A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations

Shaoqiang Tang, Thomas Y. Hou*, Wing Kam Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


In this paper, we propose a pseudo-spectral multiscale method for simulating complex systems with more than one spatial scale. Using a spectral decomposition, we split the displacement into its mean and fluctuation parts. Under the assumption of localized nonlinear fluctuations, we separate the domain into an MD (Molecular Dynamics) subdomain and an MC (MacrosCopic) subdomain. An interfacial condition is proposed across the two scales, in terms of a time history treatment. In the special case of a linear system, this is the first exact interfacial condition for multiscale computations. Meanwhile, we design coarse grid equations using a matching differential operator approach. The coarse grid discretization is of spectral accuracy. We do not use a handshaking region in this method. Instead, we define a coarse grid over the whole domain and reassign the coarse grid displacement in the MD subdomain with an average of the MD solution. To reduce the computational cost, we compute the dynamics of the coarse grid displacement and relate it to the mean displacement. Our method is therefore called a pseudo-spectral multiscale method. It allows one to reach high resolution by balancing the accuracy at the coarse grid with that at the interface. Numerical experiments in one- and two-space dimensions are presented to demonstrate the accuracy and the robustness of the method.

Original languageEnglish (US)
Pages (from-to)57-85
Number of pages29
JournalJournal of Computational Physics
Issue number1
StatePublished - Mar 20 2006


  • Coarse grid equations
  • Interfacial conditions
  • Multiscale method

ASJC Scopus subject areas

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


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