MultiBench Code Overview

The MultiBench test suite is a unified implementation of fourteen leading multiscale methods for static loading conditions studied

In 2009, Miller and Tadmor published a paper providing a unified framework and performance benchmark for fourteen leading multiscale methods including QC [136]. The code used in the performace benchmark testing, called "MultiBench", is available here. The methods supported by MultiBench are:

Method Acronym Key References
Quasicontinuum QC [16, 12]
Coupling of Length Scales CLS [11]
Bridging Domain BD [18]
Bridging Scale Method BSM [17, 10]
Composite Grid Atomistic Continuum Method CACM [3]
Cluster-Energy Quasicontinuum CQC-E [4]
Ghost-Force Corrected Quasicontinuum QC-GFC [13]
Ghost-Force Corrected Cluster-Energy Quasicontinuum CQC-GFC [4]
Finite-Element/Atomistics Method FEAt [7]
Coupled Atomistics and Discrete Dislocations CADD [14, 15]
Hybrid Simulation Method HSM [8]
Concurrent Atomistic to Continuum Coupling AtC [5, 1, 2, 9]
Ghost-Force Corrected Concurrent Atomistic to Continuum Coupling AtC-GFC unpublished
Cluster-Force Quasicontinuum CQC-F [6]

A description of the unified framework encompassing all fourteen methods and the results of a benchmark comparing them are available in these publications:

  • R. E. Miller and E. B. Tadmor, "A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods", Model. Simul. Mater. Sci. Eng., 17, 053001 (2009). Preprint available here.
  • Chapter 12 in E. B. Tadmor and R. E. Miller, Modeling Materials: Continuum, Atomistic and Multiscale Techniques, Cambridge University Press (2011). More information on this book is available at http://modelingmaterials.org.

The complete MultiBench test suite, including the benchmark test case studied in the article, is available for download here.

References

[1] S. Badia, P. Bochev, R. Lehoucq, M. L. Parks, J. Fish, M. Nuggehally, and M. Gunzburger. A force-based blending model for atomistic-to-continuum coupling. International Journal for Multiscale Computational Engineering, 5(5):387-406, 2007.

[2] Santiago Badia, Michael Parks, Pavel Bochev, Max Gunzburger, and Richard Lehoucq. On atomistic-to-continuum coupling by blending. Multiscale Modeling & Simulation, 7(1):381-406, 2008.

[3] D. K. Datta, R. Catalin Picu, and Mark S. Shephard. Composite grid atomistic continuum method: An adaptive approach to bridge continuum with atomistic analysis. Intl. J. Multiscale Computational Engineering, 2(3):71-90, 2004.

[4] B. Eidel and A. Stukowski. A variational formulation of the quasicontinuum method based on energy sampling of clusters. J. Mech. Phys. Sol., 57(1):87-108, 2009.

[5] Jacob Fish, Mohan A. Nuggehally, Mark S. Shephard, Catalin R. Picu, Santiago Badia, Michael L. Parks, and Max Gunzburger. Concurrent AtC coupling based on a blend of the continuum stress and the atomistic force. Computer Methods in Applied Mechanics and Engineering, 196(45-48):4548-4560, 2007.

[6] J. Knap and M. Ortiz. An analysis of the quasicontinuum method. J. Mech. Phys. Sol., 49:1899-1923, 2001.

[7] S. Kohlhoff, P. Gumbsch, and H. F. Fischmeister. Crack propagation in bcc crystals studied with a combined finite-element and atomistic model. Phil. Mag. A 64(4):851-878, 1991.

[8] B. Q. Luan, S. Hyun, J. F. Molinari, N. Bernstein, and Mark O. Robbins. Multiscale modeling of two-dimensional contacts. Phys. Rev. E, 74:046710, 2007.

[9] Michael L. Parks, Pavel B. Bochev, and Richard B. Lehoucq. Connecting atomistic-to-continuum coupling and domain decomposition. Multiscale Modeling & Simulation, 7(1):362-380, 2008.

[10] D. Qian, G. J. Wagner, and Wing Kam Liu. A multiscale projection method for the analysis of carbon nanotubes. Computer Methods in Applied Mechanics and Engineering, 193:1603-1632, 2004.

[11] Robert E. Rudd and J. Q. Broughton. Concurrent coupling of length scales in solid state systems. Phys. Stat Solidi B, 217:251-291, 2000.

[12] V. B. Shenoy, R. Miller, E. B.Tadmor, R. Phillips, and M. Ortiz. Quasicontinuum models of interfacial structure and deformation. Phys. Rev. Lett., 80(4):742-745, 1998.

[13] V. B. Shenoy, R. Miller, E. B. Tadmor, D. Rodney, R. Phillips, and M. Ortiz. An adaptive methodology for atomic scale mechanics: The quasicontinuum method. J. Mech. Phys. Sol., 47:611-642, 1999.

[14] L. E. Shilkrot, R. E. Miller, and W. A. Curtin. Coupled atomistic and discrete dislocation plasticity. Phys. Rev. Lett., 89(2):025501, 2002.

[15] L. E. Shilkrot, R. E. Miller, and W. A. Curtin. Multiscale plasticity modeling: Coupled atomistic and discrete dislocation mechanics. J. Mech. Phys. Sol., 52(4):755-787, 2004.

[16] E. B. Tadmor, M. Ortiz, and R. Phillips. Quasicontinuum analysis of defects in solids. Phil. Mag. A, 73(6):1529-1563, 1996.

[17] G.J. Wagner and W.K. Liu. Coupling of atomistic and continuum simulations using a bridging scale decomposition. J. Comput. Phys., 190:249-274, 2003.

[18] S. P. Xiao and T. Belytschko. A bridging domain method for coupling continua with molecular dynamics. Computer Methods in Applied Mechanics and Engineering, 193:1645-1669, 2004.