eikonal equation sentence in Hindi
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- We can solve the eikonal equation using the method of characteristics.
- For the eikonal equation, many numerical schemes are available.
- In geometric optics, the eikonal equation describes the phase fronts of waves.
- :I don't think we have any artickle on the eikonal equation.
- The second equation is the eikonal equation.
- For the Eikonal equation, this correction can be done by solving a boundary value problem.
- This is due to this being effectively the temporal integration of the Eikonal equation with a fixed front velocity.
- Sweeping algorithms are highly efficient for solving Eikonal equations when the corresponding characteristic curves do not change direction very often.
- For the Eikonal equation, due to the good behavior of the refraction index just a simple Shooting method can be used.
- Sethian's "'fast marching method ( FMM ) "'was the first " fast and efficient " algorithm created to solve the Eikonal equation.
- Although fast sweeping methods have existed in control theory, it was first proposed for Eikonal equations by Hongkai Zhao, an applied mathematician at the University of California, Irvine.
- The fast sweeping method is an iterative method which uses upwind difference for discretization and uses Gauss Seidel iterations with alternating sweeping ordering to solve the discretized Eikonal equation on a rectangular grid.
- Sweeping algorithms such as the "'fast sweeping method ( FSM ) "'are highly efficient for solving Eikonal equations when the corresponding characteristic curves do not change direction very often.
- The more technical eikonal equation can be solved using standard differential equations solvers offered by a few numerical software packages mentioned in the Wikipedia List of numerical analysis software and it offers a higher precision order.
- Under reasonable hypothesis on the " initial " data, the eikonal equation admits a local solution, but a global smooth solution ( e . g . a solution for all time in the geometrical optics case ) is not possible.
- If " ? " is a subset of the Euclidean space "'R " "'n " with piecewise smooth boundary, then the signed distance function is differentiable almost everywhere, and its gradient satisfies the eikonal equation
- In the case of an Eikonal equation, the first method to do so was developed by Jon N . Tsitsiklis using a control-theoretic approach : followed shortly by Sethian's work on high order finite difference Dijkstra-like Fast Marching Methods.
- Given that a smooth data fitting curve n ( altitude ) is provided by the ITU for the refraction index n, and that the values of n differs from 1 only by something of the order 10 & minus; 4, a numerical solution of the eikonal equation can be considered.
- With the definition k : = \ nabla _ x \ varphi, \ omega : =-\ varphi _ t, the eikonal equation is precisely the dispersion relation that results by plugging the plane wave solution e ^ { i ( k \ cdot x-\ omega t ) } into the wave equation.
- Ray optics and electromagnetism are related by the fact that the eikonal equation gives a second electromagnetic formula of the same form as the potential equation above where the line of constant potential has been replaced by a line of constant phase, and the force lines have been replaced by normal vectors coming out of the constant phase line at right angles.
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