DD17 Strobl
On the Multiscale Solution of Constrained Problems in Linear Elasticity

Speaker: Rolf Krause

Abstract

In the talk, an abstract algorithmic framework for the solution of constrained convex minimization problems by monotone multigrid methods is presented, which is applicable to geometric as well as algebraic multigrid methods. Particular emphasis is put on the multiscale representation of the constraint set within a multilevel hierarchy, which is of crucial importance for the overall performance and convergence of multigrid based solution strategies for constraint problems. This is discussed in the context of frictional contact problems in elasticity. Although the method is based on the primal variables, i.e. the displacements, a close connection to the dual variables can be established by employing mortar methods for the discretization of the constraints and frictional nonlinearities at the contact interface. For the case of time dependent contact problems, we furthermore discuss, how undesirable oscillations at the contact boundary emerging from the time discretization can be significantly reduced by simply adding an additional projection at the interface. In combination with an implicit time discretization, this gives rise to an efficient and stable simulation method for time dependent contact problems in linear elasticity.

Finally, as an example for the flexibility of our approach, we consider the numerical solution of a multi-component phase-field model for elastically stressed solids.


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