WebApr 1, 1991 · The eikonal equation: stability of reaction—diffusion waves on a sphere. Applied computing. Physical sciences and engineering. Physics. Mathematics of computing. Mathematical analysis. Numerical analysis. Comments. Login options. Check if you have access through your login credentials or your institution to get full access on this article. ... WebThe eikonal equation is an equation describing the optimal path of wave propagation, which is the mathematical expression of Fermat’s principle in a physical sense 2 . Since the Fermat's ...
Solution of eikonal equation is locally the distance from a ...
WebThe eikonal equation can also be solved directly without rays. This includes recent finite- difference methods for traveltimes. These methods avoid the ambiguity of multi- valued time-fields by tracking only minimum traveltimes. The direct, numerical solution of the eikonal equation is illustrated by several examples using forward and WebConsider the Eikonal equation (with right handside 1) $$\sum_{i=1}^{n}(\frac{\partial u}{\partial x_i})^2=1$$ I want to see why any solution to this is locally the sum of a distance function from a hypersurface plus a constant. I think I came up with a way but I wonder if there is a simpler way to argue this. Here is what I did: peirch corp
Tug of War games and PDEs on graphs with applications in image …
WebJan 31, 2024 · The eikonal equation is a first-order nonlinear hyperbolic partial differential equation. It represents the high-frequency asymptotic approximation of the wave equation. The fast marching and sweeping methods are commonly used due to their efficiency in numerically solving the eikonal equation. However, these methods suffer from numerical ... An eikonal equation (from Greek εἰκών, image ) is a non-linear first-order partial differential equation that is encountered in problems of wave propagation. The classical eikonal equation in geometric optics is a differential equation of the form $${\displaystyle \nabla u(x) =n(x)}$$ (1) See more The term "eikonal" was first used in the context of geometric optics by Heinrich Bruns. However, the actual equation appears earlier in the seminal work of William Rowan Hamilton on geometric optics See more Several fast and efficient algorithms to solve the eikonal equation have been developed since the 1990s. Many of these algorithms take … See more An eikonal equation is one of the form $${\displaystyle H(x,\nabla u(x))=0}$$ $${\displaystyle u(0,x')=u_{0}(x'),{\text{ for }}x=(x_{1},x')}$$ See more • Hamilton–Jacobi–Bellman equation • Hamilton–Jacobi equation • Fermat's principle • One-way wave equation See more Continuous shortest-path problems Suppose that $${\displaystyle \Omega }$$ is an open set with suitably smooth boundary $${\displaystyle \partial \Omega }$$. The solution to the eikonal equation can be interpreted … See more For simplicity assume that $${\displaystyle \Omega }$$ is discretized into a uniform grid with spacings $${\displaystyle h_{x}}$$ and $${\displaystyle h_{y}}$$ in the x and y directions, … See more • A concrete application is the computation of radiowave attenuation in the atmosphere. • Finding the shape from shading in … See more Webeikonal equation for an initially curved wavefront will be shown in the examples. Evanescent waves and tracking of beam-fields can be analysed by solving the eikonal equation with … mecenat flixbus