Multiscale Methods

Bridging the Scales in Science and Engineering

Edited by Jacob Fish

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Multiscale Methods

Bridging the Scales in Science and Engineering

Edited by Jacob Fish

Description

Small scale features and processes occurring at a nanometer and femtoseconds scales have a profound impact on what happens at a larger scale and over 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 to quantify variability of physical parameters at multiple scales and how to account for it to ensure design robustness?

Various 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 is discussed in several, which focus on hierarchy of multiscale models and a posterior model error estimation including uncertainty quantification. Component software that can be effectively combined to address a wide range of multiscale simulations is described as well. Applications range from advanced materials, to nanoelectromechanical systems (NEMS), to biological systems, and nanoporous catalysts where physical phenomena operate across 12 orders of magnitude in time scales and 10 orders of magnitude in spatial scales. 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.

Multiscale Methods

Bridging the Scales in Science and Engineering

Edited by Jacob Fish

Preface
I. Information-Passing Multiscale Methods in Space
1. 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. Soare
3. N-scale Model Reduction Theory, J. Fish and Z. Yuan (Rensselaer)
II. Concurrent Multiscale Methods in Space
4. 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 Methods
7. 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 Quantification
10. 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 Software
12. Component Software for Multiscale Simulation, M.S. Shephard, M.A. Nuggehally, B. Franz Dale, C.R. Picu and J. Fish (Rensselaer)
VI. Selected Multiscale Applications
13. 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)

Multiscale Methods

Bridging the Scales in Science and Engineering

Edited by Jacob Fish

Author Information

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.

Contributors:

J. E. Aarnes (SINTEF, Norway), Y. Efendiev (Texas A&M), T.Y. Hou (Caltech), L. Jiang (Texas A&M)
R.C. Picu and M.A. Soare
J. Fish and Z. Yuan (Rensselaer)
T. Belytschko, R. Gracie and M. Xu (Northwestern)
R.E. Rudd (Lawrence Livermore National Laboratory)
M. Gunzburger (FSU), P. Bochev, R. Lehoucq (Sandia)
A. Brandt (Weizmann Institute and UCLA)
G. Samaey (Leuven, Belgium), A. J. Roberts (U. of Southern Queensland, Australia), and I. G. Kevrekidis (Princeton)
P. Ladeveze, D. Neron, J.-C. Passieux (LMT-Cachan, France)
J. T. Oden, S. Prudhomme, P. Bauman, and L. Chamoin (U. of Texas)
D. Estep (U. Colorado)
M.S. Shephard, M.A. Nuggehally, B. Franz Dale, C.R. Picu and J. Fish (Rensselaer)
Z. Tang and N. R. Aluru (University of Illinois at Urbana-Champaign)
Sidney Yip (MIT)
Tamar Schlick (NYU)
Marc-Olivier Coppens (Rensselaer and Delft)