Case Study: Lennard Jones Potentials - Fall 2002 | CS 6230, Study Guides, Projects, Research of Computer Science

Download Case Study: Lennard Jones Potentials - Fall 2002 | CS 6230 and more Study Guides, Projects, Research Computer Science in PDF only on Docsity! CS 6230 Case Study Lennard-Jones Potentials Spring 2002 The Lennard-Jones potential is a standard example used in many introductory textbooks in physical chemistry and computational molecular physics. Its beauty is that it is a very simple function to write, yet captures the inherent physics of most molecular bonds. It has a repulsive core (to prevent everything from collapsing to the center), a weakly attractive tail (to induce atoms to come together), and some preferred minimum distance. ∑ =                 −        = N j ijij i rr1 612 4 σσεε ∑ ∑∑ − = +==                 −        == 1 1 1 612 1 4 2 1 N i N ij ijij N i i rr E σσεε k r z j r y i r x r r rr F ij ij ij ij ij ij ij ij N j ijij i ˆˆˆˆ ˆ161124 1 713 ++=                 −        =∑ = r It is standard practice to set σ = ε = 1. Thus these reduce to considerably simpler expressions. ! Write a serial program which reads in a data file of the following format and calculates the Energy and Force per atom: Numer_of_atoms X1 y1 z1 X2 y2 z2 etc ! Parallelize this code for a distributed memory machine using MPI. ! Parallelize this code for a shared memory machine using OpenMP or pthreads (OpenMP preferred) ! Benchmark both codes by measuring speedup for 1-8 processors for at least 3 different problem sizes (small, medium, and large).