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arXiv · 1506.05271

Convergence of a Fast Explicit Operator Splitting Method for the Molecular Beam Epitaxy Model

Xiao Li·Zhonghua Qiao·Hui Zhang
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Abstract

A fast explicit operator splitting (FEOS) method for the molecular beam epitaxy model has been presented in [Cheng, et al., Fast and stable explicit operator splitting methods for phase-field models, J. Comput. Phys., submitted]. The original problem is split into linear and nonlinear subproblems. For the linear part, the pseudo-spectral method is adopted; for the nonlinear part, a 33-point difference scheme is constructed. Here, we give a compact center-difference scheme involving fewer points for the nonlinear subproblem. Besides, we analyze the convergence rate of the algorithm. The global error order $\mathcal{O}(\tau^2+h^4)$ in discrete $L^2$-norm is proved theoretically and verified numerically. Some numerical experiments show the robustness of the algorithm for small coefficients of the fourth-order term for the one-dimensional case. Besides, coarsening dynamics are simulated in large domains and the $1/3$ power laws are observed for the two-dimensional case.

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Xiao Li, Zhonghua Qiao, Hui Zhang. 2015-06-17. Convergence of a Fast Explicit Operator Splitting Method for the Molecular Beam Epitaxy Model. https://arxiv.org/abs/1506.05271

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