A new MOX report entitled “Convergence analysis and optimization of a Robin Schwarz waveform relaxation method for periodic parabolic optimal control problems” by Ciaramella, G.; Halpern, L.; Mechelli, L. has appeared in the MOX Report Collection.
The report can be donwloaded at the following link:
https://www.mate.polimi.it/biblioteca/add/qmox/62/2022.pdf
Abstract: This paper is concerned with a novel convergence analysis of the optimized Schwarz waveform relaxation method (OSWRM) for the solution of optimal control problems governed by periodic parabolic partial differential equations (PDEs). The new analysis is based on Fourier-type technique applied to a semidiscrete in time form of the optimality condition. This leads to a precise characterization of the convergence factor of the method at the semidiscrete level. Using this characterization, the optimal transmission condition parameter is obtained at the semidiscrete level and its asymptotic behavior as the time discretization converges to zero is analyzed in detail.
