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Numerical Algorithms
Erschienen in: Numerical Algorithms 2/2022

18.04.2022 | Original Paper

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

verfasst von: Zdeněk Dostál, David Horák, Jakub Kružík, Tomáš Brzobohatý, Oldřich Vlach

Erschienen in: Numerical Algorithms | Ausgabe 2/2022

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Abstract

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.
Vorheriger Artikel Cocoercivity, smoothness and bias in variance-reduced stochastic gradient methods
Nächster Artikel Anderson accelerating the preconditioned modulus approach for linear complementarity problems on second-order cones

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Metadaten
Titel
Highly scalable hybrid domain decomposition method for the solution of huge scalar variational inequalities
verfasst von
Zdeněk Dostál
David Horák
Jakub Kružík
Tomáš Brzobohatý
Oldřich Vlach
Publikationsdatum
18.04.2022
Verlag
Springer US
Erschienen in
Numerical Algorithms / Ausgabe 2/2022
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-022-01281-3

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