We develop a family of fast methods for approximating the solutions to a wide class of static
Hamilton--Jacobi PDEs; these fast methods include both semi-Lagrangian and fully Eulerian …

Additive manufacturing enables the nearly uncompromised production of optimized
topologies. However, due to the overhang limitation, some designs require a large number …

We introduce a modification of the fast-marching algorithm, which solves the anisotropic
eikonal equation associated to an arbitrary continuous Riemannian metric \calM on a two-or …

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 …

The optimal path planning problem is considered for rovers. Tip-over risk is accurately
modelled using direction dependence. In the previous direction-independent model, the …

We introduce a new and efficient numerical method for multicriterion optimal control and
single criterion optimal control under integral constraints. The approach is based on …

In this work we provide a novel approach to homogenization for a class of static Hamilton–
Jacobi (HJ) equations, which we call metric HJ equations. We relate the solutions of the HJ …

Stochastic shortest path (SSP) problems arise in a variety of discrete stochastic control
contexts. An optimal solution to such a problem is typically computed using the value …

A novel mathematical framework for modeling folds in structural geology is presented. All the
main fold classes from the classical literature: parallel folds, similar folds, and other fold …

We introduce a family of highly efficient (non-iterative) numerical methods for a wide class of
hybrid control systems. The application of Dijkstra's classical method to a discrete optimal …