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arXiv · 1303.5311

Stable Numerical Integration of an Epitaxial Growth Model with Slope Selection

Gregory M. Seyfarth·Benjamin P. Vollmayr-Lee
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Abstract

We consider a continuum phase field model for crystal growth via molecular beam epitaxy, with the goal of determining stable numerical time integration methods for the dynamics. We parametrize a class of semi-implicit methods that are linear in the updated field, which allows for efficient implementation with fast Fourier transforms. We perform unconditional von Neumann stability analysis to identify the region of stability in parameter space, and then test these predictions numerically for gradient stability. We find strong agreement between the approaches.

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Gregory M. Seyfarth, Benjamin P. Vollmayr-Lee. 2013-03-21. Stable Numerical Integration of an Epitaxial Growth Model with Slope Selection. https://doi.org/10.1142/s0129183118500596

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