Generating numerical solutions to the eikonal equation and its many variations has a broad range of applications in both the natural and computational sciences. Efficient solvers on cutting-edge, parallel architectures require new algorithms that may not be theoretically optimal, but that are designed to allow asynchronous solution updates and have limited memory access patterns. This paper pre...

Applying the fast marching method to solve the eikonal equation on the 3-D SEG/EAGE salt-dome model demonstrates two key features of the method, stability and efficiency. Such an application, also reveals some of the accuracy deficiencies of the Cartesian-coordinate implementation of the fast marching method. The accuracy is improved by applying the fast marching method in spherical coordinates...

Approximating light charged point-like particles in terms of (nonextremal) dilatonic black holes is shown to lead to certain pathologies in Planckian scattering in the eikonal approximation, which are traced to the presence of a (naked) curvature singularity in the metric of these black holes. The existence of such pathologies is confirmed by analyzing the problem in an 'external metric' formul...

We discuss present predictions for the total γγ and γp cross-sections, highlighting why predictions differ. We present results from the Eikonal Minijet Model and improved predictions based on soft gluon resummation.

I discuss recent progress in the calculation of two-loop QCD corrections in the eikonal approximation. I present specific results for the UV structure of the corrections. Presented at DPF2002, Williamsburg, Virginia, May 24-28, 2002

It is known that the Hamiltonian of the eikonal equation for an anisotropic medium may be nonconvex, which excludes the application of Fermat’s minimum-time principle related to minimum-time control problems. The idea proposed in this paper consists in finding a conflict control problem (differential game) whose Hamiltonian coincides with the Hamiltonian of the eikonal equation. It turns out th...

Spectroscopic properties of nuclei are accessible with projectile fragmentation reactions, but approximations made in the reaction theory can limit the accuracy of the determinations. We examine here two models that have rather different approximations for the nucleon wave function, the target interaction, and the treatment of the finite duration of the reaction. The nucleon-target interaction ...

The fast marching algorithm, and its variants, solves numerically the generalized eikonal equation associated to an underlying riemannian metric M. A major challenge for these algorithms is the non-isotropy of the riemannian metric, which magnitude is characterized by the anisotropy ratio κ(M) ∈ [1,∞]. Applications of the eikonal equation to image processing [1, 3] often involve large anisotrop...

We present and analyze a fast algorithm for directly computing the measure of a generalized Voronoi region associated with generators of arbitrary co-dimension. The algorithm is based upon solving one Eikonal equation to generate a kernel-based operator whose iteration accumulates “mass” along the closest generator. In particular, the algorithm does not require the computation of the ridge set ...

This paper presents a novel solver for the eikonal equation that is designed to run efficiently on massively parallel systems. The proposed method manages a list of active nodes and iteratively updates the solutions on those grid points until they converge. The management of the list does not entail the extra burden of ordered data structures. The proposed method has suboptimal worst-case perfo...