"Pt\u00E1k, Svatopluk" . "Contact modelling is still a challenging problem of non-linear computational mechanics. If the FETI method is applied to the contact problems, the same methodology can be used to prescribe conditions of non-penetration between bodies. We shall obtain a new minimization problem with additional nonnegativity constraints which replace more complex general non-penetration conditions. In this paper we are concerned with application of one of a new variant of the FETI domain decomposition method, called TFETI (Total FETI) method, to the solution of contact problems. Both compatibility between adjacent subdomains and Dirichlet boundary conditions are enforced by Lagrange multipliers acting along the boundary or mutual interfaces. We describe theoretical foundation of the TFETI algorithm and its implementation into the inner loop of the code which treats the material and geometrical effects in the outer loop." . . "P(GA101/05/0423)" . "27240" . "[6A828EFB0B3A]" . "Scalable algorithms for contact problems with geometrical and material nonlinearities"@en . . . . "280"^^ . "contact problem; domain decomposition; numerical scalability; geometric nonlinearity; material nonlinearity; finite element method"@en . . . . . "Scalable algorithms for contact problems with geometrical and material nonlinearities"@en . . . "Scalable algorithms for contact problems with geometrical and material nonlinearities" . . "RIV/61989100:27240/06:00013638!RIV07-GA0-27240___" . . "RIV/61989100:27240/06:00013638" . "4"^^ . . . . "2006-06-16+02:00"^^ . . . "2006-06-12+02:00"^^ . "Brunel University, West London, UK" . "Dobi\u00E1\u0161, Ji\u0159\u00ED" . . . "300"^^ . "2"^^ . "Dost\u00E1l, Zden\u011Bk" . "Scalable algorithms for contact problems with geometrical and material nonlinearities" . "Kontaktn\u00ED modelov\u00E1n\u00ED je st\u00E1le velmi n\u00E1ro\u010Dn\u00FD probl\u00E9m neline\u00E1rn\u00ED v\u00FDpo\u010Detn\u00ED matematiky. V \u010Dl\u00E1nku se budeme zab\u00FDvat aplikac\u00ED zcela nov\u00E9 varianty FETI metody rozlo\u017Een\u00ED oblasti naz\u00FDvan\u00E9 TFETI (Total FETI) metoda pro \u0159e\u0161en\u00ED kontaktn\u00EDch \u00FAloh. Kompatibilita mezi podoblastmi stejn\u011B jako Dirichletovy okrajov\u00E9 podm\u00EDnky se zaji\u0161\u0165uj\u00ED prost\u0159ednictv\u00EDm Lagrangeov\u00FDch multiplik\u00E1tor\u016F p\u0159edepisovan\u00FDch pod\u00E9l vz\u00E1jemn\u00FDch rozhran\u00ED a hranic. Pop\u00ED\u0161eme teoretick\u00FD z\u00E1klad t\u00E9to metody a jej\u00ED implementaci do vnit\u0159n\u00ED smy\u010Dky algoritmu, kter\u00FD \u0159e\u0161\u00ED materi\u00E1lov\u00E9 a geometrick\u00E9 nelinearity prost\u0159ednictv\u00EDm vn\u011Bjs\u00ED smy\u010Dky. Pro \u0159e\u0161en\u00ED kontaktn\u00EDch \u00FAloh pomoc\u00ED FETI a TFETI metod pou\u017E\u00EDv\u00E1me %22Modified Proportioning with Reduced Gradient Projection%22 (MPRGP) algoritmy."@cs . . . "498472" . "Contact modelling is still a challenging problem of non-linear computational mechanics. If the FETI method is applied to the contact problems, the same methodology can be used to prescribe conditions of non-penetration between bodies. We shall obtain a new minimization problem with additional nonnegativity constraints which replace more complex general non-penetration conditions. In this paper we are concerned with application of one of a new variant of the FETI domain decomposition method, called TFETI (Total FETI) method, to the solution of contact problems. Both compatibility between adjacent subdomains and Dirichlet boundary conditions are enforced by Lagrange multipliers acting along the boundary or mutual interfaces. We describe theoretical foundation of the TFETI algorithm and its implementation into the inner loop of the code which treats the material and geometrical effects in the outer loop."@en . "\u0160k\u00E1lovateln\u00E9 algoritmy pro kontaktn\u00ED \u00FAlohy s geometrick\u00FDmi a materi\u00E1lov\u00FDmi nelinearitami"@cs . "\u0160k\u00E1lovateln\u00E9 algoritmy pro kontaktn\u00ED \u00FAlohy s geometrick\u00FDmi a materi\u00E1lov\u00FDmi nelinearitami"@cs . "Vondr\u00E1k, V\u00EDt" .