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Showing papers by "Stanley Osher published in 1991"


Journal ArticleDOI
TL;DR: In this paper, high-order essentially nonoscillatory (ENO) schemes for Hamilton-Jacobi (H-J) equations are investigated, which yield uniform highorder accuracy in smooth regions and sharply resolve discontinuities in the derivatives.
Abstract: Hamilton–Jacobi (H–J) equations are frequently encountered in applications, eg, in control theory and differential games H–J 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 high-order essentially nonoscillatory (ENO) schemes for H–J equations are investigated, which yield uniform high-order accuracy in smooth regions and sharply resolve discontinuities in the derivatives The ENO scheme construction procedure is adapted from that for hyperbolic conservation laws The schemes are numerically tested on a variety of one-dimensional and two-dimensional problems, including a problem related to control optimization, and high-order accuracy in smooth regions, good resolution of discontinuities in the derivatives, and convergence to viscosity solutions are observed

680 citations


Journal ArticleDOI
TL;DR: The presented semiconductor simulations reveal temporal and spatial velocity overshot, as well as overshoot relative to an electric field induced by the Poisson equation.
Abstract: Simulation results for the hydrodynamic model are presented for an n/sup +/-n-n/sup +/ diode by use of shock-capturing numerical algorithms applied to the transient model with subsequent passage to the steady state. The numerical method is first order in time, but of high spatial order in regions of smoothness. Implementation typically requires a few thousand time steps. These algorithms, termed essentially nonoscillatory, have been successfully applied in other contexts to model the flow in gas dynamics, magnetohydrodynamics, and other physical situations involving the conservation laws of fluid mechanics. The presented semiconductor simulations reveal temporal and spatial velocity overshot, as well as overshoot relative to an electric field induced by the Poisson equation. Shocks are observed in the transient simulations for certain low-temperature parameter regimes. >

106 citations


Journal ArticleDOI
TL;DR: In this paper, simple inequalities are presented for the viscosity solution of a Hamilton-Jacobi equation in N space dimension when neither the initial data nor the Hamiltonian need be convex (or concave).
Abstract: Simple inequalities are presented for the viscosity solution of a Hamilton–Jacobi equation in N space dimension when neither the initial data nor the Hamiltonian need be convex (or concave). The initial data are uniformly Lipschitz and can be written as the sum of a convex function in a group of variables and a concave function in the remaining variables, therefore including the nonconvex Riemann problem. The inequalities become equalities wherever a “maxmin” equals a “minmax” and thus a representation formula for this problem is then obtained, generalizing the classical Hopf s formulas.

73 citations


Proceedings ArticleDOI
TL;DR: Two new filters for image enhancement are developed, extending the early work of the authors, which uses a new nonlinear time dependent partial differential equation and its discretization.
Abstract: Two new filters for image enhancement are developed, extending the early work of the authors. One filter uses a new nonlinear time dependent partial differential equation and its discretization, the second uses a discretization which constrains the backwards heat equation and keeps it variation bounded. The evolution of the initial image as t increases through U(x,y,t) is the filtering process. The processed image is piecewise smooth, nonoscillatory and apparently an accurate reconstruction. The algorithms are fast and easy to program.

51 citations


Journal ArticleDOI
TL;DR: 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 are obtained.

22 citations


Book ChapterDOI
01 Jan 1991
TL;DR: The hydrodynamic model as mentioned in this paper treats electron flow in a semiconductor device through the Euler equations of gas dynamics, with the addition of a heat conduction term, and has hyperbolic, parabolic, and elliptic modes.
Abstract: The hydrodynamic model treats electron flow in a semiconductor device through the Euler equations of gas dynamics, with the addition of a heat conduction term. Thus the hydrodynamic model PDEs have hyperbolic, parabolic, and elliptic modes.

22 citations