A unifying theory for nonlinear additively and multiplicatively preconditioned globalization strategies [Elektronische Ressource] : convergence results and examples from the field of nonlinear elastostatics and elastodynamics / vorgelegt von Christian Groß

A Unifying Theory for Nonlinear Additively andMultiplicatively Preconditioned Globalization Strategies:Convergence Results and Examples From the Field ofNonlinear Elastostatics and ElastodynamicsDissertationzurErlangung des Doktorgrades (Dr. rer. nat.)derMathematisch-Naturwissenschaftlichen Fakulta¨tderRheinischen Friedrich-Wilhelms-Universita¨t BonnVorgelegt vonChristian GroßausRemagenBonn, Juli 2009IAngefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakulta¨t der RheinischenFriedrich-Wilhelms Univerversita¨t Bonn1. Gutachter: Prof. Dr. Rolf Krause2. Gutachter: Prof. Dr. Helmut HarbrechtTag der Promotion: 11.09.2009Diese Arbeit ist mit Unterstu¨tzung der von der Deutschen Forschungsgemeinschaft getragenenBonn International Graduate School (BIGS) und des SFB 611 entstanden.IIMano BranguteiFu¨r meine LiebsteAbstractThe solution of nonlinear programming problems is of paramount interest for various applications,such as for problems arising from the field of elasticity. Here, the objective function is a smooth,but nonlinear and possibly nonconvex functional describing the stress-strain relationship for materialclasses. Often, additional constraints are added to model, for instance, contact. The discretizationof the resulting partial differential equations, for example with Finite Elements, gives rise to a finitedimensional minimization problem of the kindnu∈B⊂R :J(u) = min! (M)nwheren ∈N, andJ :R →R, sufficiently smooth.