Inner product free iterative solution and elimination methods for linear systems of a three-by-three block matrix form

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F21%3A00534467" target="_blank" >RIV/68145535:_____/21:00534467 - isvavai.cz</a>

Alternative codes found

RIV/61989100:27240/21:10245743

Result on the web

<a href="https://www.sciencedirect.com/science/article/pii/S0377042720304088" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0377042720304088</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cam.2020.113117" target="_blank" >10.1016/j.cam.2020.113117</a>

Result language

angličtina

Original language name

Inner product free iterative solution and elimination methods for linear systems of a three-by-three block matrix form

Original language description

Large scale systems of algebraic equations are frequently solved by iterative solution methods, such as the conjugate gradient method for symmetric or a generalized conjugate gradient or generalized minimum residual method for nonsymmetric linear systems. In practice, to get an acceptable elapsed computing time when solving large scale problems, one shall use parallel computer platforms. However, such methods involve orthogonalization of search vectors which requires computation of many inner products and, hence, needs global communication of data, which will be costly in computer times. In this paper, we propose various inner product free methods, such as the Chebyshev acceleration method. We study the solution of linear systems arising from optimal control problems for PDEs, such as the edge element discretization of the time-periodic eddy current optimal control problem. Following a discretize-then-optimize scheme, the resulting linear system is of a three-by-three block matrix form. Various solution methods based on an approximate Schur complement and inner product free iterative solution methods for this linear system are analyzed and compared with an earlier used method for two-by-two block matrices with square blocks. The convergence properties and implementation details of the proposed methods are analyzed to show their effectiveness and practicality. Both serial and parallel numerical experiments are presented to further investigate the performance of the proposed methods compared with some other existing methods.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

<a href="/en/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2021

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Computational and Applied Mathematics

ISSN

0377-0427

e-ISSN

—

Volume of the periodical

383

Issue of the periodical within the volume

February 2021

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

19

Pages from-to

113117

UT code for WoS article

000574895400017

EID of the result in the Scopus database

2-s2.0-85089350230