Preconditioning for boundary control problems in incompressible fluid\n dynamics

2015/11/23 by Gennadij Heidel, Heidel, Gennadij, Andy Wathen +1
Computer Science · Engineering · Mathematics · #49K20 #49M25 #65F08 #65F10 #65F50 #76D05 #76D07 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1511.07375

openalex publication_date 2015/11/23 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

PDE-constrained optimization is a field of numerical analysis that combines\nthe theory of PDEs, nonlinear optimization and numerical linear algebra.\nOptimization problems of this kind arise in many physical applications,\nprominently in incompressible fluid dynamics. In recent research, efficient\nsolvers for optimization problems governed by the Stokes and Navier--Stokes\nequations have been developed which are mostly designed for distributed\ncontrol. Our work closes a gap by showing the effectiveness of an appropriately\nmodified preconditioner to the case of Stokes boundary control. We also discuss\nthe applicability of an analogous preconditioner for Navier--Stokes boundary\ncontrol and provide some numerical results.\n

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