Towards Robust Algebraic Multigrid Methods for Nonsymmetric Problems

This thesis presents a rigorous, abstract analysis of multigrid methods for positive nonsymmetric problems, particularly suited to algebraic multigrid, with a completely new approach to nonsymmetry which is based on a new concept of absolute value for nonsymmetric operators.

Multigrid, and in particular algebraic multigrid, has become an indispensable tool for the solution of discretizations of par...