The article is concerned with the development and comparison of three di erent algorithms for the computation of rst-arrival traveltimes: the fast marching method (FMM), the group marching method (GMM), and a secondorder nite di erence eikonal solver. GMM is introduced as a variant of FMM. It proceeds the solution by advancing a selected group of grid points at a time, rather than sorting the s...

Abstract In this paper, we study a nonlocal approximation of the time-dependent (local) Eikonal equation with Dirichlet-type boundary conditions, where kernel in problem is properly scaled. Based on theory viscosity solutions, prove existence and uniqueness solutions both local problems, as well regularity properties these time space. We then derive error bounds between solution to that one, co...

The response of Michelson interferometers to weak plane gravitational waves is computed at one order accuracy beyond the eikonal equation. modulation electromagnetic field amplitude and polarisation are taken into account by solving transport equations geometrical optics with boundary conditions adapted laser interferometry. Considering both DC balanced homodyne readout schemes, explicit formul...

We characterize the denseness of singular set distance function from a $\mathcal{C}^1$-hypersurface in terms an inner ball condition and we address problem existence viscosity solutions Eikonal equation whose (i.e. non-differentiability points) is not no-where dense.