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 …

The level set method was devised by S. Osher and JA Sethian (1988, J. Comput. Phys. 79,
12–49) as a simple and versatile method for computing and analyzing the motion of an …

In this paper a fast swee** method for computing the numerical solution of Eikonal
equations on a rectangular grid is presented. The method is an iterative method which uses …

We describe and implement an algorithm for computing the set of reachable states of a
continuous dynamic game. The algorithm is based on a proof that the reachable set is the …

We present a real-time crowd model based on continuum dynamics. In our model, a
dynamic potential field simultaneously integrates global navigation with moving obstacles …

Interface problems arise in many applications. For example, when there are two different
materials, such as water and oil, or the same material but at different states, such as water …

This paper gives a systematic introduction to HMM, the heterogeneous multiscale methods,
including the fundamental design principles behind the HMM philosophy and the main …

A wide range of computer vision applications require an accurate solution of a particular
Hamilton-Jacobi (HJ) equation, known as the Eikonal equation. In this paper, we propose an …

It is well known that time-dependent Hamilton–Jacobi–Isaacs partial differential equations
(HJ PDEs) play an important role in analyzing continuous dynamic games and control theory …

In this paper, we propose a PDE-based level set method. Traditionally, interfaces are
represented by the zero level set of continuous level set functions. Instead, we let the …