Numerical Method for the Deterministic Kardar-Parisi-Zhang Equation in Unbounded Domains (Communications in Computational Physics, 2006)
We propose an artificial boundary method for solving the deterministicKardar-Parisi-Zhang equation in one-, two- and three- dimensional unbounded domains.The exact artificial boundary conditions are obtained on the artificial boundaries. Thenthe original problems are reduced to equivalent problems in bounded domains. A finite difference method is applied to solve the reduced problems, and some numericalexamples are provided to show the effectiveness of the method.
Keywords: Quasilinear parabolic equation; artificial boundary condition; viscous HamiltonJacobi equation; unbounded domain.