We study a new formulation for the eikonal equation |∇u| = 1 on a bounded subset of R. Instead of a vector field ∇u, we consider a field P of orthogonal projections on 1-dimensional subspaces, with div P ∈ L. We prove that solutions of this equation propagate direction as in the classical eikonal equation. We also show that solutions exist if and only if the domain is a tubular neighbourhood of...

We present a practical regular grid wave traveltime calculation that is based on Huygens wavefront expansion and grid traveltime mapping. Wavefront expansion is carried out by finite difference approximations to the equations that are equivalent to the Eikonal equation with a fixed time interval. Mapping traveltime from wavefront to regular grids is based on a dynamic ray tracing paraxial appro...

We present an efficient solution to the eikonal equation on parametric manifolds, based on the fast marching approach. This method overcomes the problem of a non-orthogonal coordinate system on the manifold by creating an appropriate numerical stencil. The method is tested numerically and demonstrated by calculating distances on various parametric manifolds. It is further used for two applicati...

We develop a level set method for the computation of multi-valued physical observables (density, velocity, energy, etc.) for the high frequency limit of symmetric hyperbolic systems in any number of space dimensions. We take two approaches to derive the method. The first one starts with a decoupled system of an eikonal eikonal for phase S and a transport equations for density ρ: ∂t S+H(x,∇S) = ...

Abstract We show a connection between global unconstrained optimization of continuous function f and weak KAM theory for an eikonal-type equation arising also in ergodic control. A solution v the critical Hamilton–Jacobi is built by small discount approximation as well long time limit associated evolutive equation. Then represented value control problem with target, whose optimal trajectories a...