An integral equation method for epitaxial step-flow growth simulations

Authors:
Jingfang Huang;Ming-Chih Lai;Yang Xiang
Affiliations:
Department of Mathematics, University of North Carolina, Chapel Hill, NC;Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan;Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Venue:
Journal of Computational Physics
Year:
2006

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Abstract

In this paper, we describe an integral equation approach for simulating diffusion problems with moving interfaces. The solutions are represented as moving layer potentials where the unknowns are only defined on the interfaces. The resulting integro-differential equation (IDE) system is solved using spectral deferred correction (SDC) techniques developed for general differential algebraic equations (DAEs), and the time dependent potentials are evaluated efficiently using fast convolution algorithms. The numerical solver is applied to the BCF model for the epitaxial step-flow growth of crystals, for which the solutions are calculated accurately instead of using quasi-static approximations. Numerical results in 1 + 1 dimensions are compared with available results in the literature.