Luskin, Mitchell Barry and Ortner, Christoph (2012) Linear stationary iterative methods for the force-based quasicontinuum approximation. In: Engquist, Björn, 1945- and Runborg, Olof and Tsai, Yen-Hsi R., (eds.) Numerical Analysis of Multiscale Computations. Lecture notes in computational science and engineering, Volume 82 . Berlin: Springer, pp. 331-368. ISBN 9783642219429
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Abstract
Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known pointwise consistent methods for coupling a general atomistic model to a finite element continuum model. However, the development of efficient and reliable iterative solution methods for the force-based approximation presents a challenge due to the non-symmetric and indefinite structure of the linearized force-based quasicontinuum approximation, as well as to its unusual stability properties. In this paper, we present rigorous numerical analysis and computational experiments to systematically study the stability and convergence rate for a variety of linear stationary iterative methods.
| Item Type: | Book Item |
|---|---|
| Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics |
| Library of Congress Subject Headings (LCSH): | Multiscale modeling, Continuum mechanics, Crystalline polymers -- Defects -- Mathematical models |
| Series Name: | Lecture notes in computational science and engineering |
| Publisher: | Springer |
| Place of Publication: | Berlin |
| ISBN: | 9783642219429 |
| ISSN: | 1439-7358 |
| Book Title: | Numerical Analysis of Multiscale Computations |
| Editor: | Engquist, Björn, 1945- and Runborg, Olof and Tsai, Yen-Hsi R. |
| Official Date: | 2012 |
| Dates: | Date Event 2012 Published |
| Volume: | Volume 82 |
| Page Range: | pp. 331-368 |
| DOI: | 10.1007/978-3-642-21943-6_14 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| Date of first compliant deposit: | 28 July 2016 |
| Date of first compliant Open Access: | 28 July 2016 |
| Funder: | National Science Foundation (U.S.) (NSF), Institute for Mathematics and Its Applications (IMA), University of Minnesota. Supercomputer Institute, United States. Department of Energy, Engineering and Physical Sciences Research Council (EPSRC) |
| Grant number: | DMS-0757355 (NSF), DMS-0811039 (NSF), OISE-0967140 (NSF), DE-SC0002085 (DOE), EP/H003096/1 (EPSRC) |
| URI: | https://wrap.warwick.ac.uk/43774/ |
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