Multiresolution adaptive space refinement in geophysical fluid dynamics simulation

  • Aimé Fournier
  • Gregory Beylkin
  • Vani Cheruvu
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 41)


We review part of the methodology for multiresolution adaptive solution of PDEs introduced by Alpert et al. (2002) in 1D (§2.1), and introduce a 2D generalization and implementation (§2.2). This methodology is similar to the spectral-element method (SEM, e.g., Fournier et al. 2004) in that it combines spectral accuracy with finite-element efficiency, but is not exactly SEM. We present 2D dynamical test cases (§2.3) that exhibit decreasing range of active scales (Heat Eq.), or else increasing range due to strong nonlinearities (Burgers Eq.).We conclude by showing that our methodology adapts to such evolving phenomena in these PDEs (§3), thereby saving computational cost, while preserving a high preselected representation accuracy per time step.


Truncation Error Adaptive Solution Spectral Accuracy Methodology Adapt Save Computation Cost 
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  1. ABGV02.
    B. Alpert, G. Beylkin, D. Gines, and L. Vozovoi. Adaptive solution of partial differential equations in multiwavelet bases. J. Comput. Phys., 182(1):149–190, October 2002.MathSciNetCrossRefzbMATHGoogle Scholar
  2. BKV98.
    G. Beylkin, J. M. Keiser, and L. Vozovoi. A new class of time discretization schemes for the solution of nonlinear pdes. J. Comput. Phys., 147:362–387, 1998.MathSciNetCrossRefzbMATHGoogle Scholar
  3. FTT03.
    Aimée Fournier, Mark A. Taylor, and Joseph J. Tribbia. The Spectral Element Atmosphere Model (SEAM): High-resolution parallel computation and localized resolution of regional dynamics. Mon. Wea. Rev., 132:726–748, 2004.CrossRefGoogle Scholar
  4. PFTV88.
    W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Aimé Fournier
    • 1
  • Gregory Beylkin
    • 2
  • Vani Cheruvu
    • 2
  1. 1.Department of Meteorology, College of Computer, Mathematical, and Physical SciencesUniversity of Maryland at College ParkUSA
  2. 2.Department of Applied MathematicsUniversity of Colorado at BoulderUSA

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