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An Adaptive Parallel-in-Time Method with Application to a Membrane Problem

  • Noha Makhoul Karam
  • Nabil Nassif
  • Jocelyne Erhel
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 98)

Abstract

In a previous work (Nassif et al., In: V.A. al (ed.) ICCS 06. Computer Science, pp. 148–155. Springer, New York, 2006), we introduced an approach for solving the initial value problem \(\frac{\mathit{dY}} {\mathit{dt}} = F(t,Y ),\,Y (0) = Y _{0}\) in a time-parallel way. The main feature of the method is its capacity to automatically generate a non-regular time grid, adapted to the behavior of the solution. Parallel integration is made possible by introducing a “shooting function” that partitions the problem into a sequence of shooting value problems, each defined on a time slice of the coarse grid. After rescaling the variables on each slice, a prediction data model that permits accurate predictions of the solution at the beginning of every slice, leads to an Adaptive Parallel Time Integration (APTI) algorithm. In this paper, the method is applied to a membrane problem having oscillatory and unbounded solutions on (0, ).

Keywords

Coarse Grid Waveform Relaxation Membrane Problem Multiple Shoot Method Asymptotic Similarity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Noha Makhoul Karam
    • 1
  • Nabil Nassif
    • 2
  • Jocelyne Erhel
    • 3
  1. 1.Université Saint JosephBeyrouthLebanon
  2. 2.American University of BeirutBeirutLebanon
  3. 3.INRIARennesFrance

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