Spectral methods for mesoscopic models of pattern formation

David J. Horntrop, Markos A. Katsoulakis, Dionisios G. Vlachos

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


In this paper we present spectral algorithms for the solution of mesoscopic equations describing a broad class of pattern formation mechanisms, focusing on a prototypical system of surface processes. These models are in principle stochastic integrodifferential equations and are derived directly from microscopic lattice models, containing detailed information on particle-particle interactions and particle dynamics. The enhanced computational efficiency and accuracy of spectral methods versus finite difference methods are also described.

Original languageEnglish (US)
Pages (from-to)364-390
Number of pages27
JournalJournal of Computational Physics
Issue number1
StatePublished - Oct 10 2001

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


  • Interacting particle systems
  • Mesoscopic models
  • Monte Carlo
  • Spectral methods


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