TAILIEUCHUNG - Báo cáo "A new formulation for fast calculation of far field force in molecular dynamics simulations "

We have developed a new formulation for fast calculation of far-field force of fast multipole method (FMM)in molecular dynamics simulations. FMM is a linear algorithm to calculate force for molecular dynamics simulations. GRAPE is a special-purpose computer dedicated to Coulombic force calculation. It runs 100-1000 times faster than normal computer at the same price. However FMM cannot be implemented directly on GRAPE. We have succeeded to implement FMM on GRAPE and developed a new formulation for far-field force calculation. . | VNU Journal of Science Mathematics - Physics 23 2007 1-8 A new formulation for fast calculation of far field force in molecular dynamics simulations Nguyen Hai Chau Department of Infomation Technology College of Technology VNU 144 Xuan Thuy Cau Giay Hanoi Vietnam Received 25 November 2006 received in revised form 7 August 2007 Abstract. We have developed a new formulation for fast calculation of far-field force of fast multipole method FMM in molecular dynamics simulations. FMM is a linear algorithm to calculate force for molecular dynamics simulations. GRAPE is a special-purpose computer dedicated to Coulombic force calculation. It runs 100-1000 times faster than normal computer at the same price. However FMM cannot be implemented directly on GRAPE. We have succeeded to implement FMM on GRAPE and developed a new formulation for far-field force calculation. Numerical tests show that the performance of FMM using our new formulation on GRAPE is approximately 2-5 times faster than that of FMM using conventional far field formulation. 1. Introduction Molecular dynamics MD simulations often require high calculation cost. The most intensive part of MD is calculation of Coulombic force among particles . atoms and ions . In naive direct-summation algorithm cost of the force calculation scales as O N2 where N is the number of particles. In order to reduce the cost of force calculation fast algorithms such as Barnes-Hut treecode 1 and fast multipole method 2 have been designed. Calculation cost of these algorithms are O N. log N and O N respectively. These fast algorithms are widely used in the field of MD simulation 3 4 . Another approach to accelerate the force calculation is to use hardware dedicated to the calculation of inter-particle force. GRAPE GRAvity PipE 5 6 is one of the most widely used hardware of that kind. Figure 1 shows basic structure of a GRAPE system. It consists of a GRAPE processor board and a general-purpose computer hereafter the host computer . A

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