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Ghost-Force Corrected Concurrent Atomistic to Continuum Coupling AtC-GFC unpublished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

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


[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.