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

0556736 - ÚGN 2023 RIV NL eng J - Journal Article
Dostál, Z. - Horák, David - Kružík, Jakub - Brzobohatý, T. - Vlach, O.
Highly scalable hybrid domain decomposition method for the solution of huge scalar variational inequalities.
Numerical Algorithms. Roč. 91, č. 2 (2022), s. 773-801. ISSN 1017-1398. E-ISSN 1572-9265
R&D Projects: GA MŠMT LQ1602; GA ČR(CZ) GA19-11441S
Grant - others:Ministerstvo školství, mládeže a tělovýchovy - GA MŠk(CZ) LM2018140
Institutional support: RVO:68145535
Keywords : domain decomposition * variational inequality * scalability * massively parallel algorithms * hybrid TFETI-DP
OECD category: Applied mathematics
Impact factor: 2.1, year: 2022
Method of publishing: Limited access
https://link.springer.com/content/pdf/10.1007/s11075-022-01281-3.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0330955