Matrix-based multigrid : theory and applications

Author(s)

• Shapira, Yair

Bibliographic Information

Matrix-based multigrid : theory and applications

Yair Shapira

（Numerical methods and algorithms, v.2）

Springer, c2008

2nd ed.

Note

Includes bibliographical references (p. [305]-311) and index

Description and Table of Contents

Description

Matrix-Based Multigrid introduces and analyzes the multigrid approach for the numerical solution of large sparse linear systems arising from the discretization of elliptic partial differential equations. Special attention is given to the powerful matrix-based-multigrid approach, which is particularly useful for problems with variable coefficients and nonsymmetric and indefinite problems. This book can be used as a textbook in courses in numerical analysis, numerical linear algebra, and numerical PDEs at the advanced undergraduate and graduate levels in computer science, math, and applied math departments. The theory is written in simple algebraic terms and therefore requires preliminary knowledge only in basic linear algebra and calculus.

Table of Contents

List of Figures List of Tables Preface Part I. Concepts and Preliminaries 1. The Multilevel-Multiscale Approach 2. Preliminaries Part II. Partial Differential Equations and Their Discretization 3. Finite Differences and Volumes 4. Finite Elements Part III. Numerical Solution of Large Sparse Linear Systems 5. Iterative Linear System Solvers 6. The Multigrid Iteration Part IV. Multigrid for Structured Grids 7. Automatic Multigrid 8. Applications in Image Processing 9. Black-Box Multigrid 10. The Indefinite Helmholtz Equation 11. Matrix-Based Semicoarsening Part V. Multigrid for Semi-Structured Grids 12. Multigrid for Locally Refined Meshes 13. Application to Semi-Structured Grids Part VI. Multigrid for Unstructured Grids 14. Domain Decomposition 15. The Algebraic Multilevel Method 16. Applications 17. Semialgebraic Multilevel for Systems of PDEs Part VII. Appendices 18. Time-Dependent Parabolic PDEs 19. Nonlinear Equations References Index

by "Nielsen BookData"

Details

• NCID: BA86483411
• ISBN:
  • 9780387497648
• LCCN: 2003051640
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: New York
• Pages/Volumes: xxiii, 318 p.
• Size: 25 cm
• Classification:
  • LCC : QA377
  • DC21 : 515/.353
• Subject Headings:
  • LCSH : Differential equations, Partial -- Numerical solutions
  • LCSH : Multigrid methods (Numerical analysis)
  • LCSH : Matrices
• Parent Bibliography ID:
  • BA58479992