@PhDThesis{ itlic:2005-006,
author = {Erik B{\"a}ngtsson},
title = {Robust Preconditioned Iterative Solution Methods for
Large-Scale Nonsymmetric Problems},
school = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2005},
number = {2005-006},
type = {Licentiate thesis},
month = nov,
day = {3},
note = {Typos corrected 2005-11-21},
abstract = {We study robust, preconditioned, iterative solution
methods for large-scale linear systems of equations,
arising from different applications in geophysics and
geotechnics.
The first type of linear systems studied here, which are
dense, arise from a boundary element type of discretization
of crack propagation in brittle material. Numerical
experiment show that simple algebraic preconditioning
strategies results in iterative schemes that are highly
competitive with a direct solution method.
The second type of algebraic systems are nonsymmetric and
indefinite and arise from finite element discretization of
the partial differential equations describing the elastic
part of glacial rebound processes. An equal order finite
element discretization is analyzed and an optimal
stabilization parameter is derived.
The indefinite algebraic systems are of 2-by-2-block form,
and therefore block preconditioners of block-factorized or
block-triangular form are used when solving the indefinite
algebraic system. There, the required Schur complement is
approximated in various ways and the quality of these
approximations is compared numerically.
When the block preconditioners are constructed from
incomplete fac\-toriza\-tions of the diagonal blocks, the
iterative scheme show a growth in iteration count with
increasing problem size. This growth is stabilized by
replacing the incomplete factors with an inner iterative
scheme with a (nearly) optimal order multilevel
preconditioner.}
}