Chapman and Hall/CRC
315 pages | 92 B/W Illus.
Efficient Methods to Solve Complex Coupled Systems
Coupled Systems: Theory, Models, and Applications in Engineering explains how to solve complicated coupled models in engineering using analytical and numerical methods. It presents splitting multiscale methods to solve multiscale and multiphysics problems and describes analytical and numerical methods in time and space for evolution equations arising in engineering problems.
The book discusses the effectiveness, simplicity, stability, and consistency of the methods in solving problems that occur in real-life engineering tasks. It shows how MATLAB® and Simulink® are used to implement the methods. The author also covers the coupling of separate, multiple, and logical scales in applications, including microscale, macroscale, multiscale, and multiphysics problems.
Covering mathematical, algorithmic, and practical aspects, this book brings together innovative ideas in coupled systems and extends standard engineering tools to coupled models in materials and flow problems with respect to their scale dependencies and their influence on each time and spatial scale.
"The book brings together many novel ideas for solving multiscale and multiphysics problems. It also presents simulation results for many interesting engineering models. To decouple different scales into simpler equations, various multiscale methods are employed. A combination of numerical methods is discussed to solve engineering models. A big advantage of the presented schemes is the combination of modern multiscale technique with the known splitting approaches.
It is a good resource for graduate students and researchers who are involved with solving coupled systems. The book especially covers many ideas for solving coupled systems derived from engineering applications."
—Sanjay Khattri, Professor of Applied Mathematics, Stord/Haugesund University College, Norway
"Coupled Systems: Theory, Models and Applications in Engineering provides the latest research results from combined multi-scale and multi-physics explorations. It provides not only clear images of the theory and considerations but also some of the most brilliant computational experimentation. The latter is particularly important to many researchers, engineers, and those who work in frontier modeling and applications. The book addresses several interesting issues, such as why a decomposed, or split, system may be key to many important applications in multiple scaled territories, and why iterative splitting methods can be powerful and more appropriate for well-balanced coupled nonlinear problems.
The study of stochastic differential equation solvers is extremely useful to investigators and graduate students who have been troubled by multiple body/particle simulation algorithm designs and computations. I would definitely consider the book in my seminar course and recommend it to colleagues and graduate students in multi-physics environments. The book may also be adopted in our upper-level classes in computational mathematics as well as in physics and engineering fields."
— Professor Qin Sheng, Department of Mathematics and Center for Astrophysics, Space Physics, and Engineering Research, Baylor University, Waco, Texas, USA
"Coupled Systems: Theory, Models, and Applications in Engineering is a brilliant book. It contains theoretical and practical aspects of solving multiscale and multiphysics models in engineering. Analytical as well as numerical methods are described in time and space. The book covers an overview of different coupled (weak and strong) equation systems. It is an excellent choice for graduate students and researchers to select and start their projects related to multiscale and multiphysics simulations. A great merit of this research monograph is the combination of modern multiscale techniques together with splitting schemes. In particular, theoretical analysis and practical implementations allow the reader to get an impression of different applications in hydrogeological, fluid dynamical, and plasma physics problems."
—Professor Shuyu Sun, King Abdullah University of Science and Technology, Saudi Arabia
Outline of the Book
Coupled Systems as Interdisciplinary Research
General Principle for Coupled Systems
Applications to Multiscale Expansions
Nonlinear Reaction Example: Averaging
PECVD-Process: Upscaled Reaction Process
Stochastic Differential Equations: Particle Simulation for Coulomb Collisions
Particle-In-Cell: Multiscale Method with Applications
Application to Multiscale Problem in Transport-Reaction Problems
Application to Multiscale Problem in Heat Transfer in Porous Media
Application to Multiscale Problem in Porous Media Based on a Model of a Parallel Plate PECVD Apparatus
Monte Carlo Simulations Concerning Modeling DC and High Power Pulsed Magnetron Sputtering
Splitting Methods as Coupling Schemes: Theory and Application to Electro-Magnetic Fields
Improvement of Multiscale Methods via Zassenhaus Expansion: Theory and Application to Multiphase Problems
Improvement of Multiscale Methods via Disentanglement of Exponential Operators
Multiscale Problem with Embedded Analytical Solutions of the Microscale Part
Multiscale Approaches to Solve Time-Dependent Burgers' Equations
Step-Size Control in Simulation of Diffusive CVD Processes Based on Adaptive Schemes
Summary and Perspectives
Software Package r3t
Benchmark Software: MULTI-OPERA