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Computing Geodesic Paths on Manifolds
 Proc. Natl. Acad. Sci. USA
, 1998
"... The Fast Marching Method [8] is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. In this paper we extend the Fast Marching Method to triangulated domains with the same computational complexity. A ..."
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Cited by 294 (28 self)
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. As an application, we provide an optimal time algorithm for computing the geodesic distances and thereby extracting shortest paths on triangulated manifolds. 1 Introduction Sethian`s Fast Marching Method [8], is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M
The level set method for the mean curvature flow on (IR
, 1997
"... A special numerical method for the mean curvature flow in Euclidean space has been developed by Osher and Sethian in 1988. In the present paper the so called level set method is extended to (IR 3 ; g), where g is an arbitrary metric on IR 3 . By this natural extension it is possible to calculat ..."
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Cited by 5 (0 self)
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A special numerical method for the mean curvature flow in Euclidean space has been developed by Osher and Sethian in 1988. In the present paper the so called level set method is extended to (IR 3 ; g), where g is an arbitrary metric on IR 3 . By this natural extension it is possible
A SecondOrder Fast Marching Eikonal Solver
, 2000
"... INTRODUCTION The fast marching method (Sethian, 1996) is widely used for solving the eikonal equation in Cartesian coordinates. The method's principal advantages are: stability, computational efficiency, and algorithmic simplicity. Within geophysics, fast marching traveltime calculations (Popo ..."
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Cited by 1 (0 self)
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INTRODUCTION The fast marching method (Sethian, 1996) is widely used for solving the eikonal equation in Cartesian coordinates. The method's principal advantages are: stability, computational efficiency, and algorithmic simplicity. Within geophysics, fast marching traveltime calculations
Level Set Methods, with an Application to Modeling the Growth of Thin Films
 in Free Boundary Value Problems, Theory and Applications
, 1998
"... The level set method was devised in 1987 by S. Osher and J.A. Sethian [OSe] as a versatile and useful tool for analyzing the motion of fronts. It has proven to be phenomenally successful as both a theoretical and computational device. In this paper we review its properties, discuss the advances in l ..."
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Cited by 8 (4 self)
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The level set method was devised in 1987 by S. Osher and J.A. Sethian [OSe] as a versatile and useful tool for analyzing the motion of fronts. It has proven to be phenomenally successful as both a theoretical and computational device. In this paper we review its properties, discuss the advances
Convergence of the Optimal Feedback Policies in a. . .
, 1998
"... Introduction to Partial Differential Equations, Princeton University Press, New Jersey, 1976. [18] H. J. Kushner, Probability Methods for Approximations in Stochastic Control and for Elliptic Equations, Academic Press, New York, 1977. [19] H. J. Kushner and P. Dupuis, Numerical Methods for Stochasti ..."
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Introduction to Partial Differential Equations, Princeton University Press, New Jersey, 1976. [18] H. J. Kushner, Probability Methods for Approximations in Stochastic Control and for Elliptic Equations, Academic Press, New York, 1977. [19] H. J. Kushner and P. Dupuis, Numerical Methods
Fast Vortex Methods
 in Proceedings of 1996 ASME Fluids Eng. Summer Meeting
, 1996
"... We present three fast adaptive vortex methods for the 2D Euler equations. All obtain longtime accuracy at almost optimal cost by using four tools: adaptive quadrature, freeLagrangian formulation, the fast multipole method and a nonstandard error analysis. Our error analysis halves the differentiab ..."
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Cited by 1 (0 self)
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the differentiability required of the flow, suggests an efficient new balance of smoothing parameters, and combines naturally with fast summation schemes. Numerical experiments with our methods confirm our theoretical predictions and display excellent longtime accuracy. INTRODUCTION Vortex methods solve the 2D
2D Asymptotic Linearized Inversion Using Upwind Finite Difference Amplitudes
"... High frequency asymptotic inversion for constant density acoustics has been incorporated into TRIP 2D commonshot and commonoffset Kirchhoff code. This approximate solution operator for the linearized constant density acoustic inverse problem uses finite difference solvers for the eikonal and trans ..."
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the inversion output as input) of the data come quite close to fitting it. INTRODUCTION High order essentially nonoscillatory (ENO) finite difference methods give very accurate traveltimes without tracing rays, Osher and Sethian (1988). Using this technique Symes et. al., (1994) have given direct evidence
Optimal Algorithm for Shape from Shading
, 2000
"... An optimal numerical algorithm for the reconstruction of a surface from its shading image is presented. The algorithm solves the 3D reconstruction from a single shading image problem. The shading image is treated as a penalty function and the hight of the reconstructed surface is a weighted distance ..."
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distance. A first order numerical scheme based on Sethian's Fast Marching Method is used to compute the reconstructed surface. The surface is a viscosity solution of an Eikonal equation for the vertical light source case. For the oblique light source case, the surface is the viscosity solution to a
Subscale Capturing in Computational Fluid Dynamics
"... We shall describe numerical methods which were devised for the purpose of computing small scale behavior in fluid dynamics without either fully resolving the whole solution or explicitly tracking certain singular parts of it. These include shockcapturing and frontcapturing. These methods have rece ..."
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with J. Sethian, and more recent work in this area with E. Harabetian, B. Merriman, P. Smereka, M. Sussman, T. Hou and graduate students M. Kang and S. Chen. 1 Introduction In this paper we shall describe numerical methods which were devised for the purpose of computing small scale behavior in fluid
1 Evolving Curves and Surfaces
, 2005
"... sent these boundaries implicitly and model their propagation using appropriate partial differential equations. The boundary is given by level sets of a function φ(x), and they named their technique the Level Set Method. These notes give a short introduction to the method, and for more details we ref ..."
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sent these boundaries implicitly and model their propagation using appropriate partial differential equations. The boundary is given by level sets of a function φ(x), and they named their technique the Level Set Method. These notes give a short introduction to the method, and for more details we
Results 1  10
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