PinTOpt: Parallel-in-time solvers for linear optimality systems

This implementation contains both the ParaOpt and ParaDiag algorithms to perform parallel-in-time (PinT) optimal control. Detailed documentation can be found in the M-files of the methods themselves, as well as in Appendix C of the thesis which this code accompanies.

ParaDiag: Solving the all-at-once system with circulant preconditioners

The paradiag function uses the ParaDiag method for solving the all-at-once system arising in a time discretisation of the optimality system. See this paper by Wu et al. for the base method, and the thesis for extensions and improvements.

ParaOpt: A Parareal variant for boundary value problems

The paraopt function uses the ParaOpt method that sub-divides the time interval into smaller parts. The original terminal-cost method is described in this paper by Gander et al., and extensions are offered in the thesis. In particular, the function supports subspace enhancement and ParaDiag-based preconditioners.

Tests

The test_paradiag.m and test_paraopt.m files contain tests of the paradiag and paraopt functions, respectively, demonstrating their main features.