We compare the computational performance of the Fast Marching Method, the Fast Sweeping Method and the Fast Iterative Method to determine a numerical solution to the eikonal equation. We point out how the Fast Iterative Method outperforms the other two thanks to its parallel processing capabilities.

A method is presented for computing the cross-spectral density of a special class of partially coherent fields in which the coherent modes obey an eikonal equation. This method allows for statistical analysis of optical systems based on simple ray tracing.

We prove the convergence of a first order finite difference scheme approximating a non local eikonal Hamilton-Jacobi equation. The non local character of the problem makes the scheme not monotone in general. However, by using in a convenient manner the convergence result for monotone scheme of Crandall Lions, we obtain the same bound |∆X| + ∆t for the rate of convergence.

The medial-axis transform, also called skeleton, is a shape abstraction proposed by computer vision. The concept is closely related to cyclographic maps, a tool developed by descriptive geometry to investigate distance functions, and to the solu tion of the eikonal equation. We discuss these connections and their implications on techniques for computing the skeleton.

We prove existence of a solution for a polymer crystal growth model describing the movement of a front (Γ(t)) evolving with a nonlocal velocity. In this model the nonlocal velocity is linked to the solution of a heat equation with source δΓ. The proof relies on new regularity results for the eikonal equation, in which the velocity is positive but merely measurable in time and with Hölder bounds...

We present a class of self-similar solutions of the kinematic model equation, introduced by V.A. Davydov, A.S. Mikhailov, and V.S. Zykov. This equation is designed to describe the dynamics of spiral waves in excitable media. In this model the sharply located spiral fronts are regarded as planar curves. If the tip neither grows nor retracts in the tangential direction and if their normal velocit...

The concept of physics-informed neural networks has become a useful tool for solving differential equations due to its flexibility. A few approaches use this solve the eikonal equation that describes first-arrival traveltimes waves propagating in smooth heterogeneous velocity models. However, challenge is exacerbated by models producing caustics, resulting instabilities and deterioration accura...

This paper is devoted to both theoretical and numerical study of a system involving an eikonal equation of Hamilton-Jacobi type and a linear conservation law as it comes out of the geometrical optics expansion of the wave equation or the semiclassical limit for the Schrödinger equation. We first state an existence and uniqueness result in the framework of viscosity and duality solutions. Then w...

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...

Transmission Ultrasound Computed Tomography (CT) is strongly affected by the acoustic refraction properties of the imaged tissue, and proper modeling and correction of these effects is crucial to achieving high-quality image reconstructions. A method that can account for these refractive effects solves the governing Eikonal equation within an iterative reconstruction framework, using a wave-fro...