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Fan, Hongtao; Li, Yajing; Zhang, Hongbing; Zhu, Xinyun

Preconditioners based on matrix splitting for the structured systems from elliptic PDE-constrained optimization problems. (English) Zbl 07764784

Appl. Math. Comput. 463, Article ID 128341, 8 p. (2024).
Summary: With regard to the structured systems of linear equations, which arises from the Galerkin finite element discretizations of elliptic PDE-constrained optimization problems, some new preconditioners based on coefficient matrix splitting are established to speed up the convergence rate of Krylov subspace methods such as GMRES. Additionally, eigenvalue distribution of the corresponding preconditioned matrices is deeply discussed. Numerical simulations are carried out, the results of which exhibit that the corresponding preconditioned GMRES methods perform very well with the theoretical analysis results and are superior to other newly devised preconditioners.

MSC:

65F08 Preconditioners for iterative methods
65F10 Iterative numerical methods for linear systems
49M41 PDE constrained optimization (numerical aspects)

Keywords:

elliptic PDE-constrained optimization problems; preconditioner; matrix splitting; eigenvalue distribution; preconditioned GMRES
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References:

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