The Multigrid Beta Function Approach for Modeling of Background Error Covariance in the Real-Time Mesoscale Analysis (RTMA)

We describe a method for the efficient generation of the covariance operators of a variational data assimilation scheme which is suited to implementation on a massively parallel computer. The elementary components of this scheme are what we call ‘beta filters’, since they are based on the same spatial profiles possessed by the symmetric beta distributions of probability theory. These approximately Gaussian (bell-shaped) polynomials blend smoothly to zero at the ends of finite intervals, which makes them better suited to parallelization than the present quasi-Gaussian ‘recursive filters’ used in operations at NCEP. These basic elements are further combined at a hierarchy of different spatial scales into an overall multigrid structure formulated to preserve the necessary self-adjoint attribute possessed by any valid covariance operator. This paper describes the underlying idea of the beta filter and discusses how generalized Helmholtz operators can be enlisted to weight the elementary contributions additively in such a way that the covariance operators may exhibit realistic negative sidelobes, which are not easily obtained through the recursive filter paradigm. The main focus of the paper is on the basic logistics of the multigrid structure by which more general covariance forms are synthesized from the basic quasi-Gaussian elements. We describe several ideas on how best to organize computation, which led us to a generalization of this structure which made it practical so that it can efficiently perform with any rectangular arrangement of processing elements. Some simple idealized examples of the applications of these ideas are given.

Genetic programming for iterative numerical methods

We introduce GPLS (Genetic Programming for Linear Systems) as a GP system that finds mathematical expressions defining an iteration matrix. Stationary iterative methods use this iteration matrix to solve a system of linear equations numerically. GPLS aims at finding iteration matrices with a low spectral radius and a high sparsity, since these properties ensure a fast error reduction of the numerical solution method and enable the efficient implementation of the methods on parallel computer architectures. We study GPLS for various types of system matrices and find that it easily outperforms classical approaches like the Gauss–Seidel and Jacobi methods. GPLS not only finds iteration matrices for linear systems with a much lower spectral radius, but also iteration matrices for problems where classical approaches fail. Additionally, solutions found by GPLS for small problem instances show also good performance for larger instances of the same problem.

A Novel Tradeoff Analysis between Traffic Congestion and Packing Density of Interconnection Networks for Massively Parallel Computers

From disaster prevention to mitigation, drug analysis to drug design, agriculture to food security, IoT to AI, and big data analysis to knowledge or sentiment mining, a high computation power is a prime necessity at present. As such, massively parallel computer (MPC) systems comprising a large number of nodes are gaining popularity. To interconnect these huge numbers of nodes efficiently, hierarchical interconnection networks are an attractive and feasible option. A Tori-connected flattened butterfly network (TFBN) has been proposed by the authors in a prior work for future generation MPC systems. In the previous study, the static network performance and static cost-effectiveness were evaluated. In this research, a novel trade-off factor named message traffic congestion vs. packing density trade-off factor has been proposed, which characterizes the message congestion in the network and its packing density. The factor is used to statically assess the suitability of the implementation of an interconnection network. The message traffic density, packing density, and new factor have been evaluated for the proposed network and similar competitive networks such as TTN, TESH, 2D-Mesh, 3D-Mesh, 2D-Torus, and 3D-Torus. It has been found that the performance of the TFBN is superior to the other networks.

Fractal dimension of coastline of Australia

Coastlines are irregular in nature having (random) fractal geometry and are formed by various natural activities. Fractal dimension is a measure of degree of geometric irregularity present in the coastline. A novel multicore parallel processing algorithm is presented to calculate the fractal dimension of coastline of Australia. The reliability of the coastline length of Australia is addressed by recovering the power law from our computational results. For simulations, the algorithm is implemented on a parallel computer for multi-core processing using the QGIS software, R-programming language and Python codes.

The Graph of Our Mind

Graph theory in the last two decades penetrated sociology, molecular biology, genetics, chemistry, computer engineering, and numerous other fields of science. One of the more recent areas of its applications is the study of the connections of the human brain. By the development of diffusion magnetic resonance imaging (diffusion MRI), it is possible today to map the connections between the 1–1.5 cm2 regions of the gray matter of the human brain. These connections can be viewed as a graph. We have computed 1015-vertex graphs with thousands of edges for hundreds of human brains from one of the highest quality data sources: the Human Connectome Project. Here we analyze the male and female braingraphs graph-theoretically and show statistically significant differences in numerous parameters between the sexes: the female braingraphs are better expanders, have more edges, larger bipartition widths, and larger vertex cover than the braingraphs of the male subjects. These parameters are closely related to the quality measures of highly parallel computer interconnection networks: the better expanding property, the large bipartition width, and the large vertex cover characterize high-quality interconnection networks. We apply the data of 426 subjects and demonstrate the statistically significant (corrected) differences in 116 graph parameters between the sexes.

High Performance Computing in Parallel Electromagnetics Simulation Code suite ACE3P

A comprehensive set of parallel finite-element codes suite ACE3P (Advanced Computational Electromagnetics 3D Parallel) is developed by SLAC for multi-physics modeling of particle accelerators running on massively parallel computer platforms for high fidelity and high accuracy simulation. ACE3P enables rapid virtual prototyping of accelerator and RF component design, optimization and analysis. Advanced modeling capabilities have been facilitated by implementations of novel algorithms for numerical solvers. Code performance on state-of-the-art high performance computing (HPC) platforms for large-scale RF modeling in accelerator applications will be presented in this paper. All the simulations have been performed on the supercomputers at National Energy Research Computer Center (NERSC).

TFBN: A Cost Effective High Performance Hierarchical Interconnection Network

In order to fulfill the increasing demand for computation power to process a boundless data concurrently within a very short time or real-time in many areas such as IoT, AI, machine learning, smart grid, and big data analytics, we need exa-scale or zetta-scale computation in the near future. Thus, to have this level of computation, we need a massively parallel computer (MPC) system that shall consist of millions of nodes; and, for the interconnection of these massive numbers of nodes, conventional topologies are infeasible. Thus, a hierarchical interconnection network (HIN) is a rational way to connect huge nodes. Through this article, we are proposing a new HIN, which is a tori-connected flattened butterfly network (TFBN) for the next generation MPC system. Numerous basic modules are hierarchically interconnected as a toroidal connection, whereby the basic modules are flattened butterfly networks. We have studied the network architecture, static network performance, and static cost-effectiveness of the proposed TFBN in detail; and compared static network and cost-effectiveness performance of the TFBN to those of TTN, torus, TESH, and mesh networks. It is depicted that TFBN possesses low diameter and average distance, high arc connectivity, and temperate bisection width. It also has better cost-effectiveness and cost-performance trade-off factor compared to those of TTN, torus, TESH, and mesh networks. The only shortcoming is that the complexity of wiring of the TFBN is higher than that of those networks; this is because the basic module necessitates some extra short length link to form the flattened butterfly network. Therefore, TFBN is a high performance and cost-effective HIN, and it will be a good option for the next generation MPC system.