The MGRIT algorithm [1] enables a scalable and non-intrusive parallel-in-time approach by applying multigrid reduction to the time dimension. See XBraid for more information and a place to download the XBraid software.

  1. S. Friedhoff, R. D. Falgout, T. V. Kolev, S. P. MacLachlan, and J. B. Schroder, “A Multigrid-in-Time Algorithm for Solving Evolution Equations in Parallel,” in Presented at: Sixteenth Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO, United States, Mar 17 - Mar 22, 2013, 2013 [Online]. Available at: http://www.osti.gov/scitech/servlets/purl/1073108
    @inproceedings{FriedhoffEtAl2013,
      author = {Friedhoff, S. and Falgout, R.~D. and Kolev, T.~V. and MacLachlan, Scott P. and Schroder, Jacob B.},
      booktitle = {{Presented at: Sixteenth Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO, United States, Mar 17 - Mar 22, 2013}},
      title = {{A Multigrid-in-Time Algorithm for Solving Evolution Equations in Parallel}},
      url = {http://www.osti.gov/scitech/servlets/purl/1073108},
      year = {2013}
    }