Multiscale Methods
Bridging the Scales in Science and Engineering
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Product details:
- Publisher OUP Oxford
- Date of Publication 22 October 2009
- ISBN 9780199233854
- Binding Hardback
- No. of pages624 pages
- Size 240x160x40 mm
- Weight 1056 g
- Language English
- Illustrations 168 BW line and 24 colour line illustrations, 1 halftone 0
Categories
Short description:
This volume is intended as a reference book for scientists, engineers and graduate students practicing in traditional engineering and science disciplines as well as in emerging fields of nanotechnology, biotechnology, microelectronics and energy.
MoreLong description:
Small scale features and processes occurring at nanometer and femtosecond scales have a profound impact on what happens at a larger scale and over an extensive period of time. The primary objective of this volume is to reflect the state-of-the-art in multiscale mathematics, modeling, and simulations and to address the following barriers: What is the information that needs to be transferred from one model or scale to another and what physical principles must be satisfied during the transfer of information? What are the optimal ways to achieve such transfer of information? How can variability of physical parameters at multiple scales be quantified and how can it be accounted for to ensure design robustness?
The multiscale approaches in space and time presented in this volume are grouped into two main categories: information-passing and concurrent. In the concurrent approaches various scales are simultaneously resolved, whereas in the information-passing methods the fine scale is modeled and its gross response is infused into the continuum scale. The issue of reliability of multiscale modeling and simulation tools which focus on a hierarchy of multiscale models and an a posteriori model of error estimation including uncertainty quantification, is discussed in several chapters. Component software that can be effectively combined to address a wide range of multiscale simulations is also described. Applications range from advanced materials to nanoelectromechanical systems (NEMS), biological systems, and nanoporous catalysts where physical phenomena operates across 12 orders of magnitude in time scales and 10 orders of magnitude in spatial scales.
This volume is a valuable reference book for scientists, engineers and graduate students practicing in traditional engineering and science disciplines as well as in emerging fields of nanotechnology, biotechnology, microelectronics and energy.
Table of Contents:
Preface
1. Information-Passing Multiscale Methods in Space
Mixed multiscale finite element methods on adaptive unstructured grids using limited global information
Formulations of Mechanics problems for materials with self-similar multiscale microstructure
N-scale Model Reduction Theory
2. Concurrent Multiscale Methods in Space
Concurrent Coupling of Atomistic and Continuum Models
Coarse-grained molecular dynamics: Concurrent Multiscale Simulation at Finite Temperature
Atomistic to continuum coupling
3. Space-Time Scale Bridging Methods
Methods of Systematic Upscaling
Equation-free computation: an overview of patch dynamics
On multiscale computational mechanics with time-space homogenization
4. Adaptivity, Error Estimation and Uncertainty Quantification
Estimation and Control of Modeling Error: A General Approach to Multiscale Modeling
Error Estimates for Multiscale Methods for Multiphysics Problems
5. Multiscale Software
Component Software for Multiscale Simulation
6. Selected Multiscale Applications
Finite Temperature Multiscale Methods for Silicon NEMS
Multiscale materials
From Macroscopic to Mesoscopic Models of Chromatin Folding
Multiscale Nature Inspired Chemical Engineering
