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Abstract We present a novel preconditioning technique for Krylov subspace algorithms to solve fluid‐structure interaction (FSI) linearized systems arising from finite element discretizations. An outer Krylov subspace solver preconditioned with a geometric multigrid (GMG) algorithm is used, where for the multigrid level subsolvers, a field‐split (FS) preconditioner is proposed. The block structure of the FS preconditioner is derived using the physical variables as splitting strategy. To solve the subsystems originated by the FS preconditioning, an additive Schwarz (AS) block strategy is employed. The proposed FS preconditioner is tested on biomedical FSI applications. Both 2D and 3D simulations are carried out considering aneurysm and venous valve geometries. The performance of the FS preconditioner is compared with that of a second preconditioner of pure domain decomposition type.
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This content will become publicly available on February 1, 2026
Krylov Subspace Based FISTA‐Type Methods for Linear Discrete Ill‐Posed Problems
ABSTRACT Several iterative soft‐thresholding algorithms, such as FISTA, have been proposed in the literature for solving regularized linear discrete inverse problems that arise in various applications in science and engineering. These algorithms are easy to implement, but their rates of convergence may be slow. This paper describes novel approaches to reduce the computations required for each iteration by using Krylov subspace techniques. Specifically, we propose to impose sparsity on the coefficients in the representation of the computed solution in terms of a Krylov subspace basis. Several numerical examples from image deblurring and computerized tomography are used to illustrate the efficiency and accuracy of the proposed methods.
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- Award ID(s):
- 2410699
- PAR ID:
- 10610685
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Numerical Linear Algebra with Applications
- Volume:
- 32
- Issue:
- 1
- ISSN:
- 1070-5325
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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