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Wednesday, April 29, 2020 | History

2 edition of High order WENO schemes for Hamilton-Jacobi equations on triangular meshes found in the catalog.

High order WENO schemes for Hamilton-Jacobi equations on triangular meshes

Yong-Tao Zhang

High order WENO schemes for Hamilton-Jacobi equations on triangular meshes

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  • 18 Currently reading

Published by ICASE, NASA Langley Research Center, NASA Center for Aerospace Information, [distributor] in Hampton, Va, Hanover, MD .
Written in English

    Subjects:
  • Computational grids (Computer systems),
  • Finite element method.,
  • Hamilton-Jacobi equations.,
  • Multigrid methods (Numerical analysis),
  • Nonlinear theories.

  • Edition Notes

    Other titlesICASE
    StatementYong-Tao Zhang and Chi-Wang Shu.
    SeriesICASE report -- no. 2001-38, NASA/CR -- 2001-211256, NASA contractor report -- NASA CR-2001-211256.
    ContributionsShu, Chi-Wang., Institute for Computer Applications in Science and Engineering., Langley Research Center.
    Classifications
    LC ClassificationsTL521.3.C6 A3 no.211256
    The Physical Object
    Pagination31 p. :
    Number of Pages31
    ID Numbers
    Open LibraryOL19028239M

    Another example in using the Hamilton-Jacobi Method (t-dependent H) (G ) Suppose we are given a Hamiltonian to a system as, 2 2 p H mAtq m where A is a constant tq pmv 0, 0, Our task is to solve for the equation of motion by means of the Hamilton’s principle function S with the initial conditions The Hamilton-Jacobi equation for S is:File Size: KB. Regularity and global structure of solutions to Hamilton-Jacobi equations II. Convex initial data, J. Hyperbol. Differ. Eq. 6 (), no. 4, Y. Di, R. Li, and T. Tang, A general moving mesh framework in 3D and its application for simulating the mixture of multi-phase flows, Commun. Comput. Phys. 3 (),


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High order WENO schemes for Hamilton-Jacobi equations on triangular meshes by Yong-Tao Zhang Download PDF EPUB FB2

High-order algorithms for H-J equations on unstructured meshes, are relatively few. We have the very good first- and second-order finite volume–type schemes of Abgrall [2] and ENO- or limiter-type high-order version of Augoula and Abgrall [4].The. High-Order WENO Schemes for Hamilton--Jacobi Equations on Triangular Meshes.

Related Databases A Second Order Central Scheme for Hamilton-Jacobi Equations on Triangular Grids. Numerical Analysis and Its Applications, Central WENO Schemes for Hamilton–Jacobi Equations on Triangular Meshes.

SIAM Journal on Scientific Computing Cited by: In andZhang and Shu [27] and Li and Chan [14] developed high order WENO schemes for solving HJ equations on triangular meshes. And some methods on the finite volume framework were.

We derive Godunov‐type semidiscrete central schemes for Hamilton–Jacobi equations on triangular meshes. High‐order schemes are then obtained by combining our new numerical fluxes with high‐order WE Cited by:   High-order schemes for Hamilton–Jacobi equations on triangular meshes.

Author links open overlay panel Xiang-Gui Li a C.K. Chan b. Then P WENO (x,y) is approximately the algebraic average of Q r (x,y) we construct high-order schemes on triangular by:   Hamilton-Jacobi-Isaacs equations High-order schemes Semi-Lagrangian schemes Finite volume methods Optimal control Differential games This research was supported by the following grants: AFOSR Grant no.

FA, ITN-Marie Curie Grant no. SADCO, and the FWF-START project Sparse Approximation and Optimization in High Cited by: 1. As a result, comparing with the original WENO with Runge–Kutta time discretizations schemes (WENO-RK) of Jiang and Peng [G.

Jiang, D. Peng, Weighted ENO. Osher and C.-W. Shu, High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations, SIAM Journal on Numerical Analysis, v28 (), pp.

– MathSciNet zbMATH CrossRef Google ScholarCited by: Y.-T. Zhang and C.-W. Shu, High order WENO schemes for Hamilton-Jacobi equations on triangular meshes, SIAM Journal on Scientific Computing, v24 (), pp High Order Schemes for HJ Equations 3 that is evolved in time with a rst-order monotone ux.

The Weighted ENO (WENO) interpolant of [18, 32] was used for constructing high-order upwind methods for the HJ equations in [17], and extensions of these methods for triangular meshes were introduced in[1,40].Cited by: 2. The construction of Hermite WENO schemes for the Hamilton–Jacobi equations.

In this section, we firstly give the framework of solving the Hamilton–Jacobi equations briefly and then develop the procedures of the third and fourth order HWENO schemes on unstructured meshes for the Hamilton–Jacobi equations in details.

The frameworkCited by: Publications in Refereed Conference Proceedings and Book Chapters [1] Y.-T. Zhang, J. Shi, C.-W. Shu and Y. Zhou, Resolution of high order WENO schemes and Navier-Stokes simulation of the Rayleigh-Taylor instability problem, in Computational Fluid and Solid MechanicsK.J. Bathe, Editor, the Proceedings of the Second MIT Conference on Computational Fluid and.

work, we mention the WENO schemes for solving the HJ equations [10] by Jiang and Peng, based on the WENO schemes for solving conservation laws [17,11], and Hermite WENO schemes in [22]. Zhang and Shu [29] further developed high-orderWENO schemes on unstructured meshes for solving two-dimensional HJ equations.

WENO is a spatial. High-Order Central WENO Schemes for 1D Hamilton-Jacobi Equations Steve Bryson 1 and Doron Levy 2 1 Program in Scientific Computing/Computational Mathematics, Stanford University and the NASA Advanced Supercomputing Division, NASA Ames Research Center, MoItett Field, CA ; [email protected] for Multi-Dimensional Hamilton-Jacobi Equations Steve Bryson Doron Levyy Abstract We present the rst fth-order, semi-discrete central-upwind method for ap-proximating solutions of multi-dimensional Hamilton-Jacobi equations.

Unlike most of the commonly used high-order upwind schemes, our scheme is formulated as a Godunov-type by: tured meshes. Recently, Zhang and Shu [12], Li and Chan [13] investigated high order WENO schemes for solving two-dimensional Hamilton-Jacobi equations by the usage of the nodal based WENO polynomial reconstructions on triangular meshes.

And some finite element methods for arbitrary triangular meshes were proposed in [14–17]. equations. Then, a high order of WeightedENO (WENO) scheme was proposedby Jiang and Peng [7].

Recently, Qiu [16,17] and with Shu [20] also proposed Hermite WENO schemes for solving the Hamilton-Jacobi equations on structured meshes.

InLafon and Osher [10] constructed the ENO schemes for solving the Hamilton-Jacobi equations on. Stanley Osher and Chi-Wang Shu, High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations, SIAM J.

Numer. Anal. Anal. 28 (), no. 4, –Author: Lili Hu, Yao Li, Yingjie Liu. methods. We adapt high order schemes for time dependent Hamilton-Jacobi equations in [24, 14, 39] to the static H-J equations in a novel way.

First-order sweeping schemes are used as building blocks in our high order methods. The high order accuracy in our schemes results from the high order approximations for the partial derivatives because. We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations.

The proposed method is single-stage (i.e., it has no internal stages to store), single-step (i.e., it has no time history that needs to be stored), maintains a discrete divergence-free condition on the magnetic field, and has the capacity to preserve Author: J ChristliebAndrew, FengXiao, C SealDavid, TangQi.

In this paper, we build second-order methods for arbitrary unstructured meshes on manifolds and in R n and show how certain static Hamilton–Jacobi equations in the plane can be recast as Eikonal equations on appropriately chosen manifolds.

Our interest in unstructured meshes stems from our intent to solve Hamilton–Jacobi equations on by: Stanford Libraries' official online search tool for books, media, journals, databases, government documents and more. In mathematics, the Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations, and is a special case of the Hamilton–Jacobi–Bellman is named for William Rowan Hamilton and Carl Gustav Jacob Jacobi.

In physics, the Hamilton–Jacobi equation is an alternative formulation of. The emphasis is on Stanley Osher's contribution in these areas and the impact of his work. We will start with shock capturing methods and will review the Engquist-Osher scheme, TVD schemes, entropy conditions, ENO and WENO schemes, and numerical schemes for Hamilton-Jacobi type by: 1.

Y.-T. Zhang and C.-W. Shu, High order WENO schemes for Hamilton-Jacobi equations on triangular meshes, SIAM Journal on Scientific Computing, 24 (), doi: /S Google Scholar [30]Author: Ruijun Zhao, Yong-Tao Zhang, Shanqin Chen.

In this paper, we consider high-order approximations to stationary Hamilton–Jacobi equa-tions. We prove an abstract convergence result for high-order methods relaxing the mono-tonicity assumption to ε-montonicity and show how some known schemes fit into this theory.

Consider, as a prototype problem, the following Hamilton–Jacobi–Bellman PDE. equation is a system of n second-order ODE whose unknown is x(t).

In contrast, Hamilton’s equations are a system of 2n rst-order ODE whose unknowns are p(t) and x(t). AN OVERVIEW OF THE HAMILTON-JACOBI EQUATION 3 AN OVERVIEW OF THE HAMILTON-JACOBI EQUATION 5 Since () shows that the di erential 1-form pdx PdX is closed, we know the File Size: KB.

The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent cturer: Springer.

The high-order character of the scheme provides an efficient way towards accurate approximations with coarse grids. We assess the performance of the scheme with a set of problems arising in minimum time optimal control and pursuit-evasion games.

Keywords: Hamilton-Jacobi-Isaacs equations,high-order schemes, semi-Lagrangian schemes. High-order and coupled schemes for Hamilton-Jacobi-Bellman equations Supervisor: Prof.

Maurizio Falcone Candidate: Smita Sahu matricola June Anno Accademico Dipartimento di Matematica ‘Guido Castelnuovo’. Key words. Hyperbolic systems, central difference schemes, high-order accuracy, WENO reconstruc-tion, Runge-Kutta methods. AMS(MOS) subject classification.

65M06, 35L60, 65L06, 76M 1 Introduction Shock capturing schemes for the numerical approximation of systems of conservation laws have been. Abstract. In this paper, we present a weighted ENO (essentially non-oscillatory) scheme to approximate the viscosity solution of the Hamilton-Jacobi equation: OE t +H(x 1 ; \Delta \Delta \Delta ; x d ; t; OE; OE x1 ; \Delta \Delta \Delta ; OE xd) = 0: This weighted ENO scheme is constructed upon and has the same stencil nodes as the 3 rd order ENO scheme but can be.

Further Generalizations: ff Processes Can be generalized further (suppressing dependence of x and W on t) dx = (x)dt +˙(x)dW where and ˙ are any non-linear etc etc functions.

This is called a ff process" () is called the drift and ˙() the ff all results can. : Generalized Solutions of Hamilton-Jacobi Equations (Research Notes In mathematics Series, 69) (): P. Lions: BooksCited by: 3 The Hamilton-Jacobi equation To find canonical coordinates Q,P it may be helpful to use the idea of generating functions.

Let us use F(q,Q,t). Then we will have p= ∂F ∂q, P= − ∂F ∂Q, 0 = H+ ∂F ∂t (19) If we know F, we can find the canonical File Size: KB. including higher order versions on Cartesian grids and unstruc-tured meshes, on manifolds and in Rn; we also explore the connections to more general static Hamilton–Jacobi equations.

For the sake of notational simplicity, the discussion below is limited to R2, R3, and two-dimensional manifolds; the results hold for arbitrary dimension. Hamilton Jacobi equations Intoduction to PDE The rigorous stu from Evans, mostly. We discuss rst @ tu+ H(ru) = 0; (1) where H(p) is convex, and superlinear at in nity, lim jpj!1 H(p) jpj = +1 This by comes by integration from special hyperbolic systems of the form (n= m) @ tv+ F j(v)@ jv= 0 when there exists a pontental for F j, i.e.

F j = @ jH. solutions of the Cauchy problem for first-order partial differential equations of Hamilton-Jacobi type. Most of the presentation here will be in the context of problems of the form j du/dt + H(Du) = 0 inR^), \u(x,0) = u0(x) inR", where H G C(RN) (the continuous functions on R"), u0 G BUQR") (the bounded.

Matthew Brown and Margot Gerritsen An Energy-Stable High-Order Central Difference Scheme for the Two-Dimensional Shallow Water Equations Th. Tsangaris and Y.-S.

Smyrlis and A. Karageorghis A Matrix Decomposition MFS Algorithm for Problems in Hollow Axisymmetric Domains Peter Benner and Enrique S. Quintana-Ortí Solving Stable. This is the Hamilton–Jacobi equation. The most important result of the Hamilton–Jacobi theory is Jacobi's theorem, which states that a complete integral of equation (2), i.e.

the solution of this equation, which will depend on the parameters (provided that), makes it possible to obtain the complete integral of the equation for the Euler functional (1) or, which is the same thing, of the.

In this paper, we propose a complete framework for 3D geometry modeling and processing that uses only fast geodesic computations. The basic building block for these techniques is a novel greedy algorithm to perform a uniform or adaptive remeshing of a triangulated surface.“Uniformly High Order Accurate Essentially Non-Oscillatory Schemes”.

In: Upwind and High-Resolution Schemes. Springer, Berlin Heidelberg,pp. – [40] Stanley Osher and Chi-Wang Shu. “High-Order Essentially Nonoscillatory Schemes for Hamilton–Jacobi Equations”. In: SIAM Journal on Numerical Analysis (), pp.

several book series runs several conferences (from CS&E to Imaging Science) Cost for SISC, annual subscription, hard copy Software and High-Performance Computing. Papers in this category should Central WENO Schemes for Hamilton Jacobi Equations on Triangular Meshes, Doron Levy, Suhas Nayak, Chi-Wang Shu, and Yong-Tao Zhang.