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

2024/04/20 by Soura Sana, Sana, Soura, Bankim C. Mandal +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #NMR spectroscopy and applications #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2404.13283

openalex publication_date 2024/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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