Optimal Control of a Sub-diffusion Model using Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation Algorithms

Abstract: This paper explores the convergence behavior of two waveform relaxation algorithms, namely the Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation algorithms, for an optimal control problem with a sub-diffusion partial differential equation (PDE) constraint. The algorithms are tested on regular 1D domains with multiple subdomains, and the analysis focuses on how different constant values of the generalized diffusion coefficient affect the convergence of these algorithms.