Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics

Paperback | July 5, 2014

byHoward Elman, David Silvester, Andy Wathen

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This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described.The 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 andNavier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite andnonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughoutthe book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory" provided by the software.Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduatelevel.

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From the Publisher

This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described.The focus is on finite element approximation methods and fast iterative solut...

Howard Elman is a Professor in the Computer Science Department and the Institute for Advanced Computer Studies at the University of Maryland, College Park. He received his doctorate in Computer Science from Yale University in 1982. He has held visiting positions at Stanford University, the University of Manchester Institute of Science...
Format:PaperbackDimensions:496 pages, 9.21 × 6.14 × 1.09 inPublished:July 5, 2014Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199678804

ISBN - 13:9780199678808

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Table of Contents

Models of incompressible fluid flow1. The Poisson equation2. Solution of discrete Poisson problems3. The Stokes equations4. Solution of discrete Stokes problems5. Optimization with PDE constraints6. The convection - diffusion equation7. Solution of discrete convection - diffusion problems8. The Navier - Stokes equations9. Solution of discrete Navier - Stokes problems10. Solution of unsteady Navier - Stokes equations11. Solution of models of buoyancy-driven flow

Editorial Reviews

"The text offers a valuable contribution to all finite element researchers who would like to broaden both their fundamental and applied knowledge of the field." --Journal of Fluid Mechanics