Efficient iterative solvers, coarse spaces and optimal preconditioning

Prof. Ludmil Zikatanov

June 12, 2012, 1:30 p.m. S2 416

In this talk, we present recent progress in both the theoretical analysis as well as the design of robust solvers for linear systems arising in the discretizations of Partial Differential Equations (PDEs).

Our approach falls into the class of auxiliary space multilevel conditioners, in which the multilevel hierarchy is generated on an auxiliary space where it is easier to obtain such hierarchy. The coarse degrees of freedom are selected using an aggregation approach in combination with Algebraic Multilevel Iteration (AMLI) methods. This leads to optimal methods for wide class of problems (including non-symmetric and indefinite). We present numerical experiments for applications in oil reservoir modeling and the results demonstrate the efficacy of the Fast Auxiliary Space Preconditioning (FASP) approach. In addition, we show that this class of methods perform robustly in handling more complicated situations, for example discretizations of coupled systems of partial differential equations describing complex flows in porous media.