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The iterative methods play an important role in solving linear equations that
arise in real-world applications. Numerous properties of the problem may affect
the efficiency of the solution. This book deals with algorithms for the solution of
linear systems of algebraic equations with large-scale sparse matrices, with a focus
on problems that are obtained after discretization of partial differential equations
using finite element methods.
The monograph provides a comprehensive presentation of the recent advances
in robust algebraic multilevel methods and algorithms including, e.g., the preconditioned
conjugate gradient method, the algebraic multilevel iteration (AMLI) preconditioners,
some relations to the classical algebraic multigrid (AMG) method
and its recent modifications.
The first five chapters can serve as a short introductory course on the theory
of AMLI methods and algorithms. The next part of the monograph is devoted to
more advanced topics, including related issues of AMG methods, AMLI methods
for discontinuous Galerkin systems, locking-free algorithms for coupled problems
etc., ending with important aspects of implementation and one challenging application.
This second part is addressed 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.
During the years, each of us cooperated with several coauthors on topics included
in this volume. They definitely influenced and enriched our understanding
of the field. Special thanks are due to them. Working on the monograph, we had
a lot of fruitful discussions with Ludmil Zikatanov. We highly appreciate his suggestions
and remarks. We thank also Petia Boyanova, and Ivan Georgiev for their
careful reading of parts of preliminary drafts of the book.
This volume is intended for mathematicians, engineers, natural scientists etc.
The monograph is partly based on, and initially stimulated by, the lecture course on
Robust Parallel Algebraic Multigrid and Multilevel Techniques given in the frame
of the Special Radon Semester on Computational Mechanics – Linz, October 3 –
December 16, 2005.
We gratefully acknowledge the support by the Austrian Academy of Sciences.
The work on this monograph has been also partially supported by the Bulgarian
Academy of Sciences as well as by Austrian Science Foundation FWF Project
P19170-N18, and the Bulgarian NSF Grants DO 02-147/08 and DO 02-338/08. |
