Results 1 - 10 of 21

Central WENO schemes for Hamilton-Jacobi equations on triangular meshes

by Doron Levy, Suhas Nayak, Chi-wang Shu, Yong-tao Zhang - J. Sci. Comput , 2005
"... Abstract. We derive Godunov-type semidiscrete central schemes for Hamilton–Jacobi equa-tions on triangular meshes. High-order schemes are then obtained by combining our new numerical fluxes with high-order WENO reconstructions on triangular meshes. The numerical fluxes are shown to be monotone in ce ..."
Abstract - Cited by 7 (0 self) - Add to MetaCart
Abstract. We derive Godunov-type semidiscrete central schemes for Hamilton–Jacobi equa-tions on triangular meshes. High-order schemes are then obtained by combining our new numerical fluxes with high-order WENO reconstructions on triangular meshes. The numerical fluxes are shown to be monotone

High-Order Central WENO Schemes for 1D Hamilton-Jacobi Equations

by Steve Bryson, Doron Levy , 2002
"... this paper we derive fully-discrete Central WENO (CWENO) schemes for approximating solutions of (1), which combine our previous works [2, 13, 14]. We introduce third- and fifth-order accurate schemes, which are the first central schemes for the HJ equations of order higher than two. The core ingredi ..."
Abstract - Cited by 4 (3 self) - Add to MetaCart
this paper we derive fully-discrete Central WENO (CWENO) schemes for approximating solutions of (1), which combine our previous works [2, 13, 14]. We introduce third- and fifth-order accurate schemes, which are the first central schemes for the HJ equations of order higher than two. The core

Spatially adaptive techniques for level set methods and incompressible flow

by Frank Losasso, Ronald Fedkiw, Stanley Osher - Comput. Fluids
"... Since the seminal work of [92] on coupling the level set method of [69] to the equations for two-phase incompressible flow, there has been a great deal of interest in this area. That work demonstrated the most powerful aspects of the level set method, i.e. automatic han-dling of topological changes ..."
Abstract - Cited by 73 (15 self) - Add to MetaCart
to both its popularity and stringent accuracy requirements. Thus, we discuss higher order accurate numerical meth-ods such as Hamilton-Jacobi WENO [46], methods for maintaining a signed distance function, hybrid methods such as the particle level set method [27] and the coupled level set volume of fluid

High Order Fast Sweeping Methods for Static Hamilton-Jacobi Equations

by Yong-Tao Zhang, Hong-Kai Zhao, Jianliang Qian
"... We construct high order fast sweeping numerical methods for computing viscosity solutions of static Hamilton-Jacobi equations on rectangular grids. These methods combine high order weighted essentially non-oscillatory (WENO) approximation to derivatives, monotone numerical Hamiltonians and Gauss Sei ..."
Abstract - Cited by 17 (4 self) - Add to MetaCart
We construct high order fast sweeping numerical methods for computing viscosity solutions of static Hamilton-Jacobi equations on rectangular grids. These methods combine high order weighted essentially non-oscillatory (WENO) approximation to derivatives, monotone numerical Hamiltonians and Gauss

Compact central WENO schemes for multidimensional conservation laws

by Steve Bryson, Doron Levy - SIAM J. Sci. Comput , 2000
"... We present new third- and fifth-order Godunov-type central schemes for approximating solutions of the Hamilton-Jacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greate ..."
Abstract - Cited by 60 (12 self) - Add to MetaCart
is then extended to a multi-dimensional fifth-order scheme. Our numerical examples in one, two and three space dimensions verify the expected order of accuracy of the schemes. Key words. Hamilton-Jacobi equations, central schemes, high order, WENO, CWENO.

A weighted essentially nonoscillatory, large time-step scheme for Hamilton-Jacobi equations

by E. Carlini, R. Ferretti, G. Russo - SIAM J. Sci. Comput , 2005
"... Abstract. We investigate the application of weighted essentially nonoscillatory (WENO) re-constructions to a class of semi-Lagrangian schemes for first order time-dependent Hamilton–Jacobi equations. In particular, we derive a general form of the scheme, study sufficient conditions for its convergen ..."
Abstract - Cited by 11 (2 self) - Add to MetaCart
Abstract. We investigate the application of weighted essentially nonoscillatory (WENO) re-constructions to a class of semi-Lagrangian schemes for first order time-dependent Hamilton–Jacobi equations. In particular, we derive a general form of the scheme, study sufficient conditions for its

Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws

by Chi-wang Shu , 1998
"... In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations. ENO and WENO schemes are high order accurate nite di ere ..."
Abstract - Cited by 270 (26 self) - Add to MetaCart
In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations. ENO and WENO schemes are high order accurate nite di

Numerical Methods for Computing Discontinuous Solutions of aClass of Hamilton-Jacobi Equations Using aLevel Set Method

by Yen-hsi Richard Giga, Yoshikazu Osher, Yen-hsi Richard Tsai *\dagger
"... In this article, we first introduce aLax-Friedrichs type finite difference method to compute the $\mathrm{L}$-solution, following its original definition recently proposed by the second auther in[12] using level sets. We then generalize our numerical methods to compute the proper viscosity solution ..."
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general equations developing shocks other than conservation laws. These numerical methods are generalized to higher order accuracy using WENO Local Lax-Friedrichs methods [17]. We verify that our numerical solutions approximate the proper viscosity solutions of [11] and, in particular, the entropy

Numerical Methods for Computing Discontinuous Solutions of aClass of Hamilton-Jacobi Equations Using aLevel Set Method

by Yen-hsi Richard Tsai *\dagger
"... In this article, we first introduce aLax-Friedrichs type finite difference method to compute the $\mathrm{L}$-solution, following its original definition recently proposed by the second auther in[12] using level sets. We then generalize our numerical methods to compute the proper viscosity solution ..."
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solutions in case of conservtion laws. 1Introduction Nonlinear Hamilton-Jacobi Equations arise in many different fields, including con-trol theory, and differential games. Because of the nonlinearity, the Cauchy prob-lems usually have non-classical solutions due to the crossing of characteristic curves.

Adaptive central-upwind schemes for Hamilton–Jacobi equations with nonconvex Hamiltonians, http://www.math. tulane.edu/~kurganov/pub.html

by Er Kurganov, Guergana Petrova
"... This paper is concerned with computing viscosity solutions of Hamilton–Jacobi equations using high-order Godunov-type projection-evolution methods. These schemes employ piecewise polynomial reconstructions, and it is a well-known fact that the use of more compressive limiters or higher-order polynom ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
This paper is concerned with computing viscosity solutions of Hamilton–Jacobi equations using high-order Godunov-type projection-evolution methods. These schemes employ piecewise polynomial reconstructions, and it is a well-known fact that the use of more compressive limiters or higher
Results 1 - 10 of 21