Record details

Title
    Preconditioners for Some Matrices of Two-by-Two Block Form, with Applications, I
Author
    Axelsson, Owe
Language
    anglicky
Publication type
    článek v odborném periodiku
Source title - serial
    Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications. Springer Proceedings in Mathematics and Statistics
Vol./nr.
    Roč. 45, č. 45
Pages
    s. 45-67
Year
    2013
Notes
    Autoři celkem: 1
    Projekt: ED1.1.00/02.0070, GA MŠk3cav_un_auth*0285288
    Rozsah: 23 s. : E
Subject category
    Cahn-Hilliard phase-field model
    complex-valued system
    optimal control
    preconditioning
    two-by-two block-structured matrices
Keyword
    Applications
    Block
    Form
    Matrices
    Preconditioners
    Two-by-Two
Abstract (in english)
   Matrices of two-by-two block form with matrix blocks of equal order arise in various important applications, such as when solving complex-valued systems in real arithmetics, in linearized forms of the Cahn-Hilliard diffusive phase-field differential equation model and in constrained partial differential equations with distributed control. It is shown how an efficient preconditioner can be constructed which, under certain conditions, has a resulting spectral condition number of about 2. The preconditioner avoids the use of Schur complement matrices and needs only solutions with matrices that are linear combinations of the matrices appearing in each block row of the given matrix and for which often efficient preconditioners are already available.
Contributor
    AV ČR Brno, Ústav geoniky
Contributor code
    AV ČR, ÚG
Source format
    U
Import date
    24. 10. 2014