Commun. Comput. Phys., 1 (2006), pp. 479-493.


Numerical Method for the Deterministic Kardar-Parisi-Zhang Equation in Unbounded Domains

Zhenli Xu 1*, Houde Han 2, Xiaonan Wu 3

1 Department of Mathematics, University of Science and Technology of China, Hefei 230026, P. R. China.
2 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China.
3 Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.

Received 25 July 2005; Accepted (in revised version) 24 September 2005

Abstract

We propose an artificial boundary method for solving the deterministic Kardar-Parisi-Zhang equation in one-, two- and three dimensional unbounded domains. The exact artificial boundary conditions are obtained on the artificial boundaries. Then the original problems are reduced to equivalent problems in bounded domains. A finite difference method is applied to solve the reduced problems, and some numerical examples are provided to show the effectiveness of the method.


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Key words: Quasilinear parabolic equation; artificial boundary condition; viscous Hamilton-Jacobi equation; unbounded domain.


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Correspondence to: Zhenli Xu , Department of Mathematics, University of Science and Technology of China, Hefei 230026, P. R. China. Email: xuzl@ustc.edu
 

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