Osher, Stanley
Overview
Works:  94 works in 252 publications in 2 languages and 4,522 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Collector, Other, Dedicatee 
Classifications:  QA1, 532.0151 
Publication Timeline
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Most widely held works by
Stanley Osher
Level set methods and dynamic implicit surfaces by
Stanley Osher(
Book
)
24 editions published between 1899 and 2012 in English and held by 423 WorldCat member libraries worldwide
Promotes the use of level set methods by scientists and engineers working on moving interface problems. This book presents the essential mathematical and numerical techniques. It is suitable for those interested in modeling dynamic interfaces with numerical methods that can handle topology changes and singularities
24 editions published between 1899 and 2012 in English and held by 423 WorldCat member libraries worldwide
Promotes the use of level set methods by scientists and engineers working on moving interface problems. This book presents the essential mathematical and numerical techniques. It is suitable for those interested in modeling dynamic interfaces with numerical methods that can handle topology changes and singularities
Largescale computations in fluid mechanics(
Book
)
9 editions published in 1985 in English and held by 290 WorldCat member libraries worldwide
9 editions published in 1985 in English and held by 290 WorldCat member libraries worldwide
Geometric level set methods in imaging, vision, and graphics by
Stanley Osher(
Book
)
25 editions published between 2003 and 2011 in English and held by 273 WorldCat member libraries worldwide
This title explains and apples new level set methods to problems and applications in computer vision, graphics, and imaging. It has a useful compilation of survey chapters written by leading researchers in the field, emphasizing the applications of the methods
25 editions published between 2003 and 2011 in English and held by 273 WorldCat member libraries worldwide
This title explains and apples new level set methods to problems and applications in computer vision, graphics, and imaging. It has a useful compilation of survey chapters written by leading researchers in the field, emphasizing the applications of the methods
Convergence of generalized MUSCL schemes by
Stanley Osher(
Book
)
4 editions published in 1984 in English and held by 237 WorldCat member libraries worldwide
4 editions published in 1984 in English and held by 237 WorldCat member libraries worldwide
The nonconvex multidimensional Riemann problem for HamiltonJacobi equations by
Stanley Osher(
Book
)
5 editions published in 1989 in English and held by 185 WorldCat member libraries worldwide
Simple inequalities are presented for the Riemann problem for a Hamilton Jacobi equation in N space dimension when neither the initial data nor the Hamiltonian need be convex (or concave). The initial data is globally continuous, affine in each orthant, with a possible jump in normal derivative across each coordinate plane, x sub i = 0. The inequalities become equalities whereever a maxmin equals a minmax and thus an exact closed form solution to this problem is then obtained. Keywords: Hamilton Jacobi equations; Riemann problem; Godunov scheme
5 editions published in 1989 in English and held by 185 WorldCat member libraries worldwide
Simple inequalities are presented for the Riemann problem for a Hamilton Jacobi equation in N space dimension when neither the initial data nor the Hamiltonian need be convex (or concave). The initial data is globally continuous, affine in each orthant, with a possible jump in normal derivative across each coordinate plane, x sub i = 0. The inequalities become equalities whereever a maxmin equals a minmax and thus an exact closed form solution to this problem is then obtained. Keywords: Hamilton Jacobi equations; Riemann problem; Godunov scheme
Two papers on similarity of certain Volterra integral operators by
Stanley Osher(
Book
)
17 editions published in 1967 in 3 languages and held by 184 WorldCat member libraries worldwide
17 editions published in 1967 in 3 languages and held by 184 WorldCat member libraries worldwide
Recent advances in scientific computing and partial differential equations : international conference on the occasion of Stanley
Osher's 60th birth day, December 1215, 2002, Hong Kong Baptist University, Hong Kong(
Book
)
5 editions published in 2003 in English and held by 180 WorldCat member libraries worldwide
5 editions published in 2003 in English and held by 180 WorldCat member libraries worldwide
Triangle based TVD schemes for hyperbolic conservation laws by
Institute for Computer Applications in Science and Engineering(
Book
)
6 editions published in 1990 in English and held by 177 WorldCat member libraries worldwide
A triangle based TVD (total variation diminishing) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedure. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based nonoscillatory approximations which, like this scheme, approximate the flux to second order accuracy. Numerical results for linear advection and Burgers' equation are presented. Keywords: Hyperbolic conservation laws; Limiters; Triangular threads. (jhd)
6 editions published in 1990 in English and held by 177 WorldCat member libraries worldwide
A triangle based TVD (total variation diminishing) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedure. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based nonoscillatory approximations which, like this scheme, approximate the flux to second order accuracy. Numerical results for linear advection and Burgers' equation are presented. Keywords: Hyperbolic conservation laws; Limiters; Triangular threads. (jhd)
High order essentially nonoscillatory schemes for HamiltonJacobi equations by
Stanley Osher(
Book
)
5 editions published in 1990 in English and held by 163 WorldCat member libraries worldwide
HamiltonJacobi (HJ) equations are frequently encountered in applications, e.g. in control theory and differential games. HJ equations are closely related to hyperbolic conservation laws  in one space dimension the former is simply the integrated version of the latter. Similarity also exists for the multidimensional case, and this is helpful in the design of difference approximations. In this paper we investigate high order essentially nonoscillatory (ENO) schemes for HJ equations, which yield uniform high order accuracy in smooth regions and resolve discontinuities in the derivatives sharply. The ENO scheme construction procedure is adapted from that for hyperbolic conservation laws. We numerically test the schemes on a variety of onedimensional and twodimensional problems, including a problem related to control optimization, and observe high order accuracy in smooth regions, good resolution of discontinuities in the derivatives, and convergence to viscosity solutions. (edc)
5 editions published in 1990 in English and held by 163 WorldCat member libraries worldwide
HamiltonJacobi (HJ) equations are frequently encountered in applications, e.g. in control theory and differential games. HJ equations are closely related to hyperbolic conservation laws  in one space dimension the former is simply the integrated version of the latter. Similarity also exists for the multidimensional case, and this is helpful in the design of difference approximations. In this paper we investigate high order essentially nonoscillatory (ENO) schemes for HJ equations, which yield uniform high order accuracy in smooth regions and resolve discontinuities in the derivatives sharply. The ENO scheme construction procedure is adapted from that for hyperbolic conservation laws. We numerically test the schemes on a variety of onedimensional and twodimensional problems, including a problem related to control optimization, and observe high order accuracy in smooth regions, good resolution of discontinuities in the derivatives, and convergence to viscosity solutions. (edc)
Efficient implementation of essentially nonoscillatory shock capturing schemes, II by
ChiWang Shu(
Book
)
5 editions published between 1987 and 1988 in English and held by 160 WorldCat member libraries worldwide
In the computation of discontinuous solutions of hyperbolic conservation laws, TVD (total variation diminishing), TVB (total variation bounded) and the recently developed ENO (essentially nonoscillatory) schemes have proven to be very useful. In this paper two improvements are discussed: a simple TVD RungeKutta type time discretization, and an ENO construction procedure based on fluxes rather than on cell averages. These improvements simplify the schemes considerablyespecially for multi dimensional problems or problems with forcing terms. Preliminary numerical results are also given. Keywords: Construction laws; Essentially non oscillatory; TVD; Runge Kutta method; Numerical analysis
5 editions published between 1987 and 1988 in English and held by 160 WorldCat member libraries worldwide
In the computation of discontinuous solutions of hyperbolic conservation laws, TVD (total variation diminishing), TVB (total variation bounded) and the recently developed ENO (essentially nonoscillatory) schemes have proven to be very useful. In this paper two improvements are discussed: a simple TVD RungeKutta type time discretization, and an ENO construction procedure based on fluxes rather than on cell averages. These improvements simplify the schemes considerablyespecially for multi dimensional problems or problems with forcing terms. Preliminary numerical results are also given. Keywords: Construction laws; Essentially non oscillatory; TVD; Runge Kutta method; Numerical analysis
Uniformly highorder accurate nonoscillatory schemes by
Ami Harten(
Book
)
3 editions published in 1985 in English and held by 142 WorldCat member libraries worldwide
The authors begin the construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first order accuracy, in the sense of truncation error, at extrema of the solution. This paper constructs a uniformly second order approximation, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution form its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell. Additional Keywords: Computations; Charts; operators(mathematics). (Author)
3 editions published in 1985 in English and held by 142 WorldCat member libraries worldwide
The authors begin the construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first order accuracy, in the sense of truncation error, at extrema of the solution. This paper constructs a uniformly second order approximation, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution form its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell. Additional Keywords: Computations; Charts; operators(mathematics). (Author)
Level set and PDE based reconstruction methods in imaging : Cetraro, Italy, 2008 by
Martin Burger(
Book
)
11 editions published in 2013 in English and held by 96 WorldCat member libraries worldwide
This book takes readers on a tour through modern methods in image analysis and reconstruction based on level set and PDE techniques, the major focus being on morphological and geometric structures in images. The aspects covered include edgesharpening image reconstruction and denoising, segmentation and shape analysis in images, and image matching. For each, the lecture notes provide insights into the basic analysis of modern variational and PDEbased techniques, as well as computational aspects and applications
11 editions published in 2013 in English and held by 96 WorldCat member libraries worldwide
This book takes readers on a tour through modern methods in image analysis and reconstruction based on level set and PDE techniques, the major focus being on morphological and geometric structures in images. The aspects covered include edgesharpening image reconstruction and denoising, segmentation and shape analysis in images, and image matching. For each, the lecture notes provide insights into the basic analysis of modern variational and PDEbased techniques, as well as computational aspects and applications
Entropy condtion satisfying approximations for the full potential equations of transonic flow by
Stanley Osher(
Book
)
1 edition published in 1984 in English and held by 85 WorldCat member libraries worldwide
1 edition published in 1984 in English and held by 85 WorldCat member libraries worldwide
High resolution schemes and the entropy condition by
Stanley Osher(
Book
)
3 editions published in 1983 in English and held by 85 WorldCat member libraries worldwide
3 editions published in 1983 in English and held by 85 WorldCat member libraries worldwide
Fast wavelet based algorithms for linear evolution equations by
Björn Engquist(
Book
)
6 editions published in 1992 in English and held by 81 WorldCat member libraries worldwide
We devise a class of fast wavelet based algorithms for linear evolution equations whose coefficients are time independent. The method draws on the work of Beylkin, Coifman, and Rokhlin 1 which they applied to general CalderonZygmund type integral operators. We apply a modification of their idea to linear hyperbolic and parabolic equations, with spatially varying coefficients. A significant speedup over standard methods is obtained when applied to hyperbolic equations in one space dimension and parabolic equations in multidimensions. wavelets; hyperbolic; parabolic; numerical methods
6 editions published in 1992 in English and held by 81 WorldCat member libraries worldwide
We devise a class of fast wavelet based algorithms for linear evolution equations whose coefficients are time independent. The method draws on the work of Beylkin, Coifman, and Rokhlin 1 which they applied to general CalderonZygmund type integral operators. We apply a modification of their idea to linear hyperbolic and parabolic equations, with spatially varying coefficients. A significant speedup over standard methods is obtained when applied to hyperbolic equations in one space dimension and parabolic equations in multidimensions. wavelets; hyperbolic; parabolic; numerical methods
High order filtering methods for approximating hyperbolic systems of conservation laws by
Frédéric Lafon(
Book
)
4 editions published in 1990 in English and held by 81 WorldCat member libraries worldwide
In the computation of discontinuous solutions of hyperbolic systems of conservation laws, the recently developed ENO (Essentially NonOscillatory) schemes appear to be very useful. However, they are computationally costly compared to simple central difference methods. In this paper we develop a filtering method which uses simple central differencing of arbitrarily high order accuracy, except when a novel local test indicates the development of spurious oscillations. At these points, generally few in number, we use the full ENO apparatus, maintaining the high order of accuracy, but removing spurious oscillations. Numerical results indicate the success of the method. We obtain high order of accuracy in regions of smooth flow without spurious oscillations for a wide range of problems and a significant speed up of generally a factor of almost three over the full ENO method. Keywords: Charts; Burger equation; Contract discontinuity. (kr)
4 editions published in 1990 in English and held by 81 WorldCat member libraries worldwide
In the computation of discontinuous solutions of hyperbolic systems of conservation laws, the recently developed ENO (Essentially NonOscillatory) schemes appear to be very useful. However, they are computationally costly compared to simple central difference methods. In this paper we develop a filtering method which uses simple central differencing of arbitrarily high order accuracy, except when a novel local test indicates the development of spurious oscillations. At these points, generally few in number, we use the full ENO apparatus, maintaining the high order of accuracy, but removing spurious oscillations. Numerical results indicate the success of the method. We obtain high order of accuracy in regions of smooth flow without spurious oscillations for a wide range of problems and a significant speed up of generally a factor of almost three over the full ENO method. Keywords: Charts; Burger equation; Contract discontinuity. (kr)
Essentially nonoscillatory postprocessing filtering methods by
Frédéric Lafon(
Book
)
7 editions published between 1991 and 1992 in English and held by 81 WorldCat member libraries worldwide
High order accurate centered flux approximations used in the computation of numerical solutions to nonlinear partial differential equations produce large oscillations in regions of sharp transitions. In this paper, we present a new class of filtering methods denoted by ENOLS (Essentially Nonoscillatory Least Squares) which constructs an upgraded filtered solution that is close to the physically correct weak solution of the original evolution equation. Our method relies on the evaluation of a least squares polynomial approximation to oscillatory data using a set of points which is determined via the ENO framework. Numerical results are given in one and two space dimensions for both scalar and systems of hyperbolic conservation laws. Computational running time, efficiency and robustness of the method are illustrated in various examples such as Riemann initial data for both Burgers' and Euler's equations of gas dynamics. In all standard cases the filtered solution appears to converge numerically to the correct solution of the original problem. Some interesting results based on nonstandard central difference schemes, which exactly preserve entropy, and have been recently shown generally not to be weakly convergent to a solution of the conservation law, are also obtained using out filters. ENO, Least squares, Conservation laws
7 editions published between 1991 and 1992 in English and held by 81 WorldCat member libraries worldwide
High order accurate centered flux approximations used in the computation of numerical solutions to nonlinear partial differential equations produce large oscillations in regions of sharp transitions. In this paper, we present a new class of filtering methods denoted by ENOLS (Essentially Nonoscillatory Least Squares) which constructs an upgraded filtered solution that is close to the physically correct weak solution of the original evolution equation. Our method relies on the evaluation of a least squares polynomial approximation to oscillatory data using a set of points which is determined via the ENO framework. Numerical results are given in one and two space dimensions for both scalar and systems of hyperbolic conservation laws. Computational running time, efficiency and robustness of the method are illustrated in various examples such as Riemann initial data for both Burgers' and Euler's equations of gas dynamics. In all standard cases the filtered solution appears to converge numerically to the correct solution of the original problem. Some interesting results based on nonstandard central difference schemes, which exactly preserve entropy, and have been recently shown generally not to be weakly convergent to a solution of the conservation law, are also obtained using out filters. ENO, Least squares, Conservation laws
The discrete onesided Lipschitz condition for convex scalar conservation laws by
Yann Brenier(
Book
)
3 editions published in 1986 in English and held by 75 WorldCat member libraries worldwide
3 editions published in 1986 in English and held by 75 WorldCat member libraries worldwide
Solution of the hydrodynamic device model using highorder nonoscillatory shock capturing algorithms by
Institute for Computer Applications in Science and Engineering(
Book
)
5 editions published in 1989 in English and held by 75 WorldCat member libraries worldwide
A micron N+  N  N+ silicon diode is simulated via the hydrodynamic model for carrier transport. The numerical algorithms employed are for the nonsteady case, and a limiting process is used to reach steady state. The novelty of our simulation lies in the shock capturing algorithms employed, and indeed shocks, or very rapid transition regimes, are observed in the transient case for the coupled system, consisting of the potential equation and the conservation equations describing charge, momentum, and energy transfer for the electron carriers. These algorithms, termed essentially nonoscillatory, have been successfully applied in other contests to models the flow in gas dynamics, magnetohydrodynamics and other physical situations involving the conservation laws of fluid mechanics. The method here is first order in time, but the use of small time steps allows for good accuracy. Runge Kutta methods allow one to achieve higher accuracy in time of desired. The spatial accuracy is of high order in regions of smoothness. (JHD)
5 editions published in 1989 in English and held by 75 WorldCat member libraries worldwide
A micron N+  N  N+ silicon diode is simulated via the hydrodynamic model for carrier transport. The numerical algorithms employed are for the nonsteady case, and a limiting process is used to reach steady state. The novelty of our simulation lies in the shock capturing algorithms employed, and indeed shocks, or very rapid transition regimes, are observed in the transient case for the coupled system, consisting of the potential equation and the conservation equations describing charge, momentum, and energy transfer for the electron carriers. These algorithms, termed essentially nonoscillatory, have been successfully applied in other contests to models the flow in gas dynamics, magnetohydrodynamics and other physical situations involving the conservation laws of fluid mechanics. The method here is first order in time, but the use of small time steps allows for good accuracy. Runge Kutta methods allow one to achieve higher accuracy in time of desired. The spatial accuracy is of high order in regions of smoothness. (JHD)
Efficient implementation of essentially nonoscillatory shock capturing schemes, II by
Institute for Computer Applications in Science and Engineering(
Book
)
1 edition published in 1988 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 2 WorldCat member libraries worldwide
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Related Identities
 Langley Research Center
 Fedkiw, Ronald P. 1968 Author
 Shu, ChiWang Author Editor
 Institute for Computer Applications in Science and Engineering
 Engquist, Björn 1945 Other Author Editor
 Paragios, Nikos Editor
 United States National Aeronautics and Space Administration
 Harten, Ami Author
 Somerville, Richard Other Editor
 Burger, Martin Author Editor
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Associated Subjects
Aerodynamics, Transonic Algorithms Burgers equation Cauchy problem Computer graphics Computer scienceMathematics Computer vision Conservation laws (Mathematics) Conservation laws (Mathematics)Numerical solutions Differential equations, Hyperbolic Differential equations, Partial Entropy Entropy (Information theory) Equations of motion Fluid mechanics Functional analysis Hydrodynamics Image analysis Image processingDigital techniques Image processingMathematics Image reconstruction Image reconstructionMathematics Implicit functions Integral operators Interfaces (Physical sciences)Mathematics Inverse problems (Differential equations) Least squares Level set methods Mathematics Mechanics, Applied NavierStokes equations Numerical analysis Optical pattern recognition Problem solving ScienceData processing Shock wavesMathematical models Triangle Wavelets (Mathematics)
Alternative Names
Osher, S.
Osher, S. J.
Osher, S. (Stanley)
Osher, Stanley
Osher, Stanley J.
Osher, Stanley J. 1942
Stanley Osher American mathematician
Stanley Osher Amerikaans wiskundige
Stanley Osher amerikansk matematikar
Stanley Osher amerikansk matematiker
Stanley Osher mathématicien américain
Stanley Osher USamerikanischer Mathematiker
斯坦利·奧舍
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