DEFLATION FOR THE OFF-DIAGONAL BLOCK IN SYMMETRIC SADDLE POINT SYSTEMS

Dumitrasc A, Kruse C, Rüde U (2024)

Publication Type: Journal article

Publication year: 2024

Journal

Siam Journal on Matrix Analysis and Applications Society for Industrial and Applied Mathematics

Book Volume: 45

Pages Range: 203-231

Journal Issue: 1

DOI: 10.1137/22M1537266

Abstract

Deflation techniques are typically used to shift isolated clusters of small eigenvalues in order to obtain a tighter distribution and a smaller condition number. Such changes induce a positive effect in the convergence behavior of Krylov subspace methods, which are among the most popular iterative solvers for large sparse linear systems. We develop a deflation strategy for symmetric saddle point matrices by taking advantage of their underlying block structure. The vectors used for deflation come from an elliptic singular value decomposition relying on the generalized Golub-Kahan bidiagonalization process. The block targeted by deflation is the off-diagonal one since it features a problematic singular value distribution for certain applications. One example is the Stokes flow in elongated channels, where the off-diagonal block has several small, isolated singular values, depending on the length of the channel. Applying deflation to specific parts of the saddle point system is important when using solvers such as CRAIG, which operates on individual blocks rather than the whole system. The theory is developed by extending the existing framework for deflating square matrices before applying a Krylov subspace method such as MINRES. Numerical experiments confirm the merits of our strategy and lead to interesting questions about using approximate vectors for deflation.

Authors with CRIS profile

Andrei Dumitrasc Lehrstuhl für Informatik 10 (Systemsimulation) Ulrich Rüde Lehrstuhl für Informatik 10 (Systemsimulation)

Involved external institutions

Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS) FR France (FR)

How to cite

APA:

Dumitrasc, A., Kruse, C., & Rüde, U. (2024). DEFLATION FOR THE OFF-DIAGONAL BLOCK IN SYMMETRIC SADDLE POINT SYSTEMS. Siam Journal on Matrix Analysis and Applications, 45(1), 203-231. https://doi.org/10.1137/22M1537266

MLA:

Dumitrasc, Andrei, Carola Kruse, and Ulrich Rüde. "DEFLATION FOR THE OFF-DIAGONAL BLOCK IN SYMMETRIC SADDLE POINT SYSTEMS." Siam Journal on Matrix Analysis and Applications 45.1 (2024): 203-231.

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