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NASA NTRS1988

Investigations on the usefulness of the Massively Parallel Processor for study of electronic properties of atomic and condensed matter systems

The usefulness of the Massively Parallel Processor (MPP) for investigation of electronic structures and hyperfine properties of atomic and condensed matter systems was explored. The major effort was directed towards the preparation of algorithms for parallelization of the computational procedure being used on serial computers for electronic structure calculations in condensed matter systems. Detailed descriptions of investigations and results are reported, including MPP adaptation of self-consistent charge extended Hueckel (SCCEH) procedure, MPP adaptation of the first-principles Hartree-Fock cluster procedure for electronic structures of large molecules and solid state systems, and MPP adaptation of the many-body procedure for atomic systems.

Das, T. P.↗

NASA NTRS1984

Structural dynamic analysis on a parallel computer - The finite element machine

Recent and prospective advances in parallel multiple introduction multiple data (MIMD) computers offer significant improvements in the range of structural problems that can be solved, as well as the speed of solutions. These improvements have their basis in the effective selection and implementation of algorithms exploiting parallel computation. Attention is presently given to the solution of the transient response calculations of an experimental MIMD computer designated the 'Finite Element Machine', including its algorithm and its results for representative one- and two-dimensional dynamic response test problems. A factor of 6.5 is noted for the computational speed improvement.

Storaasli, O.↗

NASA NTRS1986

Concurrent extensions to the FORTRAN language for parallel programming of computational fluid dynamics algorithms

Experiments were conducted at NASA Ames Research Center to define multi-tasking software requirements for multiple-instruction, multiple-data stream (MIMD) computer architectures. The focus was on specifying solutions for algorithms in the field of computational fluid dynamics (CFD). The program objectives were to allow researchers to produce usable parallel application software as soon as possible after acquiring MIMD computer equipment, to provide researchers with an easy-to-learn and easy-to-use parallel software language which could be implemented on several different MIMD machines, and to enable researchers to list preferred design specifications for future MIMD computer architectures. Analysis of CFD algorithms indicated that extensions of an existing programming language, adaptable to new computer architectures, provided the best solution to meeting program objectives. The CoFORTRAN Language was written in response to these objectives and to provide researchers a means to experiment with parallel software solutions to CFD algorithms on machines with parallel architectures.

Weeks, Cindy Lou↗

NASA NTRS1988

Fast Fourier Transform algorithm design and tradeoffs

The Fast Fourier Transform (FFT) is a mainstay of certain numerical techniques for solving fluid dynamics problems. The Connection Machine CM-2 is the target for an investigation into the design of multidimensional Single Instruction Stream/Multiple Data (SIMD) parallel FFT algorithms for high performance. Critical algorithm design issues are discussed, necessary machine performance measurements are identified and made, and the performance of the developed FFT programs are measured. Fast Fourier Transform programs are compared to the currently best Cray-2 FFT program.

Kamin, Ray A., III↗

NASA NTRS1993

Parallel integer sorting with medium and fine-scale parallelism

Two new parallel integer sorting algorithms, queue-sort and barrel-sort, are presented and analyzed in detail. These algorithms do not have optimal parallel complexity, yet they show very good performance in practice. Queue-sort designed for fine-scale parallel architectures which allow the queueing of multiple messages to the same destination. Barrel-sort is designed for medium-scale parallel architectures with a high message passing overhead. The performance results from the implementation of queue-sort on a Connection Machine CM-2 and barrel-sort on a 128 processor iPSC/860 are given. The two implementations are found to be comparable in performance but not as good as a fully vectorized bucket sort on the Cray YMP.

Dagum, Leonardo↗

NASA NTRS1988

Computational requirements for on-orbit identification of space systems

For the future space systems, on-orbit identification (ID) capability will be required to complement on-orbit control, due to the fact that the dynamics of large space structures, spacecrafts, and antennas will not be known sufficiently from ground modeling and testing. The computational requirements for ID of flexible structures such as the space station (SS) or the large deployable reflectors (LDR) are however, extensive due to the large number of modes, sensors, and actuators. For these systems the ID algorithm operations need not be computed in real-time, only in near real-time, or an appropriate mission time. Consequently the space systems will need advanced processors and efficient parallel processing algorithm design and architectures to implement the identification algorithms in near real-time. The MAX computer currently being developed may handle such computational requirements. The purpose is to specify the on-board computational requirements for dynamic and static identification for large space structures. The computational requirements for six ID algorithms are presented in the context of three examples: the JPL/AFAL ground antenna facility, the space station (SS), and the large deployable reflector (LDR).

Hadaegh, Fred Y.↗

NASA NTRS1997

Geopotential Error Analysis from Satellite Gradiometer and Global Positioning System Observables on Parallel Architecture

The recovery of a high resolution geopotential from satellite gradiometer observations motivates the examination of high performance computational techniques. The primary subject matter addresses specifically the use of satellite gradiometer and GPS observations to form and invert the normal matrix associated with a large degree and order geopotential solution. Memory resident and out-of-core parallel linear algebra techniques along with data parallel batch algorithms form the foundation of the least squares application structure. A secondary topic includes the adoption of object oriented programming techniques to enhance modularity and reusability of code. Applications implementing the parallel and object oriented methods successfully calculate the degree variance for a degree and order 110 geopotential solution on 32 processors of the Cray T3E. The memory resident gradiometer application exhibits an overall application performance of 5.4 Gflops, and the out-of-core linear solver exhibits an overall performance of 2.4 Gflops. The combination solution derived from a sun synchronous gradiometer orbit produce average geoid height variances of 17 millimeters.

Schutz, Bob E.↗

NASA NTRS1994

An efficient three-dimensional Poisson solver for SIMD high-performance-computing architectures

We present an algorithm that solves the three-dimensional Poisson equation on a cylindrical grid. The technique uses a finite-difference scheme with operator splitting. This splitting maps the banded structure of the operator matrix into a two-dimensional set of tridiagonal matrices, which are then solved in parallel. Our algorithm couples FFT techniques with the well-known ADI (Alternating Direction Implicit) method for solving Elliptic PDE's, and the implementation is extremely well suited for a massively parallel environment like the SIMD architecture of the MasPar MP-1. Due to the highly recursive nature of our problem, we believe that our method is highly efficient, as it avoids excessive interprocessor communication.

Cohl, H.↗

NASA NTRS1991

Rectilinear partitioning of irregular data parallel computations

New mapping algorithms for domain oriented data-parallel computations, where the workload is distributed irregularly throughout the domain, but exhibits localized communication patterns are described. Researchers consider the problem of partitioning the domain for parallel processing in such a way that the workload on the most heavily loaded processor is minimized, subject to the constraint that the partition be perfectly rectilinear. Rectilinear partitions are useful on architectures that have a fast local mesh network. Discussed here is an improved algorithm for finding the optimal partitioning in one dimension, new algorithms for partitioning in two dimensions, and optimal partitioning in three dimensions. The application of these algorithms to real problems are discussed.

Nicol, David M.↗

NASA NTRS1989

A real time, FEM based optimal control algorithm and its implementation using parallel processing hardware (transistors) in a microprocessor environment

There is an evident need to discover a means of establishing reliable, implementable controls for systems that are plagued by nonlinear and, or uncertain, model dynamics. The development of a generic controller design tool for tough-to-control systems is reported. The method utilizes a moving grid, time infinite element based solution of the necessary conditions that describe an optimal controller for a system. The technique produces a discrete feedback controller. Real time laboratory experiments are now being conducted to demonstrate the viability of the method. The algorithm that results is being implemented in a microprocessor environment. Critical computational tasks are accomplished using a low cost, on-board, multiprocessor (INMOS T800 Transputers) and parallel processing. Progress to date validates the methodology presented. Applications of the technique to the control of highly flexible robotic appendages are suggested.

Patten, William Neff↗

NASA NTRSDate not supplied

A Parallel Symmetric Successive Overrelaxation Method for OVERFLOW

The block Jacobi symmetric successive overrelaxation (SSOR) algorithm has been reformulated as a parallelized algorithm for the OVERFLOWstructured, overset grid, computational fluid dynamics flow solver. Simple changes to the flow solver required to implement the algorithm are discussed. A series of test cases are presented that demonstrate how the addition of implicit overset boundaries has improved the robustness and nonlinear convergence characteristics of the flow solver.

Computational Fluid Dynamics↗

NASA NTRS1988

On the accuracy of solving triangular systems in parallel

An error complexity analysis of two algorithms for solving a unit-diagonal triangular system is given. The results show that the unusual sequential algorithm is optimal in terms of having the minimal maximum and cumulative error complexity measures. The parallel algorithm described by Sameh and Brent is shown to be essentially equivalent to the optimal sequential one. Some numerical experiments are also taught.

Tsao, Nai-Kuan↗

NASA NTRS1988

A multistage linear array assignment problem

The implementation of certain algorithms on parallel processing computing architectures can involve partitioning contiguous elements into a fixed number of groups, each of which is to be handled by a single processor. It is desired to find an assignment of elements to processors that minimizes the sum of the maximum workloads experienced at each stage. This problem can be viewed as a multi-objective network optimization problem. Polynomially-bounded algorithms are developed for the case of two stages, whereas the associated decision problem (for an arbitrary number of stages) is shown to be NP-complete. Heuristic procedures are therefore proposed and analyzed for the general problem. Computational experience with one of the exact problems, incorporating certain pruning rules, is presented with one of the exact problems. Empirical results also demonstrate that one of the heuristic procedures is especially effective in practice.

Nicol, David M.↗

NASA NTRS1983

Finite element computation with parallel VLSI

This paper describes a parallel processing computer consisting of a 16-bit microcomputer as a master processor which controls and coordinates the activities of 8086/8087 VLSI chip set slave processors working in parallel. The hardware is inexpensive and can be flexibly configured and programmed to perform various functions. This makes it a useful research tool for the development of, and experimentation with parallel mathematical algorithms. Application of the hardware to computational tasks involved in the finite element analysis method is demonstrated by the generation and assembly of beam finite element stiffness matrices. A number of possible schemes for the implementation of N-elements on N- or n-processors (N is greater than n) are described, and the speedup factors of their time consumption are determined as a function of the number of available parallel processors.

Mcgregor, J.↗

NASA NTRS1989

Parallel processors and nonlinear structural dynamics algorithms and software

The adaptation of a finite element program with explicit time integration to a massively parallel SIMD (single instruction multiple data) computer, the CONNECTION Machine is described. The adaptation required the development of a new algorithm, called the exchange algorithm, in which all nodal variables are allocated to the element with an exchange of nodal forces at each time step. The architectural and C* programming language features of the CONNECTION Machine are also summarized. Various alternate data structures and associated algorithms for nonlinear finite element analysis are discussed and compared. Results are presented which demonstrate that the CONNECTION Machine is capable of outperforming the CRAY XMP/14.

Belytschko, Ted↗

NASA NTRS2002

Incompressible Navier-Stokes Solvers in Primative Variables and their Applications to Steady and Unsteady Flow Simulations

This paper reviews recent progress made in incompressible Navier-Stokes simulation procedures and their application to problems of engineering interest. Discussions are focused on the methods designed for complex geometry applications in three dimensions, and thus are limited to primitive variable formulation. A summary of efforts in flow solver development is given followed by numerical studies of a few example problems of current interest. Both steady and unsteady solution algorithms and their salient features are discussed. Solvers discussed here are based on a structured-grid approach using either a finite -difference or a finite-volume frame work. As a grand-challenge application of these solvers, an unsteady turbopump flow simulation procedure has been developed which utilizes high performance computing platforms. In the paper, the progress toward the complete simulation capability of the turbo-pump for a liquid rocket engine is reported. The Space Shuttle Main Engine (SSME) turbo-pump is used as a test case for evaluation of two parallel computing algorithms that have been implemented in the INS3D code. The relative motion of the grid systems for the rotorstator interaction was obtained using overact grid techniques. Unsteady computations for the SSME turbo-pump, which contains 114 zones with 34.5 million grid points, are carried out on SCSI Origin 3000 systems at NASA Ames Research Center. The same procedure has been extended to the development of NASA-DeBakey Ventricular Assist Device (VAD) that is based on an axial blood pump. Computational, and clinical analysis of this device are presented.

Kiris, Cetin C.↗

NASA NTRS1984

Dataflow computing approach in high-speed digital simulation

New computational tools and methodologies for the digital simulation of continuous systems were explored. Programmability, and cost effective performance in multiprocessor organizations for real time simulation was investigated. Approach is based on functional style languages and data flow computing principles, which allow for the natural representation of parallelism in algorithms and provides a suitable basis for the design of cost effective high performance distributed systems. The objectives of this research are to: (1) perform comparative evaluation of several existing data flow languages and develop an experimental data flow language suitable for real time simulation using multiprocessor systems; (2) investigate the main issues that arise in the architecture and organization of data flow multiprocessors for real time simulation; and (3) develop and apply performance evaluation models in typical applications.

Ercegovac, M. D.↗

NASA NTRS1985

Moving target, distributed, real-time simulation using Ada

Research on a precompiler solution is described for the moving target compiler problem encountered when trying to run parallel simulation algorithms on several microcomputers. The precompiler is under development at NASA-Lewis for simulating jet engines. Since the behavior of any component of a jet engine, e.g., the fan inlet, rear duct, forward sensor, etc., depends on the previous behaviors and not the current behaviors of other components, the behaviors can be modeled on different processors provided the outputs of the processors reach other processors in appropriate time intervals. The simulator works in compute and transfer modes. The Ada procedure sets for the behaviors of different components are divided up and routed by the precompiler, which essentially receives a multitasking program. The subroutines are synchronized after each computation cycle.

Collins, W. R.↗