A robust structured preconditioner for the time-harmonic parabolic optimal control problem

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F18%3A00495413" target="_blank" >RIV/68145535:_____/18:00495413 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/content/pdf/10.1007%2Fs11075-017-0451-5.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007%2Fs11075-017-0451-5.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11075-017-0451-5" target="_blank" >10.1007/s11075-017-0451-5</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A robust structured preconditioner for the time-harmonic parabolic optimal control problem

Popis výsledku v původním jazyce

We consider the iterative solution of optimal control problems constrained by the time-harmonic parabolic equations. Due to the time-harmonic property of the control equations, a suitable discretization of the corresponding optimality systems leads to a large complex linear system with special two-by-two block matrix of saddle point form. For this algebraic system, an efficient preconditioner is constructed, which results in a fast Krylov subspace solver, that is robust with respect to the mesh size, frequency, and regularization parameters. Furthermore, the implementation is straightforward and the computational complexity is of optimal order, linear in the number of degrees of freedom. We show that the eigenvalue distribution of the corresponding preconditioned matrix leads to a condition number bounded above by 2. Numerical experiments confirming the theoretical derivations are presented, including comparisons with some other existing preconditioners.

Název v anglickém jazyce

A robust structured preconditioner for the time-harmonic parabolic optimal control problem

Popis výsledku anglicky

We consider the iterative solution of optimal control problems constrained by the time-harmonic parabolic equations. Due to the time-harmonic property of the control equations, a suitable discretization of the corresponding optimality systems leads to a large complex linear system with special two-by-two block matrix of saddle point form. For this algebraic system, an efficient preconditioner is constructed, which results in a fast Krylov subspace solver, that is robust with respect to the mesh size, frequency, and regularization parameters. Furthermore, the implementation is straightforward and the computational complexity is of optimal order, linear in the number of degrees of freedom. We show that the eigenvalue distribution of the corresponding preconditioned matrix leads to a condition number bounded above by 2. Numerical experiments confirming the theoretical derivations are presented, including comparisons with some other existing preconditioners.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

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

Návaznosti

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

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Numerical Algorithms

ISSN

1017-1398

e-ISSN

—

Svazek periodika

79

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

22

Strana od-do

575-596

Kód UT WoS článku

000445494100011

EID výsledku v databázi Scopus

2-s2.0-85037662259