Pseudospectral versus finite-differences schemes in the numerical integration of stochastic models of surface growth

Abstract

We present a comparison between finite differences schemes and a pseudospectral method applied to the numerical integration of stochastic partial differential equations that model surface growth. We have studied, in 1+1 dimensions, the Kardar, Parisi and Zhang model (KPZ) and the Lai, Das Sarma and Villain model (LDV). The pseudospectral method appears to be the most stable for a given time step for both models. This means that the time up to which we can follow the temporal evolution of a given system is larger for the pseudospectral method. Moreover, for the KPZ model, a pseudospectral scheme gives results closer to the predictions of the continuum model than those obtained through finite difference methods. On the other hand, some numerical instabilities appearing with finite difference methods for the LDV model are absent when a pseudospectral integration is performed. These numerical instabilities give rise to an approximate multiscaling observed in the numerical simulations. With the pseudospectral approach no multiscaling is seen in agreement with the continuum model.

13 single column pages, RevTeX, 6 eps figs

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Cited by in corpus (12)

• Numerical study of the Kardar-Parisi-Zhang equation
• Discretization-related issues in the KPZ equation: Consistency, Galilean-invariance violation, and fluctuation--dissipation relation
• Unified moving boundary model with fluctuations for unstable diffusive growth
• Kinetic roughening in a realistic model of non-conserved interface growth
• Kardar-Parisi-Zhang asymptotics for the two-dimensional noisy Kuramoto-Sivashinsky equation
• Intrinsic geometry approach to surface kinetic roughening
• Static fluctuations of a thick 1D interface in the 1+1 Directed Polymer formulation: numerical study
• Transition between chaotic and stochastic universality classes of kinetic roughening
• Feedback control of surface roughness in a one-dimensional KPZ growth process
• Invited review: KPZ. Recent developments via a variational formulation
• Numerical Study of the Thermodynamic Uncertainty Relation for the KPZ-Equation
• Dynamical Renormalization Group Study for a Class of Non-local Interface Equations