Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. On Rosenbrock methods for the time integration of nearly incompressible materials and their usage for nonlinear model reduction
 Journal of computational and applied mathematics 262 (2014), pp.333345 ISSN: 03770427 ISSN: 0771050X 
 Seminar on Numerical Solution of Differential and DifferentialAlgebraic Equations (NUMDIFF) <13, 2012, Halle> 

 English 
 Journal Article, Conference Paper 
 Fraunhofer ITWM () 
Abstract
This paper deals with the time integration and nonlinear model reduction of nearly incompressible materials that have been discretized in space by mixed finite elements. We analyze the structure of the equations of motion and show that a differential algebraic system of index 1 with a singular perturbation term needs to be solved. In the limit case, the index may jump to index 3 and thus renders the time integration into a difficult problem. For the time integration, we apply Rosenbrock methods and study their convergence behavior for a test problem, which highlights the importance of the wellknown Scholz conditions for this problem class. Numerical tests demonstrate that such linearimplicit methods are an attractive alternative to established time integration methods in structural dynamics. We also combine the simulation of nonlinear materials with a model reduction step in order to prepare the ground for including such finite element structures as components in complex vehicle dynamics applications.