In this paper, we aim at solving the Biot model under stabilized finite element
discretizations. To solve the resulting generalized saddle point linear systems, some
iterative methods are proposed and compared. In the first method, we apply the GMRES
algorithm as the outer iteration. In the second method, the Uzawa method with
variable relaxation parameters is employed as the outer iteration method. In the third
approach, Uzawa method is treated as a fixed-point iteration, the outer solver is the
so-called Anderson acceleration. In all these methods, the inner solvers are preconditioners for the generalized saddle point problem. In the preconditioners, the Schur
complement approximation is derived by using Fourier analysis approach. These preconditioners are implemented exactly or inexactly. Extensive experiments are given to
justify the performance of the proposed preconditioners and to compare all the algorithms.
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Non-stationary Structure-Preserving Preconditioning for Image Restoration
Non-stationary regularizing preconditioners have recently been proposed for the acceleration of classical iterative methods for the solution of linear discrete ill-posed problems. This paper explores how these preconditioners can be combined with the flexible GMRES iterative method. A new structure-respecting strategy to construct a sequence of regularizing preconditioners is proposed. We show that flexible GMRES applied with these preconditioners is able to restore images that have been contaminated by strongly non-symmetric blur, while several other iterative methods fail to do this.
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- NSF-PAR ID:
- 10191420
- Date Published:
- Journal Name:
- Computational Methods for Inverse Problems in Imaging
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1007/978-3-030-32882-5_3
