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

TL;DR

This paper investigates the convergence of Dirichlet-Neumann and Neumann-Neumann waveform relaxation algorithms applied to an optimal control problem constrained by a sub-diffusion PDE, analyzing the impact of the diffusion coefficient on convergence in 1D domains.

Contribution

It provides a detailed analysis of the convergence behavior of two waveform relaxation algorithms for sub-diffusion PDE constrained optimal control problems, considering the influence of the diffusion coefficient.

Findings

Convergence depends on the value of the diffusion coefficient.

Algorithms perform differently across various subdomain configurations.

The study offers insights into algorithm selection for sub-diffusion control problems.

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.