Reply to "Comment on 'Domain Reduction Method for Three-Dimensional Earthquake Modeling in Localized Regions, Part I: Theory,' by J. Bielak, K. Loukakis, Y. Hisada, and C. Yoshimura, and 'Part II: Verification and Applications,' by C. Yoshimura, J. Bielak, Y. Hisada, and A. Fernandez," by E. Faccioli, M. Vanini, R. Paolucci, and M. Stupazzini

2005 ◽  
Vol 95 (2) ◽  
pp. 770-773 ◽  
Author(s):  
J. Bielak
Keyword(s):  
Reduction Method ◽  
Three Dimensional ◽  
Domain Reduction ◽  
Earthquake Modeling ◽  
Domain Reduction Method

A parallel domain reduction method

1989 ◽  
Vol 5 (3) ◽  
pp. 195-202 ◽  
Author(s):  
Franco Brezzi ◽  
Cralg C. Douglas ◽  
L. Donatella Marini
Keyword(s):  
Reduction Method ◽  
Domain Reduction ◽  
Domain Reduction Method

Domain Reduction Method for Periodic Nanostructure Modeling: Gold Nanorods, Carbon Nanotubes and Graphene Applications

2010 ◽  
Author(s):  
Eduard G. Karpov ◽  
Dong Qian
Keyword(s):  
Atomistic Simulation ◽  
Reduction Method ◽  
Atomistic Simulations ◽  
Fine Scale ◽  
Coarse Scale ◽  
Benchmark Data ◽  
Domain Reduction ◽  
Interfacial Boundary ◽  
Nanocrystalline Structures ◽  
Domain Reduction Method

A domain-reduction approach for the simulation of one- and two-dimensional nanocrystalline structures is demonstrated. In this approach, the domain of interest is partitioned into coarse and fine scale regions and the coupling between the two is implemented through a multiscale interfacial boundary condition. The atomistic simulation is used in the fine scale region, while the discrete Fourier transform is applied to the coarse scale region to yield a compact Green’s function formulation that represents the effects of the coarse scale domain upon the fine/coarse scale interface. This approach facilitates the simulations for the fine scale, without the requirement to simulate the entire coarse scale domain. Robustness of the proposed domain-reduction method is demonstrated via comparison and verification of the results with benchmark data from fully atomistic simulations. Demonstrated applications include deformation of crystalline Au (111) nanorods, CNT bending and buckling, and graphene nanoindentation.

An abstract theory for the domain reduction method

Computing ◽  
1992 ◽  
Vol 48 (1) ◽  
pp. 73-96 ◽  
Author(s):  
C. C. Douglas ◽  
J. Mandel
Keyword(s):  
Reduction Method ◽  
Abstract Theory ◽  
Domain Reduction ◽  
Domain Reduction Method
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