Multigrid techniques : 1984 guide with applications to fluid dynamics / Achi Brandt, Oren E. Livne.

Format:

Book

Author/Creator:

Brandt, Achi.

Contributor:

Livne, Oren E.

Society for Industrial and Applied Mathematics.

Series:

Classics in applied mathematics ; 67.

Classics in applied mathematics ; 67

Language:

English

Subjects (All):

Fluid dynamics--Mathematics.

Fluid dynamics.

Multigrid methods (Numerical analysis).

Differential equations, Partial--Numerical solutions.

Differential equations, Partial.

Physical Description:

1 electronic text (xxii, 218 p.) : digital file.

Edition:

Rev. ed.

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2011.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

This classic text presents the best practices of developing multigrid solvers for large-scale 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 discretization and fast solution of linear and nonlinear partial differential systems; treatment of boundary conditions, global constraints and singularities; grid adaptation, high-order approximations, and system design optimization; applications to fluid dynamics, from simple models to advanced systems; new quantitative performance predictors, a MATLABʼ sample code, and more. 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.

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 two-level cycles

Chapter 5. Boundary conditions and two-level cycling

Chapter 6. Many-level cycles

Chapter 7. Full Multi-Grid (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. Higher-order 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 [tau]

Chapter 16. Time dependent problems

Part II. Applications to fluid dynamics. Chapter 17. Cauchy-Riemann equations

Chapter 18. Steady-state Stokes equations

Chapter 19. Steady-state incompressible Navier-Stokes equations

Chapter 20. Compressible Navier-Stokes and Euler equations

Chapter 21. Remarks on solvers for transonic potential equations

Appendix. Test cycle: MATLAB code

Bibliography

Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Title from title screen, viewed 05/31/2011.

ISBN:

1-61197-075-X

Publisher Number:

CL67 SIAM