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Analysis on inexact block diagonal preconditioners for elliptic PDE-constrained optimization problems
Huang, Na1,2; Ma, Chang-Feng2
AbstractBy using the Galerkin finite element method, the distributed control problems can be discretized into a saddle point problem with a coefficient matrix of block three-by-three, which can be reduced to a linear system with lower order. We first introduce a class of inexact block diagonal preconditioners and estimate the lower and upper bounds of positive and negative eigenvalues of the preconditioned matrices, respectively. Based on the Cholesky decomposition of the known matrices, we also analyze a lower triangular preconditioner to accelerate the minimal residual method for the reduced linear system and discuss its real and complex eigenvalues respectively. Moreover, these bounds do not rely on the regularization parameter and the eigenvalues of the matrices in the discrete system. Numerical experiments are also presented to demonstrate the effectiveness and robustness of the two new preconditioners. (C) 2017 Elsevier Ltd. All rights reserved.
KeywordPDE-constrained optimization Saddle point matrices Preconditioner Cholesky decomposition Spectral bound
Funding ProjectNational Postdoctoral Program for Innovative Talents[BX201600182] ; China Postdoctoral Science Foundation[2016M600141] ; National Natural Science Foundation of China[11071041] ; Fujian Natural Science Foundation[02016J01005] ; Fujian Natural Science Foundation[2015J01578]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000415908400015
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Document Type期刊论文
Corresponding AuthorMa, Chang-Feng
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100190, Peoples R China
2.Fujian Normal Univ, Coll Math & Informat, Fujian Key Lab Math Anal & Applicat, Fuzhou 350117, Fujian, Peoples R China
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GB/T 7714
Huang, Na,Ma, Chang-Feng. Analysis on inexact block diagonal preconditioners for elliptic PDE-constrained optimization problems[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2017,74(10):2423-2437.
APA Huang, Na,&Ma, Chang-Feng.(2017).Analysis on inexact block diagonal preconditioners for elliptic PDE-constrained optimization problems.COMPUTERS & MATHEMATICS WITH APPLICATIONS,74(10),2423-2437.
MLA Huang, Na,et al."Analysis on inexact block diagonal preconditioners for elliptic PDE-constrained optimization problems".COMPUTERS & MATHEMATICS WITH APPLICATIONS 74.10(2017):2423-2437.
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