Wavelet based spatial scaling of coupled reaction diffusion fields

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Multiscale schemes for transferring information from fine to coarse scales are typically based on some sort of averaging. Such schemes smooth the fine scale features of the underlying fields, thus altering the fine scale correlations. As a superior alternative to averaging, 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. up-scaling as well as from coarse to fine, i.e. down-scaling. In addition, it retains fine scale statistics, 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 useful information. The scheme is applied in detail to the analysis of a diffusive system with chemically reacting boundary. Reactions are simulated using kinetic Monte Carlo (KMC) and diffusion is solved by finite differences. 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 local averaging, and to results from a benchmark model. The spatial scaling scheme ties to wavelet based schemes for temporal scaling, presented elsewhere by the authors.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages301-310
Number of pages10
Volume5102 LNCS
EditionPART 2
DOIs
StatePublished - 2008
Event8th International Conference on Computational Science, ICCS 2008 - Krakow, Poland
Duration: Jun 23 2008Jun 25 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume5102 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other8th International Conference on Computational Science, ICCS 2008
CountryPoland
CityKrakow
Period6/23/086/25/08

Fingerprint

Reaction-diffusion
Wavelets
Scaling
Benchmarking
Kinetics
Computational efficiency
Averaging
Kinetic Monte Carlo
Statistics
Multiscale Problems
Upscaling
Reaction-diffusion Problems
Tie
Computational Efficiency
Sort
Finite Difference
Benchmark
Grid
Alternatives

Keywords

  • Diffusion
  • Down-scaling
  • Multiscale
  • Reaction
  • Up-scaling
  • Wavelets

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

Mishra, S. K., Muralidharan, K., Deymier, P. A., Frantziskonis, G. N., Simunovic, S., & Pannala, S. (2008). Wavelet based spatial scaling of coupled reaction diffusion fields. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (PART 2 ed., Vol. 5102 LNCS, pp. 301-310). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5102 LNCS, No. PART 2). https://doi.org/10.1007/978-3-540-69387-1_33

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

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5102 LNCS PART 2. ed. 2008. p. 301-310 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5102 LNCS, No. PART 2).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Mishra, SK, Muralidharan, K, Deymier, PA, Frantziskonis, GN, Simunovic, S & Pannala, S 2008, Wavelet based spatial scaling of coupled reaction diffusion fields. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 2 edn, vol. 5102 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 2, vol. 5102 LNCS, pp. 301-310, 8th International Conference on Computational Science, ICCS 2008, Krakow, Poland, 6/23/08. https://doi.org/10.1007/978-3-540-69387-1_33
Mishra SK, Muralidharan K, Deymier PA, Frantziskonis GN, Simunovic S, Pannala S. Wavelet based spatial scaling of coupled reaction diffusion fields. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 2 ed. Vol. 5102 LNCS. 2008. p. 301-310. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 2). https://doi.org/10.1007/978-3-540-69387-1_33
Mishra, Sudib K. ; Muralidharan, Krishna ; Deymier, Pierre A ; Frantziskonis, George N ; Simunovic, Srdjan ; Pannala, Sreekanth. / Wavelet based spatial scaling of coupled reaction diffusion fields. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5102 LNCS PART 2. ed. 2008. pp. 301-310 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 2).
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