Osher, Stanley
Overview
Works:  98 works in 264 publications in 2 languages and 4,572 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 430 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 430 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
)
6 editions published in 1985 in English and held by 279 WorldCat member libraries worldwide
6 editions published in 1985 in English and held by 279 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 276 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 276 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 186 WorldCat member libraries worldwide
4 editions published in 1984 in English and held by 186 WorldCat member libraries worldwide
Two papers on similarity of certain Volterra integral operators by
Stanley Osher(
Book
)
13 editions published in 1967 in English and Italian and held by 181 WorldCat member libraries worldwide
13 editions published in 1967 in English and Italian and held by 181 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 178 WorldCat member libraries worldwide
5 editions published in 2003 in English and held by 178 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 138 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 138 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
Triangle based TVD schemes for hyperbolic conservation laws by
Institute for Computer Applications in Science and Engineering(
Book
)
5 editions published in 1990 in English and held by 130 WorldCat member libraries worldwide
5 editions published in 1990 in English and held by 130 WorldCat member libraries worldwide
High order essentially nonoscillatory schemes for HamiltonJacobi equations by
Stanley Osher(
Book
)
5 editions published in 1990 in English and held by 117 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 117 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)
Level set and PDE based reconstruction methods in imaging : Cetraro, Italy, 2008 by
Martin Burger(
Book
)
12 editions published in 2013 in English and held by 101 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
12 editions published in 2013 in English and held by 101 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
Uniformly highorder accurate nonoscillatory schemes by
Ami Harten(
Book
)
3 editions published in 1985 in English and held by 97 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 97 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)
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 80 WorldCat member libraries worldwide
1 edition published in 1984 in English and held by 80 WorldCat member libraries worldwide
Efficient implementation of essentially nonoscillatory shock capturing schemes, II by
ChiWang Shu(
Book
)
2 editions published in 1988 in English and held by 80 WorldCat member libraries worldwide
2 editions published in 1988 in English and held by 80 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 80 WorldCat member libraries worldwide
3 editions published in 1983 in English and held by 80 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 79 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 79 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 78 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 78 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 77 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 77 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
Efficient implementation of essentially nonoscillatory shock capturing schemes by
ChiWang Shu(
Book
)
5 editions published between 1987 and 1988 in English and held by 75 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 75 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
The discrete onesided Lipschitz condition for convex scalar conservation laws by
Yann Brenier(
Book
)
4 editions published in 1986 in English and held by 73 WorldCat member libraries worldwide
4 editions published in 1986 in English and held by 73 WorldCat member libraries worldwide
Splitting methods in communication, imaging, science, and engineering(
Book
)
4 editions published in 2016 in English and held by 7 WorldCat member libraries worldwide
This book is about computational methods based on operator splitting. It consists of twentythree chapters written by recognized splitting method contributors and practitioners, and covers a vast spectrum of topics and application areas, including computational mechanics, computational physics, image processing, wireless communication, nonlinear optics, and finance. Therefore, the book presents very versatile aspects of splitting methods and their applications, motivating the crossfertilization of ideas.
4 editions published in 2016 in English and held by 7 WorldCat member libraries worldwide
This book is about computational methods based on operator splitting. It consists of twentythree chapters written by recognized splitting method contributors and practitioners, and covers a vast spectrum of topics and application areas, including computational mechanics, computational physics, image processing, wireless communication, nonlinear optics, and finance. Therefore, the book presents very versatile aspects of splitting methods and their applications, motivating the crossfertilization of ideas.
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Related Identities
 Langley Research Center
 Fedkiw, Ronald P. 1968 Author
 Shu, ChiWang Author Editor
 Paragios, Nikos Editor
 Engquist, Björn 1945 Other Author Editor
 Institute for Computer Applications in Science and Engineering
 United States National Aeronautics and Space Administration
 Burger, Martin Author Editor
 Harten, Ami Author
 Somerville, Richard Other 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 Image analysis Image processing 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 Mathematical optimization Mathematics Mechanics, Applied NavierStokes equations Numerical analysis Operator theory Optical pattern recognition Problem solving ScienceData processing Shock wavesMathematical models Splitting extrapolation method 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 matemático estadounidense
Stanley Osher matematico statunitense
Stanley Osher mathématicien américain
Stanley Osher USamerikanischer Mathematiker
スタンリー・オッシャー アメリカ合衆国の数学者
斯坦利·奧舍
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