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

Nasser Mohieddin Abukhdeir,Dionisios G Vlachos,Markos Katsoulakis,Michael Plexousakis

doi:10.1016/j.jcp.2011.03.052

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

Nasser Mohieddin Abukhdeir, Dionisios G Vlachos + Show 2 more

https://doi.org/10.1016/j.jcp.2011.03.052

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Journal: Journal of Computational Physics	Publication Date: Apr 3, 2011
Citations: 10

Affiliation: University of Delaware, University of Massachusetts Amherst, University of Crete

#Linear Stability Analysis #Mesoscopic Model + Show 8 more

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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.

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