Preconditioning discretizations of systems of partial differential equations

KA Mardal, R Winther - Numerical Linear Algebra with …, 2011 - Wiley Online Library
This survey paper is based on three talks given by the second author at the London
Mathematical Society Durham Symposium on Computational Linear Algebra for Partial …

Preconditioners for Krylov subspace methods: An overview

JW Pearson, J Pestana - GAMM‐Mitteilungen, 2020 - Wiley Online Library
When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

[图书][B] Finite elements II

A Ern, JL Guermond - 2021 - Springer
The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …

Numerical solution of saddle point problems

M Benzi, GH Golub, J Liesen - Acta numerica, 2005 - cambridge.org
Large linear systems of saddle point type arise in a wide variety of applications throughout
computational science and engineering. Due to their indefiniteness and often poor spectral …

[图书][B] Matrix analysis and computations

ZZ Bai, JY Pan - 2021 - SIAM
Analysis and computation, the most important and indispensable methods for processing
matrices, are closely related but two significantly different areas. The former focuses more on …

A preconditioner for generalized saddle point problems

M Benzi, GH Golub - SIAM Journal on Matrix Analysis and Applications, 2004 - SIAM
In this paper we consider the solution of linear systems of saddle point type by
preconditioned Krylov subspace methods. A preconditioning strategy based on the …

Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems

ZZ Bai, GH Golub - IMA Journal of Numerical Analysis, 2007 - academic.oup.com
We establish a class of accelerated Hermitian and skew-Hermitian splitting (AHSS) iteration
methods for large sparse saddle-point problems by making use of the Hermitian and skew …

Theory of inexact Krylov subspace methods and applications to scientific computing

V Simoncini, DB Szyld - SIAM Journal on Scientific Computing, 2003 - SIAM
We provide a general framework for the understanding of inexact Krylov subspace methods
for the solution of symmetric and nonsymmetric linear systems of equations, as well as for …

Structured preconditioners for nonsingular matrices of block two-by-two structures

ZZ Bai - Mathematics of Computation, 2006 - ams.org
For the large sparse block two-by-two real nonsingular matrices, we establish a general
framework of practical and efficient structured preconditioners through matrix transformation …

Optimal parameters in the HSS‐like methods for saddle‐point problems

ZZ Bai - Numerical Linear Algebra with Applications, 2009 - Wiley Online Library
For the Hermitian and skew‐Hermitian splitting iteration method and its accelerated variant
for solving the large sparse saddle‐point problems, we compute their quasi‐optimal iteration …