دانلود کتاب Multigrid Techniques - 1984 Guide with Applications to Fluid Dynamics

This classic text presents the best practices of developing multigrid solvers for large-scale computational problems in science and engineering. 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 MATLAB® sample code, and more. 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. Content:• Front Matter • List of Figures • List of Tables Prefaces • Table of Contents 0. Introduction 1. Elementary Acquaintance with Multigrid •Part I. Stages in Developing Fast Solvers 2. Stable Discretization 3. Interior Relaxation and Smoothing Factors 4. Interior Two-Level Cycles 5. Boundary Conditions and Two-Level Cycling 6. Many-Level Cycles 7. Full Multi-Grid (FMG) Algorithms •Part II. Advanced Techniques and Insights 8. Full Approximation Scheme (FAS) and Applications 9. Local Refinements and Grid Adaptation 10. Higher-Order Techniques • 11. Coarsening Guided by Discretization • 12. True Role of Relaxation 13. Dealgebraization of Multigrid 14. Practical Role of Rigorous Analysis and Quantitative Predictions • 15. Chains of Problems. Frozen τ • 16. Time Dependent Problems •Part III. Applications to Fluid Dynamics 17. Cauchy-Riemann Equations 18. Steady-State Stokes Equations 19. Steady-State Incompressible Navier-Stokes Equations 20. Compressible Navier-Stokes and Euler Equations 21. Remarks on Solvers for Transonic Potential Equations Appendix A: Testcycle: Matlab Code • Bibliography Index