Density functional theory is a method for calculation of electronic structure of physical systems with a large number of atoms. In an effort to produce parallel implementation capable of solving systems with tens of thousands of atoms, in the first steps, we use Gaussian orbitals that allow relevant integrals to be calculated analytically. The main goal of this paper is the serial implementation of these integral calculations using C programming language. The analytical solutions consist of a very complex nested summations whose efficient implementation is the main contribution of this paper. We describe challenges encountered during implementation and their solutions. Results show that the given C implementation is at least three orders of magnitude faster than numerical solutions in the best available computational software programs.
This paper introduces our work on developing Krylov subspace and AMG solvers on NVIDIA GPUs. As SpMV is a crucial part for these iterative methods, SpMV algorithms for a single GPU and multiple GPUs are implemented. A HEC matrix format and a communication mechanism are established. Also, a set of specific algorithms for solving preconditioned systems in parallel environments are designed, including ILU(k), RAS and parallel triangular solvers. Based on these work, several Krylov solvers and AMG solvers are developed. According to numerical experiments, favorable acceleration performance is obtained from our Krylov solver and AMG solver under various parameter conditions.
Based on the characteristics of a huge number of data bits and reconfigurable optical processors of a ternary optical computer, a high-efficient division algorithm and realization are presented in this paper. The division algorithm adopts the SRT division to simplify operation steps and uses a two-step parallel M+B adder to speed up calculations. A number of rigorous tests for this algorithm are carried out through software simulation, which proves that the accuracy and performance of division in a ternary optical computer is superior to that of an electronic computer.
In the paper a new dispersion-relation-preserving upwind combined compact difference scheme (DRP-UCCD) to solve a time-dependent convection diffusion equations with variable coefficients is proposed. The developed scheme is constructed by making use of the high-order upwind combined compact difference operators, which can preserve the dispersion relation and enhance the convective stability. The scheme is proved to have the unconditional stability and the error accuracy is six order on space and two order on time. Numerical experiments confirm its high efficiency.
As one of the important techniques of data analysis, a clustering algorithm is widely used in data mining, image recognition, information extraction, pattern recognition and other fields. In the era of big data, with the rapid development of web applications, much of the data to be processed is characterized by massive and dynamic growth. Under this background, how to cluster the incremental data becomes a challenging problem that clustering algorithms face. In this paper, we proposed a limited incremental clustering algorithm with respect to cluster stability. Based on an assumption that the categories of data are limited, we take advantage of an existing clustering structure and deal with incremental data steadily with respect to cluster stability. Cluster reconstruction will be triggered when the stability does no longer hold or a buffer pool for undetermined data is full. At the end of the paper, we implement the limited incremental clustering algorithm with K-means. Meanwhile, we use an average density of clusters and the global stability to choose a proper value of K.
