"This dissertation explores and develops time-stepping schemes for computing solutions to the Functionalized Cahn-Hilliard (FCH) model. It is important to find a scheme that is both fast enough to compute evolution to the long-time states and to give enough accuracy to capture important geometric events. The FCH model is relatively new, and very little work has been done to develop efficient numerical schemes for its simulation, so much of this work is based on the extensive work done on the Cahn-Hilliard (CH) model. For each of the methods, the spatial approximation is computed with a Fourier spectral method. All of the schemes are adapted to be computed on a graphics processing unit (GPU) which gives significant improvements in the speed of the simulation.--From abstract.
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