Highly scalable hybrid domain decomposition method for the solution of huge scalar variational inequalities

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F22%3A00556736" target="_blank" >RIV/68145535:_____/22:00556736 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989100:27740/22:10249788 RIV/61989100:27240/22:10249788

Výsledek na webu

<a href="https://link.springer.com/content/pdf/10.1007/s11075-022-01281-3.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007/s11075-022-01281-3.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11075-022-01281-3" target="_blank" >10.1007/s11075-022-01281-3</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Highly scalable hybrid domain decomposition method for the solution of huge scalar variational inequalities

Popis výsledku v původním jazyce

The unpreconditioned hybrid domain decomposition method was recently shown to be a competitive solver for linear elliptic PDE problems discretized by structured grids. Here, we plug H-TFETI-DP (hybrid total finite element tearing and interconnecting dual primal) method into the solution of huge boundary elliptic variational inequalities. We decompose the domain into subdomains that are discretized and then interconnected partly by Lagrange multipliers and partly by edge averages. After eliminating the primal variables, we get a quadratic programming problem with a well-conditioned Hessian and bound and equality constraints that is effectively solvable by specialized algorithms. We prove that the procedure enjoys optimal, i.e., asymptotically linear complexity. The analysis uses recently established bounds on the spectrum of the Schur complements of the clusters interconnected by edge/face averages. The results extend the scope of scalability of massively parallel algorithms for the solution of variational inequalities and show the outstanding efficiency of the H-TFETI-DP coarse grid split between the primal and dual variables.

Název v anglickém jazyce

Highly scalable hybrid domain decomposition method for the solution of huge scalar variational inequalities

Popis výsledku anglicky

The unpreconditioned hybrid domain decomposition method was recently shown to be a competitive solver for linear elliptic PDE problems discretized by structured grids. Here, we plug H-TFETI-DP (hybrid total finite element tearing and interconnecting dual primal) method into the solution of huge boundary elliptic variational inequalities. We decompose the domain into subdomains that are discretized and then interconnected partly by Lagrange multipliers and partly by edge averages. After eliminating the primal variables, we get a quadratic programming problem with a well-conditioned Hessian and bound and equality constraints that is effectively solvable by specialized algorithms. We prove that the procedure enjoys optimal, i.e., asymptotically linear complexity. The analysis uses recently established bounds on the spectrum of the Schur complements of the clusters interconnected by edge/face averages. The results extend the scope of scalability of massively parallel algorithms for the solution of variational inequalities and show the outstanding efficiency of the H-TFETI-DP coarse grid split between the primal and dual variables.

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

2022

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

1572-9265

Svazek periodika

91

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

29

Strana od-do

773-801

Kód UT WoS článku

000784390700002

EID výsledku v databázi Scopus

2-s2.0-85128280893