In this paper we propose a novel computational technique to solve the Eikonal equation. The proposed method manages the list of active nodes and iteratively updates the solutions on those nodes until they converge. Nodes are added to or removed from the list based on a convergence measure, but the management of this list does not entail the the extra burden of expensive ordered data structures ...

The viscosity solution of static Hamilton-Jacobi equations with a pointsource condition has an upwind singularity at the source, which makes all formally high-order finite-difference scheme exhibit first-order convergence and relatively large errors. To obtain designed high-order accuracy, one needs to treat this source singularity during computation. In this paper, we apply the factorization i...

Recently, a path towards macroscopic, transparent optical cloaking devices that may conceal objects spanning millions of wavelengths has been proposed [1]. Such devices are designed using transformation optics (TO) [2,3]. In this paper, we offer further analysis and improvements to the concept using the method of geometrical optics extended to complex photonic media with an arbitrary dispersion...

Construction of signed distance to a given interface is a topic of special interest to level set methods. There are currently, however, few algorithms that can efficiently produce highly accurate solutions. We introduce an algorithm for constructing an approximate signed distance function through manipulation of values calculated from flow of time dependent eikonal equations. We provide operati...

Traveltime computation is an important part of seismic imaging algorithms. Conventional implementations of Kirchhoff migration require precomputing traveltime tables or include traveltime calculation in the innermost computational loop . The cost of traveltime computations is especially noticeable in the case of 3-D prestack imaging where the input data size increases the level of nesting in co...

Comparison results are obtained between infinity subharmonic and infinity superharmonic functions defined on unbounded domains. The primary new tool employed is an approximation of infinity subharmonic functions that allows one to assume that gradients are bounded away from zero. This approximation also demystifies the proof in the case of a bounded domain. A second, quite different, topic is a...

The purpose of this research is to generate high-aspect-ratioc ellsf or structured grids in the vicinity of boundaries for wall dominated phenomenas ucha sv iscous layers in aerodynamic applications. When suchd omains are discretized for complex geometries, it is importantt hat the grid fits the boundaries well, andt his becomes even more difficultt oa chievew ith strongly curved boundaries. Do...

Article history: Received 19 November 2013 Received in revised form 22 June 2014 Accepted 6 November 2014 Available online 13 November 2014

We discuss the high-energy evolution equation in Quantum Chromodynamics (QCD) in the framework of the color glass condensate. We rewrite the generating functional of QCD with the color glass condensate into a representation with the density of states and a simple eikonal coupling. In this representation we introduce an auxiliary variable which is identified as the quantum color charge density c...

In this paper we review computational techniques for efficiently computing distance functions and geodesics, thereby addressing optimal trajectory problems. These techniques are based on solving the Eikonal equation. Following [30] we first describe how we can numerically solve this equation in a Cartesian grid in O(N) operations, N being the number of grid points. This optimal run-time cost is...