PRECONDITIONING HETEROGENEOUS H(div) PROBLEMS BY ADDITIVE SCHUR COMPLEMENT APPROXIMATION AND APPLICATIONS Academic Article uri icon

abstract

  • 2016 Society for Industrial and Applied Mathematics. In this paper we propose and analyze a preconditioner for a system arising from a mixed finite element approximation of second-order elliptic problems describing processes in highly heterogeneous media. Our approach uses the technique of multilevel methods (see, e.g., [P. Vassilevski, Multilevel Block Factorization Preconditioners: Matrix-Based Analysis and Algorithms for Solving Finite Element Equations, Springer, New York, 2008]) and the recently proposed preconditioner based on additive Schur complement approximation by J. Kraus [SIAM J. Sci. Comput., 34 (2012), pp. A2872-A2895]. The main results are the design, study, and numerical justification of iterative algorithms for these problems that are robust with respect to the contrast of the media, defined as the ratio between the maximum and minimum values of the coefficient of the problem. Numerical tests provide experimental evidence for the high quality of the preconditioner and its desired robustness with respect to the material contrast. Such results for several representative cases are presented, one of which is related to the SPE10 (Society of Petroleum Engineers) benchmark problem.

published proceedings

  • SIAM JOURNAL ON SCIENTIFIC COMPUTING

author list (cited authors)

  • Kraus, J., Lazarov, R., Lymbery, M., Margenov, S., & Zikatanov, L.

complete list of authors

  • Kraus, Johannes||Lazarov, Raytcho||Lymbery, Maria||Margenov, Svetozar||Zikatanov, Ludmil

publication date

  • January 1, 2016 11:11 AM