# Robust multilevel preconditioning for heterogeneous reaction-diffusion problems

## Dipl.-Ing.in Monika Wolfmayr

April 9, 2013, 4:30 p.m. S2 059

This talk is devoted to the analysis for constructing robust and optimal
algebraic multilevel preconditioners for reaction-diffusion type
problems. We discretize these problems by the finite element method
leading to a weighted sum of stiffness and mass matrices. The weighting
parameters are often only constant on the subdomains corresponding to
the elements of the coarsest mesh partitioning. In order to solve such
problems we consider the algebraic multilevel iteration (AMLI) method.
We give a rigorous proof that the AMLI method yields a robust and fast
solver of optimal complexity for this class of problems. Moreover, we
present a time-periodic parabolic optimal control problem as motivation
and as a practical example for the relevance of constructing robust and
optimal AMLI preconditioners for system matrices which are a weighted
sum of stiffness and mass matrices.