Sparse dynamics for partial differential equations

Hayden Schaeffer, Russel Caflisch, Cory D. Hauck, Stanley Osher

Research output: Contribution to journalArticle

Abstract

We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented.Inmany cases, there are naturalbases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms.

Original languageEnglish (US)
Pages (from-to)6634-6639
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Volume110
Issue number17
DOIs
StatePublished - Apr 23 2013

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Convection
Shock

Keywords

  • Multiphysics
  • Multiscale
  • Optimization

ASJC Scopus subject areas

  • General

Cite this

Sparse dynamics for partial differential equations. / Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D.; Osher, Stanley.

In: Proceedings of the National Academy of Sciences of the United States of America, Vol. 110, No. 17, 23.04.2013, p. 6634-6639.

Research output: Contribution to journalArticle

Schaeffer, Hayden ; Caflisch, Russel ; Hauck, Cory D. ; Osher, Stanley. / Sparse dynamics for partial differential equations. In: Proceedings of the National Academy of Sciences of the United States of America. 2013 ; Vol. 110, No. 17. pp. 6634-6639.
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