Monte Carlo simulations of Quantum systems on massively parallel computers

Author(s):  
H. Q. Ding
1992 ◽  
Vol 278 ◽  
Author(s):  
C. P. Burmester ◽  
L. T. Wille ◽  
R. Gronsky

AbstractAlgorithmic considerations regarding the implementation of various materials science applications of the Monte Carlo technique to single instruction multiple data (SIMD) computer architectures are presented. In particular, implementation of the Ising model with nearest, next nearest. and long range screened Coulomb interactions on the SIMD architecture MasPar MP-1 (DEC mpp-12000) series of massively parallel computers is demonstrated. Methods of code development which optimize processor array use and minimize inter-processor communication are presented including lattice partitioning and the use of processor array spanning tree structures for data reduction. Both geometric and algorithmic parallel approaches are utilized. Benchmarks in terms of Monte Carlo updates per second for the MasPar architecture are presented and compared to values reported in the literature from comparable studies on other architectures.


1992 ◽  
Vol 278 ◽  
Author(s):  
Steven R. Lustig ◽  
J.J. Cristy ◽  
D.A. Pensak

AbstractThe fast multipole method (FMM) is implemented in canonical ensemble particle simulations to compute non-bonded interactions efficiently with explicit error control. Multipole and local expansions have been derived to implement the FMM efficiently in Cartesian coordinates for soft-sphere (inverse power law), Lennard- Jones, Morse and Yukawa potential functions. Significant reductions in execution times have been achieved with respect to the direct method. For a given number, N, of particles the execution times of the direct method scale asO(N2). The FMM execution times scale asO(N) on sequential workstations and vector processors and asymptotically0(logN) on massively parallel computers. Connection Machine CM-2 and WAVETRACER-DTC parallel FMM implementations execute faster than the Cray-YMP vectorized FMM for ensemble sizes larger than 28k and 35k, respectively. For 256k particle ensembles the CM-2 parallel FMM is 12 times faster than the Cray-YMP vectorized direct method and 2.2 times faster than the vectorized FMM. For 256k particle ensembles the WAVETRACER-DTC parallel FMM is 33 times faster than the Cray-YMP vectorized direct method.


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