Robust Solvers for Symmetric Positive Definite Operators and Weighted Poincar Inequalities Conference Paper uri icon

abstract

  • An abstract setting for robustly preconditioning symmetric positive definite (SPD) operators is presented. The term "robust" refers to the property of the condition numbers of the preconditioned systems being independent of mesh parameters and problem parameters. Important instances of such problem parameters are in particular (highly varying) coefficients. The method belongs to the class of additive Schwarz preconditioners. The paper gives an overview of the results obtained in a recent paper by the authors. It, furthermore, focuses on the importance of weighted Poincar inequalities, whose notion is extended to general SPD operators, for the analysis of stable decompositions. To demonstrate the applicability of the abstract preconditioner the scalar elliptic equation and the stream function formulation of Brinkman's equations in two spatial dimensions are considered. Several numerical examples are presented. 2012 Springer-Verlag.

published proceedings

  • Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

author list (cited authors)

  • Efendiev, Y., Galvis, J., Lazarov, R., & Willems, J.

citation count

  • 0

complete list of authors

  • Efendiev, Yalchin||Galvis, Juan||Lazarov, Raytcho||Willems, Joerg

editor list (cited editors)

  • Lirkov, I., Margenov, S., & Wasniewski, J.

publication date

  • June 2012