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SIAM Review, 1999
The author considers numerical methods for solving the nonlinear eikonal equation \[ |\nabla u(x)|= F(x)\quad\text{in }\Omega\subset \mathbb{R}^2\quad\text{or }\mathbb{R}^3,\tag{1} \] under given boundary conditions \(u=g\) on some prescribed curve or surface \(\Gamma\) in \(\Omega\).
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The author considers numerical methods for solving the nonlinear eikonal equation \[ |\nabla u(x)|= F(x)\quad\text{in }\Omega\subset \mathbb{R}^2\quad\text{or }\mathbb{R}^3,\tag{1} \] under given boundary conditions \(u=g\) on some prescribed curve or surface \(\Gamma\) in \(\Omega\).
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Generalized fast marching method: applications to image segmentation
Numerical Algorithms, 2008In this paper, we propose a segmentation method based on the generalized fast marching method (GFMM) developed by Carlini et al. (submitted). The classical fast marching method (FMM) is a very efficient method for front evolution problems with normal velocity (see also Epstein and Gage, The curve shortening flow. In: Chorin, A., Majda, A.
Carole Le Guyader +5 more
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A Generalized Fast Marching Method on Unstructured Triangular Meshes
SIAM Journal on Numerical Analysis, 2013In this paper we extend the generalized fast marching method (GFMM) presented in [E. Carlini et al., SIAM J. Numer. Anal., 46 (2008), pp. 2920--2952] to unstructured meshes. The GFMM generalizes the classical fast marching method, in the sense that it can be applied to propagate interfaces with time-dependent and changing sign velocity.
CARLINI, Elisabetta +2 more
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Some Improvements of the Fast Marching Method
SIAM Journal on Scientific Computing, 2001Summary: The fast marching method published by \textit{J. A. Sethian} [Proc. Natl. Acad. Sci. USA 93, No. 4, 1591-1595 (1996; Zbl 0852.65055)] is an optimally efficient algorithm for solving problems of front evolution where the front speed is monotonic. It has been used in a wide variety of applications such as robotic path planning [\textit{R. Kimmel}
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SPE Reservoir Evaluation and Engineering, 2019
Recently, there has been an increasing interest in enhanced oil recovery (EOR) from shale-oil reservoirs, including injection of carbon dioxide (CO2) and field gas.
Atsushi Iino +2 more
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Recently, there has been an increasing interest in enhanced oil recovery (EOR) from shale-oil reservoirs, including injection of carbon dioxide (CO2) and field gas.
Atsushi Iino +2 more
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SPE Journal, 2019
Recently, fast–marching–method (FMM) –based flow simulation has shown great promise for rapid modeling of unconventional oil and gas reservoirs. Currently, the application of FMM–based simulation has been limited to using tartan grids to model the ...
Xu Xue +4 more
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Recently, fast–marching–method (FMM) –based flow simulation has shown great promise for rapid modeling of unconventional oil and gas reservoirs. Currently, the application of FMM–based simulation has been limited to using tartan grids to model the ...
Xu Xue +4 more
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A Massive Parallel Fast Marching Method
2016In this paper we present a novel technique based on domain decomposition which enables us to perform the fast marching method (FMM) [4] on massive parallel high performance computers (HPC) for given triangulated geometries. The FMM is a widely used numerical method and one of the fastest serial state-of-the-art techniques for computing the solution to ...
Roberto Croce +4 more
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Optimal control using the Fast Marching Method
2009 35th Annual Conference of IEEE Industrial Electronics, 2009This paper presents the applications of the Fast Marching and the Buffered Fast Marching Methods to solve typical control problems. Calculus of Variations and Optimal Control problems can be solved using the Euler-Lagrange or the Pontryagin equations and solving analytically or numerically the corresponding differential equations systems.
Luis Moreno +3 more
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Robust skeletonization using the fast marching method
IEEE International Conference on Image Processing 2005, 2005We have recently developed a level set based-framework for computing medial curves or curve skeletons CS for arbitrary 2D shapes as well as tubular and articulated 3D objects. The proposed framework is robust, fully automatic, computationally efficient, and produces curve skeletons that are connected, centered, thin, and less sensitive to boundary ...
Aly A. Farag, M.S. Hassouna
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2004
The fast marching method was introduced by Sethian [190, 191, 192] as a computationally efficient solution to eikonal equations on flat domains. A related method was presented by Tsitsiklis in [205]. The fast marching method was extended to triangulated surfaces by Kimmel and Sethian in [112].
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The fast marching method was introduced by Sethian [190, 191, 192] as a computationally efficient solution to eikonal equations on flat domains. A related method was presented by Tsitsiklis in [205]. The fast marching method was extended to triangulated surfaces by Kimmel and Sethian in [112].
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