Multilevel a posteriori error estimator for greedy reduced basis algorithms

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F20%3A00340272" target="_blank" >RIV/68407700:21110/20:00340272 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21220/20:00340272

Výsledek na webu

<a href="https://doi.org/10.1007/s42452-020-2409-9" target="_blank" >https://doi.org/10.1007/s42452-020-2409-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s42452-020-2409-9" target="_blank" >10.1007/s42452-020-2409-9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Multilevel a posteriori error estimator for greedy reduced basis algorithms

Popis výsledku v původním jazyce

The goal of reduced basis algorithms is to provide a relatively small set of functions which can serve as a basis for sufficiently accurate and fast numerical solution of a parametrized problem for any choice of parameters. Such methods are often employed in parameter identification problems detecting, for instance, material qualities in diffusion problems, elasticity, or in Maxwell equations, or in time dependent problems where time plays the role of the parameter. We deal with greedy reduced basis algorithms. An important part of these algorithms is to estimate the difference between the exact solution of a discretized problem and its projection onto the space spanned by a reduced basis. We introduce a new kind of the estimate, which is based on a multilevel splitting of a discretized solution space, and we compare it with a standard estimate based on bounds to coercivity and continuity constants. Two sided guaranteed bounds to the error can be obtained for both methods. Numerical complexity as well as memory consumption of both methods are comparable, while the multilevel method provides a more accurate spatial distribution of the error.

Název v anglickém jazyce

Multilevel a posteriori error estimator for greedy reduced basis algorithms

Popis výsledku anglicky

The goal of reduced basis algorithms is to provide a relatively small set of functions which can serve as a basis for sufficiently accurate and fast numerical solution of a parametrized problem for any choice of parameters. Such methods are often employed in parameter identification problems detecting, for instance, material qualities in diffusion problems, elasticity, or in Maxwell equations, or in time dependent problems where time plays the role of the parameter. We deal with greedy reduced basis algorithms. An important part of these algorithms is to estimate the difference between the exact solution of a discretized problem and its projection onto the space spanned by a reduced basis. We introduce a new kind of the estimate, which is based on a multilevel splitting of a discretized solution space, and we compare it with a standard estimate based on bounds to coercivity and continuity constants. Two sided guaranteed bounds to the error can be obtained for both methods. Numerical complexity as well as memory consumption of both methods are comparable, while the multilevel method provides a more accurate spatial distribution of the error.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

SN Applied Sciences

ISSN

2523-3963

e-ISSN

2523-3971

Svazek periodika

2

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

19

Strana od-do

—

Kód UT WoS článku

000532826500102

EID výsledku v databázi Scopus

2-s2.0-85100824106