Parallel Solution Methods and Preconditioners for Evolution Equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F18%3A00495421" target="_blank" >RIV/68145535:_____/18:00495421 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.mla.vgtu.lt/index.php/MMA/article/view/1424/1134" target="_blank" >https://www.mla.vgtu.lt/index.php/MMA/article/view/1424/1134</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3846/mma.2018.018" target="_blank" >10.3846/mma.2018.018</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Parallel Solution Methods and Preconditioners for Evolution Equations

Popis výsledku v původním jazyce

The recent development of the high performance computer platforms shows a clear trend towards heterogeneity and hierarchy. In order to utilize the computational power, particular attention must be paid to finding new algorithms or adjust existing ones so that they better match the HPC computer architecture. In this work we consider an alternative to classical time-stepping methods based on use of time-harmonic properties and discuss solution approaches that allow efficient utilization of modern HPC resources. The method in focus is based on a truncated Fourier expansion of the solution of an evolutionary problem. The analysis is done for linear equations and it is remarked on the possibility to use two- or multilevel mesh methods for nonlinear problems, which can enable further, even higher degree of parallelization. nThe arising block matrix system to be solved admits a two-by-two block form with square blocks, for which a very efficient preconditioner exists. It leads to tight eigenvalue bounds for the preconditioned matrix and, hence, to a very fast convergence of a preconditioned Krylov subspace or iterative refinement method. The analytical background is shown as well as some illustrating numerical examples.

Název v anglickém jazyce

Parallel Solution Methods and Preconditioners for Evolution Equations

Popis výsledku anglicky

The recent development of the high performance computer platforms shows a clear trend towards heterogeneity and hierarchy. In order to utilize the computational power, particular attention must be paid to finding new algorithms or adjust existing ones so that they better match the HPC computer architecture. In this work we consider an alternative to classical time-stepping methods based on use of time-harmonic properties and discuss solution approaches that allow efficient utilization of modern HPC resources. The method in focus is based on a truncated Fourier expansion of the solution of an evolutionary problem. The analysis is done for linear equations and it is remarked on the possibility to use two- or multilevel mesh methods for nonlinear problems, which can enable further, even higher degree of parallelization. nThe arising block matrix system to be solved admits a two-by-two block form with square blocks, for which a very efficient preconditioner exists. It leads to tight eigenvalue bounds for the preconditioned matrix and, hence, to a very fast convergence of a preconditioned Krylov subspace or iterative refinement method. The analytical background is shown as well as some illustrating numerical examples.

Druh

J_imp - Článek v periodiku v databázi Web of Science

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

2018

Kód důvěrnosti údajů

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

Název periodika

Mathematical Modeling and Analysis

ISSN

1392-6292

e-ISSN

—

Svazek periodika

23

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

LT - Litevská republika

Počet stran výsledku

22

Strana od-do

287-308

Kód UT WoS článku

000439208500008

EID výsledku v databázi Scopus

2-s2.0-85046994578