Počet záznamů: 1
Inner product free iterative solution and elimination methods for linear systems of a three-by-three block matrix form
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SYSNO ASEP 0534467 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Inner product free iterative solution and elimination methods for linear systems of a three-by-three block matrix form Tvůrce(i) Axelsson, Owe (UGN-S) RID
Liang, Z.-Z. (CN)
Kružík, Jakub (UGN-S)
Horák, David (UGN-S) SAI, ORCIDCelkový počet autorů 4 Číslo článku 113117 Zdroj.dok. Journal of Computational and Applied Mathematics. - : Elsevier - ISSN 0377-0427
Roč. 383, February 2021 (2021)Poč.str. 19 s. Forma vydání Online - E Jazyk dok. eng - angličtina Země vyd. NL - Nizozemsko Klíč. slova PDE-constrained optimization ; iterative solution ; preconditioning ; global communication ; inner product free ; parallel efficiency Vědní obor RIV BA - Obecná matematika Obor OECD Applied mathematics CEP LQ1602 GA MŠMT - Ministerstvo školství, mládeže a tělovýchovy Způsob publikování Omezený přístup Institucionální podpora UGN-S - RVO:68145535 UT WOS 000574895400017 EID SCOPUS 85089350230 DOI 10.1016/j.cam.2020.113117 Anotace 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. Pracoviště Ústav geoniky Kontakt Lucie Gurková, lucie.gurkova@ugn.cas.cz, Tel.: 596 979 354 Rok sběru 2021 Elektronická adresa https://www.sciencedirect.com/science/article/pii/S0377042720304088
Počet záznamů: 1