Robust multilevel preconditioning for heterogeneous reaction-diffusion problems
Dipl.-Ing.in Monika WolfmayrApril 9, 2013, 2:30 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.