Introduced in 2003 by Farhat and Chandesris [1]. Augmented with a convergence accelerator later (missing reference) [2]. PITA is closely related to Parareal but uses a slightly different correction.

  1. C. Farhat and M. Chandesris, “Time-decomposed parallel time-integrators: theory and feasibility studies for fluid, structure, and fluid-structure applications,” International Journal for Numerical Methods in Engineering, vol. 58, no. 9, pp. 1397–1434, 2003 [Online]. Available at: http://dx.doi.org/10.1002/nme.860
    @article{FarhatEtAl2003,
      author = {Farhat, Charbel and Chandesris, M.},
      journal = {International Journal for Numerical Methods in Engineering},
      number = {9},
      pages = {1397--1434},
      title = {{Time-decomposed parallel time-integrators: theory and feasibility studies for fluid, structure, and fluid-structure applications}},
      url = {http://dx.doi.org/10.1002/nme.860},
      doi = {10.1002/nme.860},
      volume = {58},
      year = {2003}
    }
    
  2. J. Cortial and C. Farhat, “A time-parallel implicit method for accelerating the solution of non-linear structural dynamics problems,” International Journal for Numerical Methods in Engineering, vol. 77, no. 4, pp. 451–470, 2009 [Online]. Available at: http://dx.doi.org/10.1002/nme.2418
    @article{CortialFarhat2009,
      author = {Cortial, Julien and Farhat, Charbel},
      journal = {International Journal for Numerical Methods in Engineering},
      number = {4},
      pages = {451--470},
      title = {{A time-parallel implicit method for accelerating the solution of non-linear structural dynamics problems}},
      url = {http://dx.doi.org/10.1002/nme.2418},
      doi = {10.1002/nme.2418},
      volume = {77},
      year = {2009}
    }