\documentclass{complas2023-abstracts} %\usepackage{pslatex} %\usepackage{amsmath} %\usepackage{amsfonts} %\usepackage{amssymb} \title{MASSIVELY PARALLEL HYBID DOMAIN DECOMPOSITION ALGORITHMS FOR SOLVING HUGE CONTACT PROBLEMS} \author{ZDEN\v{E}K DOST\'AL$^{*\dag}$, TOM\'A\v{S} BRZOBOHAT\'Y$^{*}$ AND % DAVID HOR\'AK$^{*}$}\\ AND OLD\v{R}ICH VLACH^$^{*\dag}$} \address{$^{*}$ VSB-TU Ostrava, National Supercomputer Center IT4Innovations\\ 17 listopadu 15, CZ-70833, Ostrava\\ tomas.brzobohaty@vsb.cz; oldrich.vlach@vsb.cz \and $^{\dag}$ FEECS VSB-Technical University of Ostrava, Department of Applied Mathematics\\ 17 listopadu 15, CZ-70833, Ostrava\\ zdenek.dostal@vsb.cz} \begin{document} %\maketitle \begin{center} \bf ABSTRACT \end{center} The current development of supercomputers motivated the research of massively parallel algorithms to solve many challenging problems, including huge contact problems of elasticity. Here we shall describe how to adapt the three-level hybrid domain decomposition method proposed by Klawonn and Rheinbach to solving multibody contact problems with billions of nodal variables. The basic idea is to decompose the domains occupied by the bodies into subdomains, use the transformation of variables to join some subdomains by the rigid body motion of adjacent subdomains into clusters so that each cluster has only six rigid body modes, and then use the standard FETI/BETI methodology to get well conditioned dual quadratic programming problems with bound and equality problem which can be solved with an asymptotically optimal (linear complexity). The results of numerical experiments \cite{1}--\cite{4} show the considerable scope of scalability of both \mbox{H-TFETI} and \mbox{H-TBETI} and indicate that this method can be helpful for the solution of huge linear and contact problems. Moreover, the two-level structure of the coarse grids (split between the primal and dual variables) can be effectively exploited by the node-core design of the modern supercomputers' hardware. \begin{center} \fontsize{11}{12}\selectfont \begin{thebibliography}{99} %\bibitem{Rung} Rung T. \emph{Challenges and perspectives for maritime CFD applications}. Jahrbuch der Schiff-bautechnischen Gesellschaft, Vol. 103, 2009. %\bibitem{Celigueta} Celigueta M.A., Latorre S., Arrufat F., O\~{n}ate E. Accurate modelling of the elastic behavior of a continuum with the discrete element method. \emph{Computational Mechanics}, Vol. 60 (6), pp. 997-1010, 2017. \bibitem