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NASA NTRS2002

Effects of Ordering Strategies and Programming Paradigms on Sparse Matrix Computations

The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. For systems that are ill-conditioned, it is often necessary to use a preconditioning technique. In this paper, we investigate the effects of various ordering and partitioning strategies on the performance of parallel CG and ILU(O) preconditioned CG (PCG) using different programming paradigms and architectures. Results show that for this class of applications: ordering significantly improves overall performance on both distributed and distributed shared-memory systems, that cache reuse may be more important than reducing communication, that it is possible to achieve message-passing performance using shared-memory constructs through careful data ordering and distribution, and that a hybrid MPI+OpenMP paradigm increases programming complexity with little performance gains. A implementation of CG on the Cray MTA does not require special ordering or partitioning to obtain high efficiency and scalability, giving it a distinct advantage for adaptive applications; however, it shows limited scalability for PCG due to a lack of thread level parallelism.

Oliker, Leonid↗

NASA NTRS1991

Shared versus distributed memory multiprocessors

The question of whether multiprocessors should have shared or distributed memory has attracted a great deal of attention. Some researchers argue strongly for building distributed memory machines, while others argue just as strongly for programming shared memory multiprocessors. A great deal of research is underway on both types of parallel systems. Special emphasis is placed on systems with a very large number of processors for computation intensive tasks and considers research and implementation trends. It appears that the two types of systems will likely converge to a common form for large scale multiprocessors.

Jordan, Harry F.↗

NASA NTRS2002

Experiences Using OpenMP Based on Compiler Directed Software DSM on a PC Cluster

In this work we report on our experiences running OpenMP (message passing) programs on a commodity cluster of PCs (personal computers) running a software distributed shared memory (DSM) system. We describe our test environment and report on the performance of a subset of the NAS (NASA Advanced Supercomputing) Parallel Benchmarks that have been automatically parallelized for OpenMP. We compare the performance of the OpenMP implementations with that of their message passing counterparts and discuss performance differences.

Hess, Matthias↗

NASA NTRS1993

Computational mechanics analysis tools for parallel-vector supercomputers

Computational algorithms for structural analysis on parallel-vector supercomputers are reviewed. These parallel algorithms, developed by the authors, are for the assembly of structural equations, 'out-of-core' strategies for linear equation solution, massively distributed-memory equation solution, unsymmetric equation solution, general eigensolution, geometrically nonlinear finite element analysis, design sensitivity analysis for structural dynamics, optimization search analysis and domain decomposition. The source code for many of these algorithms is available.

Storaasli, Olaf O.↗

NASA NTRS1993

Computational mechanics analysis tools for parallel-vector supercomputers

Computational algorithms for structural analysis on parallel-vector supercomputers are reviewed. These parallel algorithms, developed by the authors, are for the assembly of structural equations, 'out-of-core' strategies for linear equation solution, massively distributed-memory equation solution, unsymmetric equation solution, general eigen-solution, geometrically nonlinear finite element analysis, design sensitivity analysis for structural dynamics, optimization algorithm and domain decomposition. The source code for many of these algorithms is available from NASA Langley.

Storaasli, O. O.↗

NASA NTRS2001

A Parallel Cartesian Approach for External Aerodynamics of Vehicles with Complex Geometry

This workshop paper presents the current status in the development of a new approach for the solution of the Euler equations on Cartesian meshes with embedded boundaries in three dimensions on distributed and shared memory architectures. The approach uses adaptively refined Cartesian hexahedra to fill the computational domain. Where these cells intersect the geometry, they are cut by the boundary into arbitrarily shaped polyhedra which receive special treatment by the solver. The presentation documents a newly developed multilevel upwind solver based on a flexible domain-decomposition strategy. One novel aspect of the work is its use of space-filling curves (SFC) for memory efficient on-the-fly parallelization, dynamic re-partitioning and automatic coarse mesh generation. Within each subdomain the approach employs a variety reordering techniques so that relevant data are on the same page in memory permitting high-performance on cache-based processors. Details of the on-the-fly SFC based partitioning are presented as are construction rules for the automatic coarse mesh generation. After describing the approach, the paper uses model problems and 3- D configurations to both verify and validate the solver. The model problems demonstrate that second-order accuracy is maintained despite the presence of the irregular cut-cells in the mesh. In addition, it examines both parallel efficiency and convergence behavior. These investigations demonstrate a parallel speed-up in excess of 28 on 32 processors of an SGI Origin 2000 system and confirm that mesh partitioning has no effect on convergence behavior.

Aftosmis, M. J.↗

NASA NTRS1984

Theory and modeling of atmospheric turbulence, part 1

The cascade transfer which is the only function to describe the mode coupling as the result of the nonlinear hydrodynamic state of turbulence is discussed. A kinetic theory combined with a scaling procedure was developed. The transfer function governs the non-linear mode coupling in strong turbulence. The master equation is consistent with the hydrodynamical system that describes the microdynamic state of turbulence and has the advantages to be homogeneous and have fewer nonlinear terms. The modes are scaled into groups to decipher the governing transport processes and statistical characteristics. An equation of vorticity transport describes the microdynamic state of two dimensional, isotropic and homogeneous, geostrophic turbulence. The equation of evolution of the macrovorticity is derived from group scaling in the form of the Fokker-Planck equation with memory. The microdynamic state of turbulence is transformed into the Liouville equation to derive the kinetic equation of the singlet distribution in turbulence. The collision integral contains a memory, which is analyzed with pair collision and the multiple collision. Two other kinetic equations are developed in parallel for the propagator and the transition probability for the interaction among the groups.

Source record↗

NASA NTRS2007

Reusable, Extensible High-Level Data-Distribution Concept

A framework for high-level specification of data distributions in data-parallel application programs has been conceived. [As used here, distributions signifies means to express locality (more specifically, locations of specified pieces of data) in a computing system composed of many processor and memory components connected by a network.] Inasmuch as distributions exert a great effect on the performances of application programs, it is important that a distribution strategy be flexible, so that distributions can be adapted to the requirements of those programs. At the same time, for the sake of productivity in programming and execution, it is desirable that users be shielded from such error-prone, tedious details as those of communication and synchronization. As desired, the present framework enables a user to refine a distribution type and adjust it to optimize the performance of an application program and conceals, from the user, the low-level details of communication and synchronization. The framework provides for a reusable, extensible, data-distribution design, denoted the design pattern, that is independent of a concrete implementation. The design pattern abstracts over coding patterns that have been found to be commonly encountered in both manually and automatically generated distributed parallel programs. The following description of the present framework is necessarily oversimplified to fit within the space available for this article. Distributions are among the elements of a conceptual data-distribution machinery, some of the other elements being denoted domains, index sets, and data collections (see figure). Associated with each domain is one index set and one distribution. A distribution class interface (where "class" is used in the object-oriented-programming sense) includes operations that enable specification of the mapping of an index to a unit of locality. Thus, "Map(Index)" specifies a unit, while "LocalLayout(Index)" specifies the local address within that unit. The distribution class can be extended to enable specification of commonly used distributions or novel user-defined distributions. A data collection can be defined over a domain. The term "data collection" in this context signifies, more specifically, an abstraction of mappings from index sets to variables. Since the index set is distributed, the addresses of the variables are also distributed.

James, Mark↗

NASA NTRS1987

Parallel discrete event simulation: A shared memory approach

With traditional event list techniques, evaluating a detailed discrete event simulation model can often require hours or even days of computation time. Parallel simulation mimics the interacting servers and queues of a real system by assigning each simulated entity to a processor. By eliminating the event list and maintaining only sufficient synchronization to insure causality, parallel simulation can potentially provide speedups that are linear in the number of processors. A set of shared memory experiments is presented using the Chandy-Misra distributed simulation algorithm to simulate networks of queues. Parameters include queueing network topology and routing probabilities, number of processors, and assignment of network nodes to processors. These experiments show that Chandy-Misra distributed simulation is a questionable alternative to sequential simulation of most queueing network models.

Reed, Daniel A.↗

NASA NTRS1988

Parallel discrete event simulation using shared memory

With traditional event-list techniques, evaluating a detailed discrete-event simulation-model can often require hours or even days of computation time. By eliminating the event list and maintaining only sufficient synchronization to ensure causality, parallel simulation can potentially provide speedups that are linear in the numbers of processors. A set of shared-memory experiments, using the Chandy-Misra distributed-simulation algorithm, to simulate networks of queues is presented. Parameters of the study include queueing network topology and routing probabilities, number of processors, and assignment of network nodes to processors. These experiments show that Chandy-Misra distributed simulation is a questionable alternative to sequential-simulation of most queueing network models.

Reed, Daniel A.↗

NASA NTRS1987

A transputer based finite element solver

The feasibility of performing FEM structural-mechanics analyses on transputer systems is investigated experimentally. Transputers are programmable microprocessors equipped with local memory and point-to-point communication links; they can be joined in a large concurrent system via a programming language which supports distributed processing; this permits parallel processing at relatively low hardware cost. The computational tasks required by FEM programs are reviewed; the hardware (one PC, one master transputer, and 12 slave transputers) employed in the test calculations is described; and results demonstrating the speed and efficiency of the transputer array in assembling a global stiffness matrix and performing Gauss-Jordan matrix inversion are presented in graphs. It is predicted that larger transputer networks could approach the power of supercomputers at minicomputer costs.

Favenesi, J. A.↗

NASA NTRS1991

An improved distributed arithmetic architecture

Speed requirements have been, and will continue to be, a major consideration in the design of hardware to implement digital signal processing functions like digital filters and transforms like the DFT and DCT. The conventional approach is to increase speed by adding hardware and increasing chip area. The real challenge is to save chip area while still maintaining high speed performance. The approach we propose is based on the distributed arithmetic implementation (DA) of digital filters. The improvement is based on two observations. Firstly, a single memory element can replace several identical memory elements in a fully parallel DA implementation. Secondly, truncation or rounding may be introduced into the computation at strategic points without increasing error unduly. Both of these approaches can be used to attain area savings without impairing speed of operation.

Guo, X.↗

NASA NTRS2001

Design and Implementation of a Parallel Multivariate Ensemble Kalman Filter for the Poseidon Ocean General Circulation Model

A multivariate ensemble Kalman filter (MvEnKF) implemented on a massively parallel computer architecture has been implemented for the Poseidon ocean circulation model and tested with a Pacific Basin model configuration. There are about two million prognostic state-vector variables. Parallelism for the data assimilation step is achieved by regionalization of the background-error covariances that are calculated from the phase-space distribution of the ensemble. Each processing element (PE) collects elements of a matrix measurement functional from nearby PEs. To avoid the introduction of spurious long-range covariances associated with finite ensemble sizes, the background-error covariances are given compact support by means of a Hadamard (element by element) product with a three-dimensional canonical correlation function. The methodology and the MvEnKF configuration are discussed. It is shown that the regionalization of the background covariances; has a negligible impact on the quality of the analyses. The parallel algorithm is very efficient for large numbers of observations but does not scale well beyond 100 PEs at the current model resolution. On a platform with distributed memory, memory rather than speed is the limiting factor.

Keppenne, Christian L.↗

NASA NTRS2003

Support of Multidimensional Parallelism in the OpenMP Programming Model

OpenMP is the current standard for shared-memory programming. While providing ease of parallel programming, the OpenMP programming model also has limitations which often effect the scalability of applications. Examples for these limitations are work distribution and point-to-point synchronization among threads. We propose extensions to the OpenMP programming model which allow the user to easily distribute the work in multiple dimensions and synchronize the workflow among the threads. The proposed extensions include four new constructs and the associated runtime library. They do not require changes to the source code and can be implemented based on the existing OpenMP standard. We illustrate the concept in a prototype translator and test with benchmark codes and a cloud modeling code.

Jin, Hao-Qiang↗

NASA NTRS1995

Newton-Krylov-Schwarz: An implicit solver for CFD

Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton's method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on aerodynamics applications emphasizing comparisons with a standard defect-correction approach, subdomain preconditioner consistency, subdomain preconditioner quality, and the effect of a coarse grid.

Cai, Xiao-Chuan↗

NASA NTRS2000

Dynamic Load-Balancing for Distributed Heterogeneous Computing of Parallel CFD Problems

The developed methodology is aimed at improving the efficiency of executing block-structured algorithms on parallel, distributed, heterogeneous computers. The basic approach of these algorithms is to divide the flow domain into many sub- domains called blocks, and solve the governing equations over these blocks. Dynamic load balancing problem is defined as the efficient distribution of the blocks among the available processors over a period of several hours of computations. In environments with computers of different architecture, operating systems, CPU speed, memory size, load, and network speed, balancing the loads and managing the communication between processors becomes crucial. Load balancing software tools for mutually dependent parallel processes have been created to efficiently utilize an advanced computation environment and algorithms. These tools are dynamic in nature because of the chances in the computer environment during execution time. More recently, these tools were extended to a second operating system: NT. In this paper, the problems associated with this application will be discussed. Also, the developed algorithms were combined with the load sharing capability of LSF to efficiently utilize workstation clusters for parallel computing. Finally, results will be presented on running a NASA based code ADPAC to demonstrate the developed tools for dynamic load balancing.

Ecer, A.↗

NASA NTRS1997

Parallel ALLSPD-3D: Speeding Up Combustor Analysis Via Parallel Processing

The ALLSPD-3D Computational Fluid Dynamics code for reacting flow simulation was run on a set of benchmark test cases to determine its parallel efficiency. These test cases included non-reacting and reacting flow simulations with varying numbers of processors. Also, the tests explored the effects of scaling the simulation with the number of processors in addition to distributing a constant size problem over an increasing number of processors. The test cases were run on a cluster of IBM RS/6000 Model 590 workstations with ethernet and ATM networking plus a shared memory SGI Power Challenge L workstation. The results indicate that the network capabilities significantly influence the parallel efficiency, i.e., a shared memory machine is fastest and ATM networking provides acceptable performance. The limitations of ethernet greatly hamper the rapid calculation of flows using ALLSPD-3D.

Fricker, David M.↗

NASA NTRS2000

Parallel and Distributed Computational Fluid Dynamics: Experimental Results and Challenges

This paper describes several results of parallel and distributed computing using a large scale production flow solver program. A coarse grained parallelization based on clustering of discretization grids combined with partitioning of large grids for load balancing is presented. An assessment is given of its performance on distributed and distributed-shared memory platforms using large scale scientific problems. An experiment with this solver, adapted to a Wide Area Network execution environment is presented. We also give a comparative performance assessment of computation and communication times on both the tightly and loosely-coupled machines.

Djomehri, Mohammad Jahed↗