A real‐time optimization algorithm for the fixed‐stress splitting scheme. (16th March 2021)

• Record Type: Journal Article
• Authors: Honório, Hermínio T.; Martins, Bruno; Maliska, Clovis R.
• Is Part Of: International journal for numerical methods in engineering. Volume 122:Number 12(2021)
• Page Start: 2891
• Page End: 2918
• Publication Date: 2021-03-16
• Subjects: coupled consolidation -- fixed‐stress -- geomechanics -- real‐time optimization -- tuning parameter; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6645
• Languages: English
• ISSNs: 0029-5981

Abstract

Abstract: The efficient solution of the systems of equations arising from coupled consolidation problems is a matter of concern worldwide. The fixed‐stress splitting scheme is an effective approach for solving these equations either in a sequential manner or as a preconditioner for a fully coupled approach. Recent studies show that it is possible to improve the convergence rate of the fixed‐stress approach by choosing a proper tuning parameter. In this work, we present an optimization algorithm that dynamically searches for the optimal tuning parameter for each time step of the simulation, hence the denomination of real‐time optimization. The numerical examples show that the optimal tuning parameter indeed can change during the simulation, which highlights the importance of the dynamic search provided by the optimization algorithm. In some situations, the optimized fixed‐stress algorithm proposed in this work is able to reduce the total number of iterations by up to 70% compared to the non‐optimized version.