Robust Algebraic Multilevel Methods and Algorithms / / Johannes Kraus, Svetozar Margenov.

• Superior document: Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1
• VerfasserIn: Kraus, Johannes,; Margenov, Svetozar,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2009]; ©2009
• Year of Publication: 2009
• Language: English
• Series: Radon Series on Computational and Applied Mathematics , 5
• Physical Description: 1 online resource (246 p.)

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 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, the classical algebraic multigrid (AMG) method and its recent modifications, namely AMG using element interpolation (AMGe) and AMG based on smoothed aggregation. The first six 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 the description of new generation AMG methods, AMLI methods for discontinuous Galerkin systems, looking-free algorithms for coupled problems etc., ending with important practical issues of implementation and challenging applications. 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 and AMG methods and their efficient application. This book is intended for mathematicians, engineers, natural scientists etc.

Table of Contents

Frontmatter -- Contents -- 1. Introduction -- 2. Algebraic multilevel iteration methods -- 3. Robust AMLI algorithms: Conforming linear finite elements -- 4. Robust AMLI algorithms: Nonconforming linear finite elements -- 5. Schur complement based multilevel preconditioners -- 6. Algebraic multigrid (AMG) -- 7. Preconditioning of Rannacher–Turek nonconforming FE systems -- 8. AMLI algorithms for discontinuous Galerkin FE problems -- 9. AMLI methods for coupled problems -- 10. Practical issues -- Backmatter