We present the results of large scale simulations of 4th order nonlinear partial differential equations of dif- fusion type that are typically encountered when modeling dynamics of thin fluid films on substrates. The simulations are based on the alternate direction implicit (ADI) method, with the main part of the compu- tational work carried out in the GPU computing environment. Efficient and accurate computations allow for simulations on large computational domains in three spatial dimensions (3D) and for long computational times. We apply the methods developed to the particular problem of instabilities of thin fluid films of nanoscale thickness. The large scale of the simulations minimizes the effects of boundaries, and also allows for simulating domains of the size encountered in published experiments. As an outcome, we can analyze the development of instabilities with an unprecedented level of detail. A particular focus is on analyzing the manner in which instability develops, in particular regarding differences between spinodal and nucleation types of dewetting for linearly unstable films, as well as instabilities of metastable films. Simulations in 3D allow for consideration of some recent results that were previously obtained in the 2D geometry (J. Fluid Mech. 841, 925 (2018)). Some of the new results include using Fourier transforms as well as topological invariants (Betti numbers) to distinguish the outcomes of spinodal and nucleation types of instabilities, describing in precise terms the complex processes that lead to the formation of satellite drops, as well as distinguishing the shape of the evolving film front in linearly unstable and metastable regimes. We also discuss direct comparison between simulations and available experimental results for nematic liquid crystal and polymer films.
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