Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

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Table Of Integrals Series And Products

Meshless methods: An overview and recent developments

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

A cohesive zone model, taking full account of finite geometry changes, is used to provide a unified framework for describing the process of void nucleation from in­itial debonding through complete decohesion. A boundary value problem simulating a periodic array of rigid spherical inclusions in an isotropically hardening elastic-viscoplastic matrix is analyzed. Dimensional considerations introduce a characteristic length into the formulation and, depending on the ratio of this characteristic length to the inclusion radius, decohesion occurs either in a "ductile" or "brittle" manner. The effect of the triaxiality of the imposed stress state on nucleation is studied and the numerical results are related to the description of void nucleation within a phenomenological constitutive framework for progressively cavitating solids. 1 Introduction The nucleation of voids from inclusions and second phase particles plays a key role in limiting the ductility and toughness of plastically deforming solids, including structural metals and composites. The voids initiate either by inclusion cracking or by decohesion of the interface, but here attention is confined to consideration of void nucleation by interfacial decohesion. Theoretical descriptions of void nucleation from second phase particles have been developed based on both continuum and dislocation concepts, e.g., Brown and Stobbs (1971), Argon et al. (1975), Chang and Asaro (1978), Goods and Brown (1979), and Fisher and Gurland (1981). These models have focussed on critical conditions for separation and have not explicitly treated propagation of the debonded zone along the interface. Interface debonding problems have been treated within the context of continuum linear elasticity theory; for example, the problem of separation of a circular cylindrical in­clusion from a matrix has been solved for an interface that supports neither shearing nor tensile normal tractions (Keer et al., 1973). The growth of a void at a rigid inclusion has been analyzed by Taya and Patterson (1982), for a nonlinear viscous solid subject to overall uniaxial straining and with the strength of the interface neglected. The model introduced in this investigation is aimed at describing the evolution from initial debonding through com­plete separation and subsequent void growth within a unified framework. The formulation is a purely continuum one using a cohesive zone (Barenblatt, 1962; Dugdale, 1960) type model for the interface but with full account taken of finite geometry

A Continuum Model for Void Nucleation by Inclusion Debonding

A mathematical analysis for indentation tests of articular cartilage.

A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques

Preface. 1. Introduction to Fracture Mechanics. 2. Distributed Dislocation Fundamentals. 3. Further Topics in Plane Crack Problems. 4. Interface Cracks. 5. Solution of Axi-Symmetric Crack Problems. 6. Three-Dimensional Cracks: An Introduction. 7. Three-Dimensional Cracks: Further Concepts. 8. Concluding Remarks. A: Dislocation Influence Functions. B: Numerical Solution of SIEs with Cauchy Kernel. C: Plane and Ring Dipole Influence Functions. D: Contour Integral and Kernel Function. References. Index.

Solution of Crack Problems: The Distributed Dislocation Technique

Solution of Crack Problems: The Distributed Dislocation Technique, by D.A. Hills, P.A. Kelly, D.N. Dai and A.M. Korsunsky: Journal of Applied Mechanics

Girffith-Inglis crack and Zener-Stroh-Koehler crack dislocation mechanics Hilbert transform and Muskhelishvili equations Bilby-Cottrell-Swinden-Dugdale (BCSD) crack crack tip shielding and antishielding by dislocations mode III crack in an elastic-plastic solid mode II crack in an elastic-plastic solid mode I crack in an elastic-plastic solid moving Yoffee crack interesting problems appendices.

Leon M. Keer

Papers

A mathematical analysis for indentation tests of articular cartilage.

A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques

Solution of Crack Problems: The Distributed Dislocation Technique

Solution of Crack Problems: The Distributed Dislocation Technique, by D.A. Hills, P.A. Kelly, D.N. Dai and A.M. Korsunsky: Journal of Applied Mechanics

Dislocation based fracture mechanics