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- W2308272502 abstract "We use a Schrwave equation formalism to solve the eikonal equation. We show that a solution to the eikonal equation is obtained in the limit as Planck's constant ~ (treated as a free parameter) tends to zero of the solution to the corresponding linear Schrequation. The Schrequation corresponding to the eikonal turns out to be a generalized, screened Poisson equation. Despite being linear, it does not have a closed-form solution for ar- bitrary forcing functions. We use a standard perturbation analysis approach to derive a new algorithm which is guaranteed to converge provided the forc- ing function is bounded and positive. The perturbation technique requires a sequence of discrete convolutions which can be performed in O(N logN) us- ing the Fast Fourier Transform (FFT) where N is the number of grid points. For the Euclidean distance function problem|a special case of the eikonal equation where the forcing function is everywhere identically equal to one| a major advantage of our approach over most other methods is that we do not require a spatial discretization of gradient operators and this contributes to the increased accuracy of our technique. The solution to the eikonal so- lution is recovered from the exponent of the wave function. Since the wave function is computed for a small but non-zero ~, the obtained solution is an approximation. We provide evidence for the usefulness of our technique by comparing the results of our approach with those obtained from popular Hamilton-Jacobi solvers such as the fast sweeping algorithm as well as with" @default.
- W2308272502 created "2016-06-24" @default.
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- W2308272502 date "2011-01-01" @default.
- W2308272502 modified "2023-09-27" @default.
- W2308272502 title "A fast eikonal equation solver using the Schrwave equation" @default.
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