Toward high‐performance computational chemistry: I. Scalable Fock matrix construction algorithms

Several parallel algorithms for Fock matrix construction are described. The algorithms calculate only the unique integrals, distribute the Fock and density matrices over the processors of a massively parallel computer, use blocking techniques to construct the distributed data structures, and use clustering techniques on each processor to maximize data reuse. Algorithms based on both square and row‐blocked distributions of the Fock and density matrices are described and evaluated. Variants of the algorithms are discussed that use either triple‐sort or canonical ordering of integrals, and dynamic or static task clustering schemes. The algorithms are shown to adapt to screening, with communication volume scaling down with computation costs. Modeling techniques are used to characterize algorithm performance. Given the characteristics of existing massively parallel computers, all the algorithms are shown to be highly efficient for problems of moderate size. The algorithms using the row‐blocked data distribution are the most efficient. © 1996 by John Wiley & Sons, Inc.

[1]  Rick Stevens,et al.  Toward high‐performance computational chemistry: II. A scalable self‐consistent field program , 1996 .

[2]  Jeff Nichols,et al.  Implementation of the direct SCF and RPA methods on loosely coupled networks of workstations , 1993, J. Comput. Chem..

[3]  Michel Dupuis,et al.  Parallel computation of molecular energy gradients on the loosely coupled array of processors (LCAP) , 1987 .

[4]  Armin Burkhardt,et al.  SCF calculations on MIMD type parallel computers , 1993 .

[5]  Ron Shepard,et al.  Elimination of the diagonalization bottleneck in parallel Direct-SCF methods , 1993 .

[6]  Michael E. Colvin,et al.  Parallel direct SCF for large-scale calculations , 1993 .

[7]  Giorgina Corongiu,et al.  Parallelism in quantum chemistry: Hydrogen bond study in DNA base pairs as an example , 1984 .

[8]  Hans Peter Lüthi,et al.  Network supercomputing: A distributed-concurrent direct SCF scheme , 1993 .

[9]  Thomas R. Furlani,et al.  Implementation of a parallel direct SCF algorithm on distributed memory computers , 1995, J. Comput. Chem..

[10]  Mark A. Spackman,et al.  Potential derived charges using a geodesic point selection scheme , 1996, J. Comput. Chem..

[11]  R. Harrison,et al.  AB Initio Molecular Electronic Structure on Parallel Computers , 1994 .

[12]  Alan Edelman,et al.  Optimal Matrix Transposition and Bit Reversal on Hypercubes: All-to-All Personalized Communication , 1991, J. Parallel Distributed Comput..

[13]  Shridhar R. Gadre,et al.  Development of a restricted Hartree—Fock program INDMOL on PARAM: A highly parallel computer , 1993, J. Comput. Chem..

[14]  Martyn F. Guest,et al.  Parallelism in computational chemistry , 1993 .

[15]  Marco Häser,et al.  Improvements on the direct SCF method , 1989 .

[16]  Rick A. Kendall,et al.  An efficient implementation of the direct-SCF algorithm on parallel computer architectures , 1993 .

[17]  Stefan Brode,et al.  Parallel direct SCF and gradient program for workstation clusters , 1993, J. Comput. Chem..

[18]  Clemens C. J. Roothaan,et al.  New Developments in Molecular Orbital Theory , 1951 .

[19]  Kristyn J. Maschhoff,et al.  Investigating the performance of parallel eigensolvers for large processor counts , 1993 .

[20]  J. Almlöf,et al.  Principles for a direct SCF approach to LICAO–MOab‐initio calculations , 1982 .

[21]  S. Lennart Johnsson,et al.  Algorithms for Matrix Transposition on Boolean n-Cube Configured Ensemble Architectures , 1988, ICPP.