Efficient algorithms for discrete lattice calculations

被引：4

作者：

Arndt, M. ^{[2
]}

Sorkin, V. ^{[1
]}

Tadmor, E. B. ^{[1
]}

机构：

[1] Univ Minnesota, Dept Aerosp Engn & Mech, Minneapolis, MN 55455 USA

[2] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2009年 / 228卷 / 13期

关键词：

Lattice algorithms; Lattice reduction; Nearest neighbor; Cluster computation; Quasicontinuum; QUASI-CONTINUUM; FINITE-ELEMENT; GEOMETRY;

D O I：

10.1016/j.jcp.2009.03.039

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We discuss algorithms for lattice-based computations, in particular lattice reduction, the detection of nearest neighbors, and the computation of clusters of nearest neighbors. We focus on algorithms that are most efficient for low spatial dimensions (typically d = 2, 3) and input data within a reasonably limited range. This makes them most useful for physically oriented numerical simulations, for example of crystalline solids. Different solution strategies are discussed, formulated as algorithms, and numerically evaluated. (c) 2009 Elsevier Inc. All rights reserved.

引用

页码：4858 / 4880

页数：23

共 16 条

[1] Closest point search in lattices [J].

Agrell, E ;

Eriksson, T ;

Vardy, A ;

Zeger, K .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2002, 48 (08) :2201-2214

[2]

CASSELS JWS, 1971, GRUNDLEHREN MATH WIS, V99

[3] LOW-DIMENSIONAL LATTICES .6. VORONOI REDUCTION OF 3-DIMENSIONAL LATTICES [J].

CONWAY, JH ;

SLOANE, NJA .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1992, 436 (1896) :55-68

[4] A multilattice quasicontinuum for phase transforming materials: Cascading Cauchy Born kinematics [J].

Dobson, M. ;

Elliott, R. S. ;

Luskin, M. ;

Tadmor, E. B. .

JOURNAL OF COMPUTER-AIDED MATERIALS DESIGN, 2007, 14 :219-237

[5]

Gauss C. F., 1801, Disquisitiones Arithmeticae

[6] ALGORITHMIC GEOMETRY OF NUMBERS [J].

KANNAN, R .

ANNUAL REVIEW OF COMPUTER SCIENCE, 1987, 2 :231-267

[7] MONTE-CARLO SIMULATIONS OF LATTICE MODELS FOR MACROMOLECULES [J].

KREMER, K ;

BINDER, K .

COMPUTER PHYSICS REPORTS, 1988, 7 (06) :259-310

[8] FACTORING POLYNOMIALS WITH RATIONAL COEFFICIENTS [J].

LENSTRA, AK ;

LENSTRA, HW ;

LOVASZ, L .

MATHEMATISCHE ANNALEN, 1982, 261 (04) :515-534

[9] CORRELATIONS AND SPONTANEOUS MAGNETIZATION OF 2-DIMENSIONAL ISING MODEL [J].

MONTROLL, EW ;

POTTS, RB ;

WARD, JC .

JOURNAL OF MATHEMATICAL PHYSICS, 1963, 4 (02) :308-&

[10] On essential and non-essential descriptions of multilattices [J].

Parry, GP .

MATHEMATICS AND MECHANICS OF SOLIDS, 2004, 9 (04) :411-418

← 1 2 →