Multigrid Techniques

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.

List of figures; List of tables; Preface to the Classics Edition; Preface; 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 ?; 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: test cycle: MATLAB code; Bibliography; Index.