An unconditionally stable spectral method for an isotropic thin-film equation
Halliwell, Garry T.
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Mathematical models for thin-film evolution equations and their coarsening behavior have been extensively studied, however a challenge for computer simulations is finding time stepping algorithms that evolve large systems to long times. The thin solid film model is a nonlinear, fourth order, parabolic partial differential equation that is first order in time. Using a semi-implicit operator splitting spectral method, we developed an algorithm that is unconditionally stable allowing arbitrarily large time steps. Stability was achieved by von Neumann analysis resulting in an adaptive parametrization of the splitting at each time step. The novel aspect of this work relative to similar work done on other coarsening models, e.g. the Cahn-Hilliard equation, is the treatment of non-local and inverse power terms. Our numerical method is robust and accurate, with coarsening results orders of magnitude shorter in computation time than Euler's Method.