Robust Algebraic Multilevel Methods and Algorithms

This book deals with algorithms for linear systems of algebraic equations with large-scale sparse matrices, with a focus on problems that are obtained from discretization of partial differential equations using finite element methods. The authors provide a systematic presentation of the recent advances in robust algebraic multilevel methods and algorithms, e.g., the preconditioned conjugate gradient method, algebraic multilevel iteration (AMLI) preconditioners, and their relation to algebraic multigrid (AMG) methods.

The first five chapters can serve as a short introductory course on the theory of AMLI methods and algorithms, while the remaining part of the monograph is devoted to more advanced topics. This second part addresses to some more experienced students and practitioners and can be used to complete a more advanced course on robust AMLI methods and their efficient application. This volume is intended for students and researchers working on mathematics, engineering or natural science.