented a new single-pass method, which is faster since it does not require SAAF. We tested this method with several anisotropic eikonal equations to make sure if it works well while significantly reducing the computational cost.

We have developed a fast single-pass method that is not using SAAF of OUM.

The result have been published in the SCI journal "Journal of Scientific Computing" under the title of "Neighbor-Gradient Single-Pass Method for solving anisotropic eikonal equation" (