Seminar

des DFG-Sonderforschungsbereichs 393

Numerische Simulation auf massiv parallelen Rechnern

Zeit:	Donnerstag, 20.12.2002, 11:00 Uhr
Ort:	Reichenhainer Straße 70, B 202
Vortragender:	Dr. Krause (FU Berlin)
Thema:	Nonlinear Monotone Multigrid Methods for Contact Problems in Linear Elasticity
The reliable simulation of contact problems is of great importance in many applications. These include, for example, the production of gear boxes or tires, the design of cars, metal forming processes, or implants in biomechanics. Since the resulting discrete nonlinear systems can be of very high dimension, fast iterative solvers as, e.g., multigrid methods, are desirable. Unfortunately, due to the intrinsic nondifferentiable nonlinearity of contact problems, standard multigrid methods cannot be applied. We present a new approach for solving the Signorini problem with Coulomb friction in linear elasticity. In contrast to regularization techniques like penalty methods or saddle-point formulations, monotone multigrid methods need neither regularization parameters nor additional dual unknowns. Our method is globally convergent and, applied to nonlinear problems, shows to be as efficient as standard multigrid methods for linear problems. In cooperation with B. Wohlmuth (Universität Stuttgart), a monotone method for elastic contact problems has been developed. It is based on the combination of nonconforming domain decomposition techniques and monotone multigrid methods. Numerical examples in 2D an 3D will be given.
Das Seminar wird von Prof. Meyer geleitet. Interessenten sind herzlich eingeladen.