Preconditioners for regularized saddle point problems with an application for heterogeneous Darcy flow problems
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Owe Axelsson [1] ; Radim Blaheta [1] ; Petr Byczanski [1] ; János Karátson [3] ; Bashir Ahmad [2]
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[1] Institute of Geonics
Institute of Geonics
Chequia
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[2] King Abdulaziz University
King Abdulaziz University
Arabia Saudí
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[3] ELTE University, Budapest, (Hungary)
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- Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 280, Nº 1 (15 May 2015), 2015, págs. 141-157
- Idioma: inglés
- DOI: 10.1016/j.cam.2014.11.044
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Resumen
Saddle point problems arise in the modeling of many important practical situations. Preconditioners for the corresponding matrices of block-triangular form, based on coupled inner–outer iteration methods, are analyzed and applied to a Darcy flow problem, possibly with strong heterogeneity and non-symmetric saddle point systems. Using proper regularized forms of the given matrix and its preconditioner, it is shown that the eigenvalues cluster about one or two points on the real axis for large values of the regularization parameters and that eigenvalue bounds do not depend on this variation. Therefore, just two outer iterations can suffice. On the other hand, several iterations may be needed to solve the inner iteration systems.
