The space-time multigrid method [1] treats the whole of the space-time problem simultaneously. The multigrid approach uses point smoothers and employs a parameter-dependent coarsening strategy that chooses either semicoarsening in space or in time on each level of the multigrid hierarchy.

  1. G. Horton and S. Vandewalle, “A Space-Time Multigrid Method for Parabolic Partial Differential Equations,” SIAM Journal on Scientific Computing, vol. 16, no. 4, pp. 848–864, 1995 [Online]. Available at: http://dx.doi.org/10.1137/0916050
    @article{HortonVandewalle1995,
      author = {Horton, Graham and Vandewalle, Stefan},
      journal = {SIAM Journal on Scientific Computing},
      number = {4},
      pages = {848--864},
      title = {{A Space-Time Multigrid Method for Parabolic Partial Differential Equations}},
      url = {http://dx.doi.org/10.1137/0916050},
      volume = {16},
      year = {1995}
    }