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Linear stationary iterative methods for the forcebased quasicontinuum approximation
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Luskin, Mitchell Barry and Ortner, Christoph (2012) Linear stationary iterative methods for the forcebased quasicontinuum approximation. In: Engquist, Björn, 1945 and Runborg, Olof and Tsai, YenHsi R., (eds.) Numerical Analysis of Multiscale Computations. Lecture notes in computational science and engineering, Volume 82 . Berlin: Springer, pp. 331368. ISBN 9783642219429

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Official URL: http://dx.doi.org/10.1007/9783642219436_14
Abstract
Forcebased 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 forcebased approximation presents a challenge due to the nonsymmetric and indefinite structure of the linearized forcebased 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 > 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:  14397358  
Book Title:  Numerical Analysis of Multiscale Computations  
Editor:  Engquist, Björn, 1945 and Runborg, Olof and Tsai, YenHsi R.  
Official Date:  2012  
Dates: 


Volume:  Volume 82  
Page Range:  pp. 331368  
Identification Number:  10.1007/9783642219436_14  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Restricted or Subscription Access  
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:  DMS0757355 (NSF), DMS0811039 (NSF), OISE0967140 (NSF), DESC0002085 (DOE), EP/H003096/1 (EPSRC)  
References:  [1] P. Bauman, H. B. Dhia, N. Elkhodja, J. Oden, , and S. Prudhomme. On the application of the 

URI:  http://wrap.warwick.ac.uk/id/eprint/43774 
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