Journal of Scientific Computing

, Volume 49, Issue 2, pp 167–179 | Cite as

Implicit Parallel Time Integrators

  • Andrew Christlieb
  • Benjamin Ong


In this work, we discuss a family of parallel implicit time integrators for multi-core and potentially multi-node or multi-gpgpu systems. The method is an extension of Revisionist Integral Deferred Correction (RIDC) by Christlieb, Macdonald and Ong (SISC-2010) which constructed parallel explicit time integrators. The key idea is to re-write the defect correction framework so that, after initial startup costs, each correction loop can be lagged behind the previous correction loop in a manner that facilitates running the predictor and correctors in parallel.

In this paper, we show that RIDC provides a framework to use p cores to generate a pth-order implicit solution to an initial value problem (IVP) in approximately the same wall clock time as a single core, backward Euler implementation (p≤12). The construction, convergence and stability of the schemes are presented, along with supporting numerical evidence.


Initial value problems Integral deferred correction Parallel computation Multi-core computing 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathMichigan State UniversityEast LansingUSA

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