Wavelet-based spatial scaling of coupled reaction-diffusion fields

Sudib K. Mishra, Krishna Muralidharan, Pierre A Deymier, George N Frantziskonis, Sreekanth Pannala, Srdjan Simunovic

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Multiscale schemes for transferring information from fine to coarse scales are typically based on homogenization techniques. Such schemes smooth the fine scale features of the underlying fields, often resulting in the inability to accurately retain the fine scale correlations. In addition, higher-order statistical moments (beyond mean) of the relevant field variables are not necessarily preserved. As a superior alternative to averaging homogenization methods, a wavelet-based scheme for the exchange of information between a reactive and diffusive field in the context of multiscale reaction-diffusion problems is proposed and analyzed. The scheme is shown to be efficient in passing information along scales, from fine to coarse, i.e., upscaling as well as from coarse to fine, i.e., downscaling. It incorporates fine scale statistics (higher-order moments beyond mean), mainly due to the capability of wavelets to represent fields hierarchically. Critical to the success of the scheme is the identification of dominant scales containing the majority of the useful information. The dominant scales in effect specify the coarsest resolution possible. The scheme is applied in detail to the analysis of a diffusive system with a chemically reacting boundary. Reactions are simulated using kinetic Monte Carlo (kMC) and diffusion is solved by finite differences (FDs). Spatial scale differences are present at the interface of the kMC sites and the diffusion grid. The computational efficiency of the scheme is compared to results obtained by averaging homogenization, and to results from a benchmark scheme that ensures spatial scale parity between kMC and FD.

Original languageEnglish (US)
Pages (from-to)281-297
Number of pages17
JournalInternational Journal for Multiscale Computational Engineering
Volume6
Issue number4
DOIs
StatePublished - 2008

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Kinetics
Homogenization method
Higher order statistics
Computational efficiency

Keywords

  • Multiscaling
  • Reaction-diffusion
  • Spatial scaling
  • Wavelets

ASJC Scopus subject areas

  • Computational Mechanics
  • Computer Networks and Communications
  • Control and Systems Engineering

Cite this

Wavelet-based spatial scaling of coupled reaction-diffusion fields. / Mishra, Sudib K.; Muralidharan, Krishna; Deymier, Pierre A; Frantziskonis, George N; Pannala, Sreekanth; Simunovic, Srdjan.

In: International Journal for Multiscale Computational Engineering, Vol. 6, No. 4, 2008, p. 281-297.

Research output: Contribution to journalArticle

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