Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
A fast level set method for propagating interfaces
Journal of Computational Physics
Semi-Lagrangian methods for level set equations
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Level set methods: an overview and some recent results
Journal of Computational Physics
Motion of curves in three spatial dimensions using a level set approach
Journal of Computational Physics
Journal of Computational Physics
High-frequency wave propagation by the segment projection method
Journal of Computational Physics
Geometric optics in a phase-space-based level set and Eulerian framework
Journal of Computational Physics
An Introduction to Eulerian Geometrical Optics (1992–2002)
Journal of Scientific Computing
Simplicial isosurfacing in arbitrary dimension and codimension
Journal of Computational Physics
Local level set method in high dimension and codimension
Journal of Computational Physics
Hi-index | 31.45 |
Wavefront construction in geometrical optics has long faced the twin difficulties of dealing with multi-valued forms and resolution of wavefront surfaces. A recent change in viewpoint, however, has demonstrated that working in phase space on bicharacteristic strips using eulerian methods can bypass both difficulties. The level set method for interface dynamics makes a suitable choice for the eulerian method. Unfortunately, in three-dimensional space, the setting of interest for most practical applications, the advantages of this method are largely offset by a new problem: the high dimension of phase space. In this work, we present new types of level set algorithms that remove this obstacle and demonstrate their abilities to accurately construct wavefronts under high resolution. These results propel the level set method forward significantly as a competitive approach in geometrical optics under realistic conditions.