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Replica time integrators

Venturini, G. and Yang, J. Z. and Ortiz, M. and Marsden, J. E. (2011) Replica time integrators. International Journal for Numerical Methods in Engineering, 88 (6). pp. 586-611. ISSN 0029-5981.

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This paper is concerned with the classical problem of wave propagation in discrete models of nonuniform spatial resolution. We develop a new class of Replica Time Integrators (RTIs) that permit the two-way transmission of thermal phonons across mesh interfaces. This two-way transmissibility is accomplished by representing the state of the coarse regions by means of replica ensembles, consisting of collections of identical copies of the coarse regions. In dimension d, RTIs afford an O(n^d) speed-up factor in sequential mode, and O(n^(d + 1)) in parallel, over regions that are coarsened n-fold. In this work, we restrict ourselves to the solution of the 3d continuous wave equation, for both linear and non-linear materials. By a combination of phase-error analysis and numerical testing, we show that RTIs are convergent and result in exact two-way transmissibility at the Courant–Friedrichs–Lewy limit for any angle of incidence. In this limit, RTIs allow step waves and high-frequency harmonics to cross mesh interfaces in both directions without internal reflections or appreciable loss or addition of energy. The possible connections of RTIs with discrete-to-continuum approaches and, in particular, with the transition between molecular dynamics and continuum thermodynamics are also pointed to by way of future outlook.

Item Type:Article
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URLURL TypeDescription DOIArticle
Ortiz, M.0000-0001-5877-4824
Additional Information:© 2011 John Wiley & Sons, Ltd. Received 9 August 2010; Revised 18 February 2011; Accepted 26 February 2011. Article first published online: 10 Jun. 2011. The authors gratefully acknowledge the support of the Department of Energy National Nuclear Security Administration under Award Number DE-FC52-08NA28613 through Caltech’s ASC/PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials. We are also grateful to Jeff Amelang and Dennis Kochmann for useful and insightful comments.
Funding AgencyGrant Number
Department of Energy (DOE) National Nuclear Security AdministrationDE-FC52-08NA28613
Issue or Number:6
Record Number:CaltechAUTHORS:20111114-145609664
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Official Citation:Venturini, G., Yang, J. Z., Ortiz, M. and Marsden, J. E. (2011), Replica time integrators. International Journal for Numerical Methods in Engineering, 88: 586–611. doi: 10.1002/nme.3202
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27774
Deposited By: Tony Diaz
Deposited On:23 Nov 2011 20:12
Last Modified:24 Nov 2020 00:44

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