Equivalent operator preconditioning for elliptic problems

0328616 - ÚGN 2010 RIV NL eng J - Journal Article
Axelsson, Owe - Karátson, J.
Equivalent operator preconditioning for elliptic problems.
Numerical Algorithms. Roč. 50, č. 3 (2009), s. 297-380. ISSN 1017-1398. E-ISSN 1572-9265
Institutional research plan: CEZ:AV0Z30860518
Keywords : Elliptic problem * Conjugate gradient method * preconditioning * equivalent operators * compact operators
Subject RIV: BA - General Mathematics
Impact factor: 0.716, year: 2009
http://en.scientificcommons.org/42514649

The numerial solution of linear elliptic partial differential equations most often involves a finite element or finite difference discretization. To preserve sparsity, the arising system is normally solved using an iterative solution method, commonly a preconditioned conjugate gradient method.Preconditioning is a crucial part of such a solution process. In order to enable the solution of very large-scale systems, it is desirable that the total computational cost will be of optimal order, i.e. proportional to the degrees of freedom of the paaroximation used, which also induces mesh independent convergence of the iteration. This paper surveys the equivalent operator approach, which has proven to provide an efficient general framework to construct such preconditioners.
Permanent Link: http://hdl.handle.net/11104/0174896