Efficient algorithms for discrete lattice calculations

Journal of Computational Physics

Volumn 228, Issue 13, 2009, Pages 4858-4880

  Arndt, M ^a   Sorkin, V ^a   Tadmor, E B ^a  

^a University of Minnesota   (United States)

Author keywords

Cluster computation; Lattice algorithms; Lattice reduction; Nearest neighbor; Quasicontinuum

Indexed keywords

COMPUTATIONAL EFFICIENCY; REDUCTION;

CLUSTER COMPUTATION; DISCRETE LATTICES; INPUT DATAS; LATTICE ALGORITHMS; LATTICE CALCULATIONS; LATTICE REDUCTION; LATTICE-BASED; NEAREST-NEIGHBOUR; QUASICONTINUUM; SPATIAL DIMENSION;

CLUSTERING ALGORITHMS;

EID: 68649084423     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.03.039     Document Type: Article

References (16)

1. Agrell E., Eriksson T., Vardy A., and Zeger K. Closest point search in lattices. IEEE Trans. Inf. Theory 48 8 (2002) 2201-2214
2. Cassels J.W.S. An Introduction to the Geometry of Numbers. Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete vol. 99 (1971), Springer-Verlag, Berlin/Heidelberg/New York
3. Conway J.H., and Sloane N.J.A. Low-dimensional lattices. VI. Voronoi reduction of three-dimensional lattices. Proc. Roy. Soc. Lond. A 436 1896 (1992) 55-68
4. Dobson M., Elliott R.S., Luskin M., and Tadmor E.B. A multilattice quasicontinuum for phase transforming materials: Cascading Cauchy Born kinematics. J. Comput. Aided Mater. Des. 14 Suppl. 1 (2007) 219-237
5. Gauss C.F. Disquisitiones Arithmeticae. (A.A. Clarke, Trans., 1966) (1801), Yale University Press, New Haven, London
6. Kannan R. Algorithmic geometry of numbers. Annu. Rev. Comput. Sci. 2 (1987) 231-267
7. Kremer K., and Binder K. Monte Carlo simulations of lattice models for macromolecules. Comp. Phys. Rep. 7 (1988) 259-310
8. Lenstra A.K., Lenstra Jr. H.W., and Lovász L. Factoring polynomials with rational coefficients. Math. Ann. 261 (1982) 515-534
9. McCoy B.M., and Wu T.T. The Two-Dimensional Ising Model (1973), Harvard University Press, Cambridge
10. Parry G.P. On essential and non-essential descriptions of multilattices. Math. Mech. Solids 9 (2004) 411-418
11. Pitteri M. Geometry and symmetry of multilattices. Int. J. Plast. 14 (1998) 139-157
12. Press W.H., Teukolsky S.A., Vetterling W.T., and Flannery B.P. Numerical Recipes in FORTRAN. The Art of Scientific Computing. second ed. (1992), Cambridge University Press, Cambridge
13. Shenoy V.B., Miller R., Tadmor E.B., Rodney D., Phillips R., and Ortiz M. An adaptive finite element approach to atomic-scale mechanics-the quasicontinuum method. J. Mech. Phys. Solids 47 3 (1999) 611-642
14. Tadmor E.B., Ortiz M., and Phillips R. Quasicontinuum analysis of defects in solids. Philos. Mag. A 73 6 (1996) 1529-1563
15. Tadmor E.B., Smith G.S., Bernstein N., and Kaxiras E. Mixed finite element and atomistic formulation for complex crystals. Phys. Rev. B 59 1 (1999) 235-245
16. Yue K., Fiebig K.M., Thomas P.D., Chan H.S., Shakhnovich E.I., and Dill K.A. A test of lattice protein folding algorithms. Proc. Natl. Acad. Sci. USA 92 (1995) 325-329