A SIMPLE AND EFFICIENT METHOD FOR A CONSERVATIVE SWIFT–HOHENBERG EQUATION WITH A STRONG NONLINEAR VACANCY POTENTIAL

초록

In this paper, we consider a conservative Swift-Hohenberg equation with a strong nonlinear vacancy potential (VCSH) to incorporate vacancies into the phase-field crystal model. We propose a simple and efficient method for solving the VCSH equation based on an operator splitting method. Although the nonlinear potentials, including the strong nonlinear vacancy potential, are difficult to treat, the resulting nonlinear subequations can be solved without a dedicated algorithm. As a result, the proposed method is simple to implement and requires only a few lines of MATLAB code. Numerical simulations show that the VCSH equation captures vacancies that exist in real materials.

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