Multiscale Methods: Bridging the Scales in Science and Engineering

by Jacob Fish (Editor)

Overview

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.

Product Details

ISBN-13:	9780191579738
Publisher:	OUP Oxford
Publication date:	10/22/2009
Sold by:	Barnes & Noble
Format:	eBook
File size:	40 MB
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About the Author

Dr Fish is The Rosalind and John J. Redfern Jr. '33 Chaired Professor in Engineering at the Renssalaer Polytechnic Institute and a Fellow of the American Academy of Mechanics, United States Association for Computational Mechanics, and the International Association for Computational Mechanics. He has written over 150 articles and book chapters on the subject of multiscale computational science. Dr. Fish received numerous NSF awards including Young Investigator Award, NASA Langley research grant related to High Speed Civil Transport (HSCT), contracts from Lockheed Missiles&Space Company, Sikorski, ALCOA, Northrop-Grumman, GE, Rolls-Royce, Allison Engines, GM, Chrysler and Ford on various aspects of structural integrity; NSF, AFOSR, ONR, SANDIA and DARPA grants for development of multiscale computational techniques. He is currently directing the National Science Foundation Nanoscale Interdisciplinary Research Teams (NIRT) program at Rensselaer.

Table of Contents

PrefaceI. Information-Passing Multiscale Methods in Space1. Mixed multiscale finite element methods on adaptive unstructured grids using limited global information, J. E. Aarnes (SINTEF, Norway), Y. Efendiev (Texas A&M), T.Y. Hou (Caltech), L. Jiang (Texas A&M)2. Formulations of Mechanics problems for materials with self-similar multiscale microstructure, R.C. Picu and M.A. Soňare3. N-scale Model Reduction Theory, J. Fish and Z. Yuan (Rensselaer)II. Concurrent Multiscale Methods in Space4. Concurrent Coupling of Atomistic and Continuum Models, T. Belytschko, R. Gracie and M. Xu (Northwestern)5. Coarse-grained molecular dynamics: Concurrent Multiscale Simulation at Finite Temperature, R.E. Rudd (Lawrence Livermore National Laboratory)6. Atomistic to continuum coupling, M. Gunzburger (FSU), P. Bochev, R. Lehoucq (Sandia)III. Space-Time Scale Bridging Methods7. Methods of Systematic Upscaling, A. Brandt (Weizmann Institute and UCLA)8. Equation-free computation: an overview of patch dynamics, G. Samaey (Leuven, Belgium), A. J. Roberts (U. of Southern Queensland, Australia), and I. G. Kevrekidis (Princeton)9. On multiscale computational mechanics with time-space homogenization, P. Ladeveze, D. Neron, J.-C. Passieux (LMT-Cachan, France)IV. Adaptivity, Error Estimation and Uncertainty Quantification10. Estimation and Control of Modeling Error: A General Approach to Multiscale Modeling, J. T. Oden, S. Prudhomme, P. Bauman, and L. Chamoin (U. of Texas)11. Error Estimates for Multiscale Methods for Multiphysics Problems, D. Estep (U. Colorado)V. Multiscale Software12. Component Software for Multiscale Simulation, M.S. Shephard, M.A. Nuggehally, B. Franz Dale, C.R. Picu and J. Fish (Rensselaer)VI. Selected Multiscale Applications13. Finite Temperature Multiscale Methods for Silicon NEMS, Z. Tang and N. R. Aluru (University of Illinois at Urbana-Champaign)14. Multiscale materials, Sidney Yip (MIT)15. From Macroscopic to Mesoscopic Models of Chromatin Folding, Tamar Schlick (NYU)16. Multiscale Nature Inspired Chemical Engineering, Marc-Olivier Coppens (Rensselaer and Delft)