Long-time integration methods for mesoscopic models of pattern-forming systems

Authors:
Nasser Mohieddin Abukhdeir;Dionisios G. Vlachos;Markos Katsoulakis;Michael Plexousakis
Affiliations:
Department of Chemical Engineering, University of Delaware, Newark, DE, USA;Department of Chemical Engineering, University of Delaware, Newark, DE, USA;Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, USA and Department of Applied Mathematics, University of Crete, Heraklion, Greece and Institute of Applied and C ...;Department of Applied Mathematics, University of Crete, Heraklion, Greece and Institute of Applied and Computational Mathematics, Foundation for Research and Technology Hellas, Heraklion, Greece
Venue:
Journal of Computational Physics
Year:
2011

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Abstract

Spectral methods for simulation of a mesoscopic diffusion model of surface pattern formation are evaluated for long simulation times. Backwards-differencing time-integration, coupled with an underlying Newton-Krylov nonlinear solver (SUNDIALS-CVODE), is found to substantially accelerate simulations, without the typical requirement of preconditioning. Quasi-equilibrium simulations of patterned phases predicted by the model are shown to agree well with linear stability analysis. Simulation results of the effect of repulsive particle-particle interactions on pattern relaxation time and short/long-range order are discussed.