Preconditioners for regularized saddle point problems with an application for heterogeneous Darcy flow problems

0438526 - ÚGN 2015 RIV NL eng J - Journal Article
Axelsson, Owe - Blaheta, Radim - Byczanski, Petr - Karátson, J. - Ahmad, B.
Preconditioners for regularized saddle point problems with an application for heterogeneous Darcy flow problems.
Journal of Computational and Applied Mathematics. Roč. 280, č. 280 (2015), s. 141-157. ISSN 0377-0427. E-ISSN 1879-1778
R&D Projects: GA MŠMT ED1.1.00/02.0070
Institutional support: RVO:68145535
Keywords : preconditioners * heterogeneous coefficients * regularized saddle point Inner–outer iterations * Darcy flow
Subject RIV: BA - General Mathematics
Impact factor: 1.328, year: 2015
http://www.sciencedirect.com/science/article/pii/S0377042714005238

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.
Permanent Link: http://hdl.handle.net/11104/0241945