2024/08/22 by Martin J. Gander, Gander, Martin Jakob, Liu‐Di Lu +1
Mathematics · Engineering · #Differential Equations and Numerical Methods #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Boundary Problems
paper · pdf · doi:10.48550/arxiv.2408.12512
We present here the classical Schwarz method with a time domain decomposition applied to unconstrained parabolic optimal control problems. Unlike Dirichlet-Neumann and Neumann-Neumann algorithms, we find different properties based on the forward-backward structure of the optimality system. Variants can be found using only Dirichlet and Neumann transmission conditions. Some of these variants are only good smoothers, while others could lead to efficient solvers.