A novel parallel algorithm for the integration of linear initial-value problems is proposed. This algorithm is based on the simple observation that homogeneous problems can typically be integrated much faster than inhomogeneous problems. An overlapping time-domain decomposition is utilized to obtain decoupled inhomogeneous and homogeneous subproblems, and a near-optimal Krylov method is used for the fast exponential integration of the homogeneous subproblems. We present an error analysis and discuss the parallel scaling of our algorithm. The efficiency of this approach is demonstrated with numerical examples.


  1. parallelization
  2. linear initial-value problem
  3. rational Krylov
  4. matrix exponential

MSC codes

  1. 65L05
  2. 65Y05
  3. 65F60

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Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: C123 - C142
ISSN (online): 1095-7197


Submitted: 21 November 2011
Accepted: 18 December 2012
Published online: 5 March 2013


  1. parallelization
  2. linear initial-value problem
  3. rational Krylov
  4. matrix exponential

MSC codes

  1. 65L05
  2. 65Y05
  3. 65F60



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