We address the numerical computation of distance maps with respect to Riemannian metrics
of strong anisotropy. For that purpose we solve generalized eikonal equations, discretized …

Nongradient SDEs with small white noise often arise when modeling biological and
ecological time-irreversible processes. If the governing SDE were gradient, the maximum …

We present algorithms for solving high-frequency acoustic scattering problems in complex
domains. The eikonal and transport partial differential equations from the WKB/geometric …

The classical setting of optimal control theory assumes full knowledge of the process
dynamics and the costs associated with every control strategy. The problem becomes much …

We develop a family of compact high-order semi-Lagrangian label-setting methods for
solving the eikonal equation. These solvers march the total 1-jet of the eikonal, and use …

We present a family of fast and accurate Dijkstra-like solvers for the eikonal equation and
factored eikonal equation which compute solutions on a regular grid by solving local …

Sound propagation in air is accurately described by a small perturbation of the ambient
pressure away from a quiescent state. This is the realm of linear acoustics, where the …

We consider three optimal control problems, which focus on continuous path-planning
applications, and each problem deals with a specific challenge. First, we introduce a new …

Surveillance-Evasion games are continuous path planning problems in which an evader
chooses his trajectory to hinder the surveillance by an enemy observer. In the classical …

Four problems at the intersection of optimization and partial differential equations are
presented. First, a problem in remote sensing of the marine atmospheric boundary layer is …