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We consider a continuum phase field model for crystal growth via molecularbeam epitaxy, with the goal of determining stable numerical time integrationmethods for the dynamics. We parametrize a class of semi-implicit methods thatare linear in the updated field, which allows for efficient implementation withfast Fourier transforms. We perform unconditional von Neumann stabilityanalysis to identify the region of stability in parameter space, and then testthese predictions numerically for gradient stability. We find strong agreementbetween the approaches.

Stable Numerical Integration of an Epitaxial Growth Model with Slope Selection