Finite Elements and Fast Iterative Solvers
with Applications in Incompressible Fluid Dynamics
Series: Numerical Mathematics and Scientific Computation;
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Product details:
- Edition number 2
- Publisher OUP Oxford
- Date of Publication 19 June 2014
- ISBN 9780199678808
- Binding Paperback
- No. of pages494 pages
- Size 236x150x27 mm
- Weight 744 g
- Language English
- Illustrations 116 b&w line illustrations 0
Categories
Short description:
A practical graduate text on Scientific Computing with a focus on numerical solution of partial differential equations and numerical linear algebra. This book, and its associated freely downloadable MATLAB software, is relevant to engineers, applied mathematicians, numerical analysts, and people working in interdisciplinary Scientific Computing.
MoreLong description:
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 and Navier-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 and nonsymmetric 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 throughout the 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 graduate level.
in my opinion this bookis a highly interesting and valuable contribution to the field of numerical methods for PDEs. ... Ph.D. students interested in this topic may find the book a very inspiring source for learning more about the subject.
Table of Contents:
Models of incompressible fluid flow
The Poisson equation
Solution of discrete Poisson problems
The Stokes equations
Solution of discrete Stokes problems
Optimization with PDE constraints
The convection–diffusion equation
Solution of discrete convection–diffusion problems
The Navier–Stokes equations
Solution of discrete Navier–Stokes problems
Solution of unsteady Navier–Stokes equations
Solution of models of buoyancy-driven flow
