
2011 / xxii + 218 / Softcover / ISBN 9781611970746 / List Price $81.50 / SIAM Member Price $57.05 / Order Code CL67
Keywords: numerical PDE, fast solvers, multigrid, adaptive local refinements, high order discretization, computational fluid dynamics
This classic text presents the best practices of developing multigrid solvers for largescale computational problems in science and engineering. By representing a problem at multiple scales and employing suitable interscale interactions, multigrid avoids slowdown due to stiffness and reduces the computational cost of classical algorithms by orders of magnitude.
Starting from simple examples, this book guides the reader through practical stages for developing reliable multigrid solvers, methodically supported by accurate performance predictors. The revised edition presents
Readers will also gain access to the Multigrid Guide 2.0 Web site, where updates and new developments will be continually posted, including a chapter on Algebraic Multigrid.
This book will be useful to practitioners and researchers, as well as students and instructors, in many areas of computational science and engineering, applied mathematics, and numerical analysis.
Audience
This book will be useful to practitioners and researchers, as well as students and instructors, in many areas of computational science and engineering, applied mathematics, and numerical analysis.
Contents
List of Figures;
List of Tables;
Preface to Classics Edition;
Preface;
Chapter 0: Introduction;
Chapter 1: Elementary Acquaintance with Multigrid;
Part I: Stages in Developing Fast Solvers;
Chapter 2: Stable Discretization;
Chapter 3: Interior Relaxation and Smoothing Factors;
Chapter 4: Interior TwoLevel Cycles;
Chapter 5: Boundary Conditions and TwoLevel Cycling;
Chapter 6: ManyLevel Cycles;
Chapter 7: Full MultiGrid (FMG) Algorithms;
Part II: Advanced Techniques and Insights;
Chapter 8: Full Approximation Scheme (FAS) and Applications;
Chapter 9: Local Refinements and Grid Adaptation;
Chapter 10: HigherOrder Techniques;
Chapter 11: Coarsening Guided By Discretization;
Chapter 12: True Role of Relaxation;
Chapter 13: Dealgebraization of Multigrid;
Chapter 14: Practical Role of Rigorous Analysis and Quantitative Predictions;
Chapter 15: Chains of Problems. Frozen τ;
Chapter 16: Time Dependent Problems;
Part II: Applications to Fluid Dynamics
Chapter 17: CauchyRiemann Equations;
Chapter 18: SteadyState Stokes Equations;
Chapter 19: SteadyState Incompressible NavierStokes Equations;
Chapter 20: Compressible NavierStokes and Euler Equations;
Chapter 21: Remarks on Solvers for Transonic Potential Equations;
Appendix: Test Cycle: MATLAB Code;
Bibliography;
Index.
About the Authors
Achi Brandt is Professor Emeritus at the Weizmann Institute of Science, Professor in Residence at the University of California, Los Angeles and the Chief Scientist of VideoSurf, Inc. In 2005 he won the SIAM/ACM Prize in Computational Science and Engineering "for pioneering modern multilevel methods, from multigrid solvers for partial differential equations to multiscale techniques for statistical physics, and for influencing almost every aspect of contemporary computational science and engineering."
Oren Livne is a Senior Software Engineer at the Office of the Associate Vice President for Health Sciences Information Technology at the University of Utah. He received his Ph.D. in applied mathematics from the Weizmann Institute of Science. His doctoral work, supervised by Achi Brandt, focused on multigrid methods for electronic structure computations in quantum chemistry.
ISBN 9781611970746