Finite Elements and Fast Iterative Solvers, 2nd edition
Howard Elman, University of Maryland;
David Silvester, University of Manchester;
Andy Wathen, University of Oxford
Oxford University Press, 2014
ISBN: 978-0-19-967879-2;
Language: English
Finite Elements and Fast Iterative Solvers offers information on how to do scientific computing for fundamental models of fluid flow. The book includes an introduction, an analysis, and algorithms, and it is closely tied to freely available MATLAB codes that utilize the methods described.
The book's focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, convection-diffusion problem, Stokes problem, and Navier-Stokes problem, and the book includes new material on time-dependent problems and models of multiphysics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite, and nonsymmetric indefinite matrix systems, respectively. For each problem and associated solvers, there are computational instructions as well as theoretical analysis that inform on appropriate approaches. Readers will also find many illustrative numerical results throughout the book, which have been computed with the freely downloadable IFISS software and depict what these computations would look like in practice. Since there is considerable scope for experimentation in the "computational laboratory" provided by MATLAB, all the numerical results should be reproducible by readers who have access to the software.
Written for advanced undergraduate students or those beginning graduate level, this book is suitable as an introduction to iterative linear solvers or more generally as a model of scientific computing. Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. Recent developments in the field are also represented in three new chapters: optimization with PDE constraints (Chapter 5), solution of unsteady Navier-Stokes equations (Chapter 10), and solution of models of buoyancy-driven flow (Chapter 11).
