Lax-Hopf Based Incorporation of Internal Boundary Conditions Into Hamilton-Jacobi Equation. Part II: Computational Methods

被引：84

作者：

Claudel, Christian G. ^{[1
,2
]}

Bayen, Alexandre M. ^{[3
]}

机构：

[1] Univ Calif Berkeley, Dept Elect Engn & Comp Sci, Berkeley, CA 94720 USA

[2] Nokia Res Ctr, Mobile Internet Serv Syst, Palo Alto, CA 94304 USA

[3] Univ Calif Berkeley, Dept Civil & Environm Engn, Berkeley, CA 94720 USA

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2010年 / 55卷 / 05期

基金：

美国国家科学基金会;

关键词：

Hamilton-Jacobi (HJ); initial conditions (ICs); Lax-Hopf formula; partial differential equation (PDE); piecewise affine (PWA); terminal conditions (TCs); CELL TRANSMISSION MODEL; VISCOSITY SOLUTIONS; REPRESENTATION; ASSIMILATION; FORMULATION; WAVES;

D O I：

10.1109/TAC.2010.2045439

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This article presents a new method for explicitly computing solutions to a Hamilton-Jacobi partial differential equation for which initial, boundary and internal conditions are prescribed as piecewise affine functions. Based on viability theory, a Lax-Hopf formula is used to construct analytical solutions for the individual contribution of each affine condition to the solution of the problem. The results are assembled into a Lax-Hopf algorithm which can be used to compute the solution to the partial differential equation at any arbitrary time at no other cost than evaluating a semi-analytical expression numerically. The method being semi-analytical, it performs at machine accuracy (compared to the discretization error inherent to finite difference schemes). The performance of the method is assessed with benchmark analytical examples. The running time of the algorithm is compared with the running time of a Godunov scheme.

引用

页码：1158 / 1174

页数：17

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