Synopses & Reviews
The simulation of matter by direct computation of individual atomic motions has become an important element in the design of new drugs and in the construction of new materials. This book demonstrates how to implement the numerical techniques needed for such simulation, thereby aiding the design of new, faster, and more robust solution schemes. Clear explanations and many examples and exercises will ensure the value of this text for students, professionals, and researchers.
Review
"Overall this is a book to be strongly recommended both for individual study and as the basis for a graduate course to a wide range of students. The arrangement of the chapters means that the description of the numerical methods and their properties is never far away from the applications that have motivated their development...Each chapter contains a set of exercises which are often quite short but very illuminating."
SIAM Review
Synopsis
Geometric integrators are time-stepping methods, designed to exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. This book outlines the principles of geometric integration and demonstrates how they can be applied to provide numerical methods for simulating conservative systems. Beginning from basic principles of geometric integration and a discussion of the advantageous properties of such schemes, the book introduces a variety of methods and includes applications to molecular dynamics and partial differential equations, providing a theoretical framework and practical guide. Includes examples and exercises.
About the Author
Ben Leimkuhler is Professor of Applied Mathematics, and Director of the Centre for Mathematical Modelling at the University of Leicester.Sebastian Reich is Professor of Computational and Mathematical Modelling at Imperial College London.
Table of Contents
1. Introduction; 2. Numerical methods; 3. Hamiltonian mechanics; 4. Geometric integrators; 5. The modified equations; 6. Higher order methods; 7. Contained mechanical systems; 8. Rigid Body dynamics; 9. Adaptive geometric integrators; 10. Highly oscillatory problems; 11. Molecular dynamics; 12. Hamiltonian PDEs.