Conference Paper

Scalable Parallel Numerical Methods and Software Tools for Material Design.

Source: DBLP


A new method of solution to the local spin density approximation to the electronic Schrödinger equation is presented. The method is based on an efficient, parallel adaptive multigrid eigenvalue solver. It is shown that adaptivity is both necessary and sufficient to accurately solve the eigenvalue problem near the singularities at the atomic centers. While preliminary, these results suggest that direct real space methods may provide a much needed method for efficiently computing the forces in complex materials.

Download full-text


Available from: John H Weare, Dec 19, 2013
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Predicting the structural and electronic properties of complex systems is one of the outstanding problems in condensed matter physics. Central to most methods used in molecular dynamics is the repeated solution of large eigenvalue problems. This paper reviews the source of these eigenvalue problems, describes some techniques for solving them, and addresses the difficulties and challenges which are faced. Parallel implementations are also discussed.
    Full-text · Article · Aug 1996 · BIT
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Parallel implementations of scientific applications often rely on elaborate dynamic data structures with complicated communication patterns. We describe a set of intuitive geometric programming abstractions that simplify coordination of irregular block-structured scientific calculations without sacrificing performance. We have implemented these abstractions in KeLP, a C++ run-time library. KeLP's abstractions enable the programmer to express complicated communication patterns for dynamic applications and to tune communication activity with a high-level, abstract interface. We show that KeLP's flexible communication model effectively manages elaborate data motion patterns arising in structured adaptive mesh refinement and achieves performance comparable to hand-coded message-passing on several structured numerical kernels.
    Full-text · Article · Apr 1998 · Journal of Parallel and Distributed Computing
  • [Show abstract] [Hide abstract]
    ABSTRACT: Results of the application of an adaptive piecewise linear finite element (FE) based solution using the FETK library of M. Holst to a density functional theory (DFT) approximation to the electronic structure of atoms and molecules are reported. The severe problem associated with the rapid variation of the electronic wave functions in the near singular regions of the atomic centers is treated by implementing completely unstructured simplex meshes that resolve these features around atomic nuclei. This concentrates the computational work in the regions in which the shortest length scales are necessary and provides for low resolution in regions for which there is no electron density. The accuracy of the solutions significantly improved when adaptive mesh refinement was applied, and it was found that the essential difficulties of the Kohn−Sham eigenvalues equation were the result of the singular behavior of the atomic potentials. Even though the matrix representations of the discrete Hamiltonian operator in the adaptive finite element basis are always sparse with a linear complexity in the number of discretization points, the overall memory and computational requirements for the solver implemented were found to be quite high. The number of mesh vertices per atom as a function of the atomic number Z and the required accuracy ε (in atomic units) was estimated to be υ(ε, Z) ≈ 122.37(Z2.2346/ε1.1173), and the number of floating point operations per minimization step for a system of NA atoms was found to be O(NA3υ(ε, Z)) (e.g., with Z = 26, ε = 0.0015 au, and NA = 100, the memory requirement and computational cost would be 0.2 terabytes and 25 petaflops). It was found that the high cost of the method could be reduced somewhat by using a geometric-based refinement strategy to fix the error near the singularities.
    No preview · Article · Apr 2009 · Journal of Chemical Theory and Computation
Show more