Implementation of a Kalman Filter for Constituent Data Assimilation of Massively Parallel Computers
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Integral equation methods are widely used in the analysis and design of electromagnetic systems.
Hardware and software for Merlin, a new kind of massively parallel computing system, are described. Eight computers are linked as a 300-MIPS prototype to develop system software for a larger Merlin network with 16 to 64 nodes, totaling 600 to 3000 MIPS. These working prototypes help refine a mapped reflective memory technique that offers a new, very general way of linking many types of computer to form supercomputers. Processors share data selectively and rapidly on a word-by-word basis. Fast firmware virtual circuits are reconfigured to match topological needs of individual application programs. Merlin's low-latency memory-sharing interfaces solve many problems in the design of high-performance computing systems. The Merlin prototypes are intended to run parallel programs for scientific applications and to determine hardware and software needs for a future Teraflops Merlin network.
The single instruction stream, multiple data stream Massively Parallel Processor (MPP) unit consists of 16,384 bit serial arithmetic processors configured as a 128 x 128 array whose speed can exceed that of current supercomputers (Cyber 205). The applicability of the MPP for solving reaction network problems is presented and discussed, including the mapping of the calculation to the architecture, and CPU timing comparisons.
Attention is given to such topics as an evaluation of block algorithm variants in LAPACK and presents a large-grain parallel sparse system solver, a multiprocessor method for the solution of the generalized Eigenvalue problem on an interval, and a parallel QR algorithm for iterative subspace methods on the CM2. A discussion of numerical methods includes the topics of asynchronous numerical solutions of PDEs on parallel computers, parallel homotopy curve tracking on a hypercube, and solving Navier-Stokes equations on the Cedar Multi-Cluster system. A section on differential equations includes a discussion of a six-color procedure for the parallel solution of elliptic systems using the finite quadtree structure, data parallel algorithms for the finite element method, and domain decomposition methods in aerodynamics. Topics dealing with massively parallel computing include hypercube vs. 2-dimensional meshes and massively parallel computation of conservation laws. Performance and tools are also discussed.
The continued fraction method for factoring large integers (CFRAC) was an ideal algorithm to be implemented on a massively parallel computer such as the Massively Parallel Processor (MPP). After much effort, the first 60 digit number was factored on the MPP using about 6 1/2 hours of array time. Although this result added about 10 digits to the size number that could be factored using CFRAC on a serial machine, it was already badly beaten by the implementation of Davis and Holdridge on the CRAY-1 using the quadratic sieve, an algorithm which is clearly superior to CFRAC for large numbers. An algorithm is illustrated which is ideally suited to the single instruction multiple data (SIMD) massively parallel architecture and some of the modifications which were needed in order to make the parallel implementation effective and efficient are described.
Techniques for managing power distribution amongst processors in a massively parallel computer architecture are disclosed. The techniques utilize a hierarchy that organizes the various processors of the massively parallel computer architecture. The hierarchy groups numbers of the processors at the lowest level. When processors complete tasks, the power assigned to those processors is distributed to other processors in the same group so that the performance of those processors can be increased. Hierarchical organization simplifies the calculations required for determining how and when to distribute power, because when tasks are complete and power is available for distribution, a relatively small number of processors are available for consideration to receive that power. The number of processors that are grouped together can be adjusted in real time based on performance factors to improve the trade-off between calculation speed and power distribution efficacy.
In numerical simulations of disordered electronic systems, one of the most common approaches is to diagonalize random Hamiltonian matrices and to study the eigenvalues and eigenfunctions of a single electron in the presence of a random potential. An effort to implement a matrix diagonalization routine for real symmetric dense matrices on massively parallel SIMD computers, the Maspar MP-1 and MP-2 systems, is described. Results of numerical tests and timings are also presented.
Systems and methods of building massively parallel computing systems using low power computing complexes in accordance with embodiments of the invention are disclosed. A massively parallel computing system in accordance with one embodiment of the invention includes at least one Solid State Blade configured to communicate via a high performance network fabric. In addition, each Solid State Blade includes a processor configured to communicate with a plurality of low power computing complexes interconnected by a router, and each low power computing complex includes at least one general processing core, an accelerator, an I/O interface, and cache memory and is configured to communicate with non-volatile solid state memory.
Research on algoriths for efficiently solving fluid flow problems on massively parallel computers is continued in the present paper. Attention is given to the implementation of a box scheme on the iPSC/860, a massively parallel computer with a peak speed of 10 Gflops and a memory of 128 Mwords. A domain decomposition approach to parallelism is used.
An apparatus for processing multidimensional data with strong spatial characteristics, such as raw image data, characterized by a large number of parallel data streams in an ordered array is described. It comprises a large number (e.g., 16,384 in a 128 x 128 array) of parallel processing elements operating simultaneously and independently on single bit slices of a corresponding array of incoming data streams under control of a single set of instructions. Each of the processing elements comprises a bidirectional data bus in communication with a register for storing single bit slices together with a random access memory unit and associated circuitry, including a binary counter/shift register device, for performing logical and arithmetical computations on the bit slices, and an I/O unit for interfacing the bidirectional data bus with the data stream source. The massively parallel processor architecture enables very high speed processing of large amounts of ordered parallel data, including spatial translation by shifting or sliding of bits vertically or horizontally to neighboring processing elements.
We present a highly parallel graph mapping technique that enables one to solve unstructured grid problems on massively parallel computers. Many implicit and explicit methods for solving discretizated partial differential equations require each point in the discretization to exchange data with its neighboring points every time step or iteration. The time spent communicating can limit the high performance promised by massively parallel computing. To eliminate this bottleneck, we map the graph of the irregular problem to the graph representing the interconnection topology of the computer such that the sum of the distances that the messages travel is minimized. We show that, in comparison to a naive assignment of processors, our heuristic mapping algorithm significantly reduces the communication time on the Connection Machine, CM-2.
Simple Skeleton Particle-in-Cell codes designed for massively parallel computers are described.
Future sensor systems will utilize massively parallel computing systems for rapid analysis of two-dimensional data. The Goddard Space Flight Center has an ongoing program to develop these systems. A single-instruction multiple data computer known as the Massively Parallel Processor (MPP) is being fabricated for NASA by the Goodyear Aerospace Corporation. This processor contains 16,384 processing elements arranged in a 128 x 128 array. The MPP will be capable of adding more than 6 billion 8-bit numbers per second. Multiplication of eight-bit numbers can occur at a rate of 2 billion per second. Delivery of the MPP to Goddard Space Flight Center is scheduled for 1983.
We report Tritium Migration Analysis Program version 8 (TMAP8), the latest version of TMAP, was developed within the framework of the Multiphysics Object-Oriented Simulation Environment (MOOSE). Created at Idaho National Laboratory (INL), MOOSE is an open-source, dimension-agnostic, fully coupled, and fully implicit multiphysics platform featuring massively parallel computation capabilities. Using TMAP8, tritium transport in a divertor monoblock was analyzed to elucidate the effects of pulsed operation (up to fifty 1,600 s plasma discharge and cool-down cycles) on the tritium in-vessel inventory source term and ex-vessel release term (i.e., tritium retention and permeation) for safety analysis. With its built-in Message Passing Interface capability, TMAP8 can, in under 2 h, simulate tritium transport in three different layered materials (i.e., tungsten, copper, and copper-chromium-zirconium alloy) in 2D geometry, using a single device/computer with 10 cores. The MOOSE-based TMAP8 code can leverage other MOOSE tools developed under the Nuclear Energy Advanced Modeling and Simulation program to perform tritium and thermal transport in complex geometries and multiphysics environments. And via its massively parallel computation, MOOSE will enable the fusion pilot plant designers to conduct high-fidelity multiphysics modeling for the design of the divertor and blanket systems as well as for the safety analysis.
We develop an Evolutionary Markov Chain Monte Carlo (EMCMC) algorithm for sampling spatial partitions that lie within a large, complex, and constrained spatial state space. Our algorithm combines the advantages of evolutionary algorithms (EAs) as optimization heuristics for state space traversal and the theoretical convergence properties of Markov Chain Monte Carlo algorithms for sampling from unknown distributions. Local optimality information that is identified via a directed search by our optimization heuristic is used to adaptively update a Markov chain in a promising direction within the framework of a Multiple-Try Metropolis Markov Chain model that incorporates a generalized Metropolis-Hastings ratio. We further expand the reach of our EMCMC algorithm by harnessing the computational power afforded by massively parallel computing architecture through the integration of a parallel EA framework that guides Markov chains running in parallel.
Some of the research programs involving the use of CFD in the aerodynamic design process at government laboratories around the United States are presented. Technology transfer issues and future directions in the discipline or CFD are addressed. The major challengers in the aerosciences as well as other disciplines that will require high-performance computing resources such as massively parallel computers are examined.