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M. Béreš^1,2 and S. Sysala¹

¹Institute of Geonics, Czech Academy of Sciences, Ostrava, Czechia
²Faculty of Electrical Engineering and Computer Science, VSB - Technical University of Ostrava, Czechia

doi:10.4203/ccc.14.2.1

M. Béreš, S. Sysala, "Deflated Krylov Method in Nonlinear Problems of Mechanics and Stochastic Analysis", in P. Iványi, J. Kruis, B.H.V. Topping, (Editors), "Proceedings of the Sixteenth International Conference on Computational Structures Technology", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 14, Paper 2.1, 2026, doi:10.4203/ccc.14.2.1

Keywords: finite element method, Newton method, Krylov method, preconditioners, deflation basis, nonlinear problems in mechanics.

Abstract

This paper focuses on the iterative solution of sequences of large-scale linear systems of equations with similar structure arising in nonlinear mechanics and stochastic analysis. To exploit this similarity, we combine preconditioned Krylov methods with deflation and update the deflation basis from previously computed vectors. The efficiency is illustrated in three different applications: the stochastic Darcy-flow systems, the strip-footing elasto-plastic benchmark solved by quasi-Newton/variable preconditioning (QNVP), and slope stability analysis solved by a continuation Newton-like method within the modified shear strength reduction framework. In all cases, deflation significantly reduces total runtime.

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Front Page Browse CCC CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Conferences ISSN 2753-3239 CCC: 14 PROCEEDINGS OF THE SIXTEENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: P. Iványi, J. Kruis and B.H.V. Topping Paper 2.1 Deflated Krylov Method in Nonlinear Problems of Mechanics and Stochastic Analysis M. Béreš^1,2 and S. Sysala¹ ¹Institute of Geonics, Czech Academy of Sciences, Ostrava, Czechia ²Faculty of Electrical Engineering and Computer Science, VSB - Technical University of Ostrava, Czechia doi:10.4203/ccc.14.2.1 Full Bibliographic Reference for this paper M. Béreš, S. Sysala, "Deflated Krylov Method in Nonlinear Problems of Mechanics and Stochastic Analysis", in P. Iványi, J. Kruis, B.H.V. Topping, (Editors), "Proceedings of the Sixteenth International Conference on Computational Structures Technology", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 14, Paper 2.1, 2026, doi:10.4203/ccc.14.2.1 Keywords: finite element method, Newton method, Krylov method, preconditioners, deflation basis, nonlinear problems in mechanics. Abstract This paper focuses on the iterative solution of sequences of large-scale linear systems of equations with similar structure arising in nonlinear mechanics and stochastic analysis. To exploit this similarity, we combine preconditioned Krylov methods with deflation and update the deflation basis from previously computed vectors. The efficiency is illustrated in three different applications: the stochastic Darcy-flow systems, the strip-footing elasto-plastic benchmark solved by quasi-Newton/variable preconditioning (QNVP), and slope stability analysis solved by a continuation Newton-like method within the modified shear strength reduction framework. In all cases, deflation significantly reduces total runtime. download the full-text of this paper (PDF, 13 pages, 704 Kb) go to the previous paper go to the next paper return to the table of contents return to the volume description
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