@TechReport{ it:2006-048,
author = {Owe Axelsson and Radim Blaheta and Maya Neytcheva},
title = {Preconditioning of Boundary Value Problems using
Elementwise {S}chur Complements},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2006},
number = {2006-048},
month = nov,
abstract = {Based on a particular node ordering and corresponding
block decomposition of the matrix we analyse an efficient,
algebraic multilevel preconditioner for the iterative
solution of finite element discretizations of elliptic
boundary value problems. Thereby an analysis of a new
version of block-factorization preconditioning methods is
presented. The approximate factorization requires an
approximation of the arising Schur complement matrix. In
this paper we consider such approximations derived by the
assembly of the local macro-element Schur complements.
The method can be applied also for non-selfadjoint problems
but for the derivation of condition number bounds we assume
that the corresponding differential operator is selfadjoint
and positive definite.}
}