PARAEXP: a parallel integrator for linear initial-value problems 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.

References in zbMATH (referenced in 16 articles , 1 standard article )

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  1. Gander, Martin J.; Halpern, Laurence; Rannou, Johann; Ryan, Juliette: A direct time parallel solver by diagonalization for the wave equation (2019)
  2. Kwok, Felix; Ong, Benjamin W.: Schwarz waveform relaxation with adaptive pipelining (2019)
  3. Neumüller, Martin; Smears, Iain: Time-parallel iterative solvers for parabolic evolution equations (2019)
  4. Badia, Santiago; Olm, Marc: Nonlinear parallel-in-time Schur complement solvers for ordinary differential equations (2018)
  5. Botchev, M. A.; Hanse, A. M.; Uppu, R.: Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources (2018)
  6. Kooij, Gijs L.; Botchev, Mike A.; Geurts, Bernard J.: An exponential time integrator for the incompressible Navier-Stokes equation (2018)
  7. Wu, Shu-Lin: Toward parallel coarse grid correction for the parareal algorithm (2018)
  8. Zhu, Shuai; Weng, Shilie: A parallel spectral deferred correction method for first-order evolution problems (2018)
  9. Gander, Martin J.; Halpern, Laurence: Time parallelization for nonlinear problems based on diagonalization (2017)
  10. Kooij, G. L.; Botchev, M. A.; Geurts, B. J.: A block Krylov subspace implementation of the time-parallel Paraexp method and its extension for nonlinear partial differential equations (2017)
  11. Gander, Martin J.; Halpern, Laurence; Ryan, Juliet; Thuy Thi Bich Tran: A direct solver for time parallelization (2016)
  12. McDonald, Eleanor; Wathen, Andy: A simple proposal for parallel computation over time of an evolutionary process with implicit time stepping (2016)
  13. Arteaga, Andrea; Ruprecht, Daniel; Krause, Rolf: A stencil-based implementation of parareal in the C++ domain specific embedded language STELLA (2015)
  14. Gander, Martin J.: 50 years of time parallel time integration (2015)
  15. Song, Bo; Jiang, Yao-Lin: Analysis of a new parareal algorithm based on waveform relaxation method for time-periodic problems (2014)
  16. Gander, Martin J.; Güttel, Stefan: PARAEXP: a parallel integrator for linear initial-value problems (2013)