We review some of the recent advances in level-set methods and their applications. In
particular, we discuss how to impose boundary conditions at irregular domains and free …

We present a review on numerical methods for simulating multiphase and free surface flows.
We focus in particular on numerical methods that seek to preserve the discontinuous nature …

In many nano (opto) electronic devices, the roughness at surfaces and interfaces is of
increasing importance, with roughness often contributing toward losses and defects, which …

The fast marching method is a widely used numerical method for solving the Eikonal
equation arising from a variety of scientific and engineering fields. It is long deemed …

We propose a deep learning strategy to estimate the mean curvature of two-dimensional
implicit interfaces in the level-set method. Our approach is based on fitting feed-forward …

The fast sweeping method is a popular algorithm for solving a variety of static Hamilton–
Jacobi equations. Fast sweeping algorithms for parallel computing have been developed …

Numerical solution of the eikonal equation is frequently used to compute first-arrival travel
times for a given velocity model in seismic applications. Computations for large three …

We present two models of perpetrators' decision-making in extracting resources from a
protected area. It is assumed that the authorities conduct surveillance to counter the …

This paper presents a new method for parallelizing geodesic algorithms on triangle meshes.
Using the half-edge data structure, we define the propagation dependency graph to …

We present a novel Eulerian numerical method to compute global isochrons of a stable
periodic orbit in high dimensions. Our approach is to formulate the asymptotic phase as a …