Martynenko, Sergey I.
The Robust Multigrid Technique
For Black-Box Software
- Presents an innovative robust multigrid method for the solution of (initial-)boundary value problems.
- Based on 25 years of robust multigrid practice and software development.
- Of interest to researchers and practitioners alike.
Aims and Scope
This book presents a detailed description of a robust pseudomultigrid algorithm for solving (initial-)boundary value problems on structured grids in a black-box manner. To overcome the problem of robustness, the presented Robust Multigrid Technique (RMT) is based on the application of the essential multigrid principle in a single grid algorithm. It results in an extremely simple, very robust and highly parallel solver with close-to-optimal algorithmic complexity and the least number of problem-dependent components. Topics covered include an introduction to the mathematical principles of multigrid methods, a detailed description of RMT, results of convergence analysis and complexity, possible expansion on unstructured grids, numerical experiments and a brief description of multigrid software, parallel RMT and estimations of speed-up and efficiency of the parallel multigrid algorithms, and finally applications of RMT for the numerical solution of the incompressible Navier Stokes equations. Potential readers are graduate students and researchers working in applied and numerical mathematics as well as multigrid practitioners and software programmers.
Introduction to multigrid
Robust multigrid technique
Parallel multigrid methods
Applications of multigrid methods in computational fluid dynamics