Parallel implementation of a mesh‐based density functional electronic structure code

We describe the implementation of the mesh‐based first‐principles density functional code DMol on nCUBE 2 parallel computers. The numerical mesh nature of DMol makes it naturally suited for a massively parallel computational environment. Our parallelization strategy consists of a domain decomposition of mesh points. This evenly distributes mesh points to all available processors and leads to a substantial computational speedup with limited communication overhead and good node balancing. To achieve better performance and circumvent memory storage limitations, the torus wrap method is used to distribute both the Hamiltonian and overlap matrices, and a parallel matrix diagonalization routine is employed to calculate eigenvalues and eigenvectors. Benchmark calculations on a 128‐node nCUBE 2 are presented. © 1995 by John Wiley & Sons, Inc.

[1]  Larson,et al.  Ab initio theory of the Si(111)-(7 x 7) surface reconstruction: A challenge for massively parallel computation. , 1992, Physical review letters.

[2]  B. Delley An all‐electron numerical method for solving the local density functional for polyatomic molecules , 1990 .

[3]  Lin,et al.  Ab initio total-energy calculations for extremely large systems: Application to the Takayanagi reconstruction of Si(111). , 1992, Physical review letters.

[4]  N. H. March,et al.  Theory of the inhomogeneous electron gas , 1983 .

[5]  D. Bethune,et al.  Bond Lengths in Free Molecules of Buckminsterfullerene, C60, from Gas-Phase Electron Diffraction , 1991, Science.

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

[7]  A. Zunger,et al.  Self-interaction correction to density-functional approximations for many-electron systems , 1981 .

[8]  Y. S. Li,et al.  How free are encapsulated atoms in C60 , 1994 .

[9]  G. C. Fox,et al.  Solving Problems on Concurrent Processors , 1988 .

[10]  Michael T. Heath,et al.  Parallel solution of triangular systems on distributed-memory multiprocessors , 1988 .

[11]  B. Delley,et al.  Analytic energy derivatives in the numerical local‐density‐functional approach , 1991 .

[12]  Benny G. Johnson,et al.  The performance of a family of density functional methods , 1993 .

[13]  J. Devreese,et al.  Electronic Structure, Dynamics, and Quantum Structural Properties of Condensed Matter , 1985 .

[14]  Jan K. Labanowski,et al.  Density Functional Methods in Chemistry , 1991 .

[15]  G. Stewart,et al.  Assignment and scheduling in parallel matrix factorization , 1986 .

[16]  C. W. Murray,et al.  Study of methane, acetylene, ethene, and benzene using Kohn-Sham theory , 1993 .

[17]  D. Bethune,et al.  NMR determination of the bond lengths in C60 , 1991 .