Shared Memory Parallel Computer Research Articles

A DYNAMIC MPI-OPENMP MODEL FOR STRUCTURED ADAPTIVE MESH REFINEMENT

We compare experimentally different parallelization models using MPI and OpenMP for structured adaptive mesh refinement on a shared-memory parallel computer, a SunFire 15K. Due to the dynamic properties of the mesh no static parallelization model with fixed number of processes and threads performs best in all stages. Different combinations of MPI and OpenMP are preferable in different settings of the application and grid hierarchy. We suggest a new dynamic approach using a mixed MPI-OpenMP model that adapts the number of threads during run time and gives good performance in all stages throughout the whole run as the solution state changes, i.e. the resolution in the computational grid changes.

A comparative study of explicit group iterative solvers on a cluster of workstations

In this paper, a group iterative scheme based on rotated (cross) five-point finite difference discretisation, i.e. the four-point explicit decoupled group (EDG) is considered in solving a second order elliptic partial differential equation (PDE). This method was firstly introduced by Abdullah [“The four point EDG method: a fast poisson solver”, Int. J. Comput. Math., 38 (1991) 61–70], where the method was found to be more superior than the common existing methods based on the standard five-point finite difference discretisation. The method was further extended to different type of PDE's, where similar improved results were established [Ali, N.H.M., Abdullah, A.R. Four Point EDG: A Fast Solver For The Navier–Stokes Equation, M.H.Hamza (ed.) Proceedings of the IASTED International Conference on Modelling Simulation And Optimization, Gold Coast, Australia, May 6–9 (1996) (CD Rom-File 242-165.pdf), ISBN: 0-88986-197-8; Ali, N.H.M., Abdullah, A.R. New Parallel Point Iterative Solutions For the Diffusion-Convection Equation Proceedings of the International Conference on Parallel and Distributed Computing and Networks Singapore, Aug. 11–13 (1997) 136–139; Ali, N.H.M., Abdullah, A.R. “New rotated iterative algorithms for the solution of a coupled system of elliptic equations” Int. J. Comput. Math. 74 (1999) 223–251]. These new iterative algorithms had been developed to run on the Sequent Balance, a shared memory parallel computer [A.R. Abdullah, N.M. Ali, The Comparative Study of Parallel Strategies For The Solution of Elliptic PDE's Parallel Algorithms and Applications Vol. 10 (1996) 93–103; Ali, N.H.M., Abdullah, A.R. “Parallel four point explicit decoupled group (EDG) method for elliptic PDE's” Proceedings of the Seventh IASTED/ISMM International Conference on Parallel and Distributed Computing and Systems (1995) 302–304 (Washington DC); Ali, N.H.M., Abdullah, A.R. New Parallel Point Iterative Solutions For the Diffusion-Convection Equation Proceedings of the International Conference on Parallel and Distributed Computing and Networks, Singapore, Aug. 11–13 (1997) 136–139; Yousif, W.S., Evans, D.J.“Explicit decoupled group iterative methods and their parallel implementations” Parallel Algorithms and Applications 7 (1995) 53–71] where they were shown to be suitable to be implemented in parallel. In this work, the four-point group algorithm was ported to run on a cluster of Sun workstations using a parallel virtual machine (PVM) programming environment together with the four-point explicit group (EG) method [Evans, D.J., Yousif, W.S. “The implementation of the explicit block iterative methods on the balance 8000 parallel computer” Parallel Computing 16 (1990) 81–97]. We describe the parallel implementations of these methods in solving the Poisson equation and the results of some computational experiments are compared and reported. rosni@cs.usm.my kokjl@hotmail.com

共有メモリー計算機における3次元時間域動弾性高速境界積分方程式法の並列化について

This paper discusses parallelisation strategies of a time domain fast boundary integral equation method for three dimensional elastodynamics for a large shared memory parallel computer. The performance of the OpenMP parallelised code is examined. Also in the case of MPI-OpenMP hybrid parallelisation, a numerical solution of the scattering probrem with more than one million DOFs is shown. It is concluded that the parallelisation with OpenMP is very effective, and that larger problem can be analysed with MPI-OpenMP hybrid parallelisation.

Performance results of a large-scale air pollution model on two parallel computers

The size of the computational task obtained after the appropriate splitting and discretisation procedures of the system of partial differential equations in large air pollution models is enormous. Even when computers with several GFLOPS top performance are in use, it is difficult to solve this problem efficiently and, furthermore, to prepare codes that can be used for operating purposes. Some performance-comparison results obtained by runs of the parallelised via MPI unified variable-grid version of the Danish Eulerian model for long-range transport of air pollutants on two parallel computer architectures are presented. The test numerical experiments are performed on a Beowulf-like cluster set-up of four two-processor Macintosh G4 machines and a multiprocessor SUN (up to 32 processors). The Message Passing Interface (MPI) standard is used on both distributed and shared memory parallel computer platforms. Timing results, speed-up and parallel efficiency of the main computational stages as well as of the whole model are presented.

Solving unsymmetric sparse systems of linear equations with PARDISO

Supernode partitioning for unsymmetric matrices together with complete block diagonal supernode pivoting and asynchronous computation can achieve high gigaflop rates for parallel sparse LU factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to extend these concepts further and unsymmetric prepermutation of rows is used to place large matrix entries on the diagonal. Complete block diagonal supernode pivoting allows dynamical interchanges of columns and rows during the factorization process. The level-3 BLAS efficiency is retained and an advanced two-level left–right looking scheduling scheme results in good speedup on SMP machines. These algorithms have been integrated into the recent unsymmetric version of the PARDISO solver. Experiments demonstrate that a wide set of unsymmetric linear systems can be solved and high performance is consistently achieved for large sparse unsymmetric matrices from real world applications.

Solving unsymmetric sparse systems of linear equations with PARDISO

Supernode partitioning for unsymmetric matrices together with complete block diagonal supernode pivoting and asynchronous computation can achieve high gigaflop rates for parallel sparse LU factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to extend these concepts further and unsymmetric prepermutation of rows is used to place large matrix entries on the diagonal. Complete block diagonal supernode pivoting allows dynamical interchanges of columns and rows during the factorization process. The level-3 BLAS efficiency is retained and an advanced two-level left–right looking scheduling scheme results in good speedup on SMP machines. These algorithms have been integrated into the recent unsymmetric version of the PARDISO solver. Experiments demonstrate that a wide set of unsymmetric linear systems can be solved and high performance is consistently achieved for large sparse unsymmetric matrices from real world applications.

Performance evaluation of the hitachi SR8000 using SPEC OMP2001 benchmarks

This paper reports the performance of a single node of the Hitachi SR8000 when using SPEC OMP2001 benchmarks. Each processing node of the SR8000 is a shared-memory parallel computer composed of eight scalar processors with pseudo-vector processing feature. We have run the all of the SPEC OMP2001 benchmarks on the SR8000. According to the results of this performance measurement, we found that the SR8000 has good scalability continuing up to 8 processors except for a few benchmark programs. The performance results demonstrate that the SR8000 achieves high performance especially for memory-intensive applications.

Quantitative Performance Analysis of the SPEC OMPM2001 Benchmarks

The state of modern computer systems has evolved to allow easy access to multiprocessor systems by supporting multiple processors on a single physical package. As the multiprocessor hardware evolves, new ways of programming it are also developed. Some inventions may merely be adopting and standardizing the older paradigms. One such evolving standard for programming shared-memory parallel computers is the OpenMP API. The Standard Performance Evaluation Corporation (SPEC) has created a suite of parallel programs called SPEC OMP to compare and evaluate modern shared-memory multiprocessor systems using the OpenMP standard. We have studied these benchmarks in detail to understand their performance on a modern architecture. In this paper, we present detailed measurements of the benchmarks. We organize, summarize, and display our measurements using a Quantitative Model. We present a detailed discussion and derivation of the model. Also, we discuss the important loops in the SPEC OMPM2001 benchmarks and the reasons for less than ideal speedup on our platform.

View consistencies and exact implementations

Numerous shared memory consistency models have appeared for the purpose of obtaining better shared memory parallel computers, ones which suffer less from long memory latency. This paper uses the primitive notion of program-order and value-order to define global view. Using this as a seed, various consistency models evolve and form hierarchies of models. The creation of these models comes naturally via one of the following means: (i) a global view is augmented with additional ordering among its operations whenever some orderings exist, or (ii) a global view should not contain certain orderings. The former involves augmentation rules, and the latter involves ordering requirements. These models may attract different implementations and a notion of exact implementation is developed. The usefulness of these models is also analyzed and exemplified.

Introduction to programming shared-memory and distributed-memory parallel computers

Introduction to programming shared-memory and distributed-memory parallel computers

Automatic data and computation decomposition on distributed memory parallel computers

To exploit parallelism on shared memory parallel computers (SMPCs), it is natural to focus on decomposing the computation (mainly by distributing the iterations of the nested Do-Loops). In contrast, on distributed memory parallel computers (DMPCs), the decomposition of computation and the distribution of data must both be handled---in order to balance the computation load and to minimize the migration of data. We propose and validate experimentally a method for handling computations and data synergistically to minimize the overall execution time on DMPCs. The method is based on a number of novel techniques, also presented in this article. The core idea is to rank the "importance" of data arrays in a program and specify some of the dominant. The intuition is that the dominant arrays are the ones whose migration would be the most expensive. Using the correspondence between iteration space mapping vectors and distributed dimensions of the dominant data array in each nested Do-loop, allows us to design algorithms for determining data and computation decompositions at the same time. Based on data distribution, computation decomposition for each nested Do-loop is determined based on either the "owner computes" rule or the "owner stores" rule with respect to the dominant data array. If all temporal dependence relations across iteration partitions are regular, we use tiling to allow pipelining and the overlapping of computation and communication. However, in order to use tiling on DMPCs, we needed to extend the existing techniques for determining tiling vectors and tile sizes, as they were originally suited for SMPCs only. The overall method is illustrated on programs for the 2D heat equation, for the Gaussian elimination with pivoting, and for the 2D fast Fourier transform on a linear processor array and on a 2D processor grid.

Parallel R-Point Explicit Block Method for Solving Second Order Ordinary Differential Equations Directly

A new parallel R-point explicit block method for solving second order ordinary differential equations (ODEs) directly is developed. The method computes the numerical solution of the equations at three points simultaneously. Each problem was tested on the shared memory parallel computer Sequent S27 using both the sequential and parallel implementations of the new method and the conventional 1-point method. Numerical results are presented comparing the two methods in terms of the number of steps taken, accuracy and execution times. The results indicate the advantages of using the parallel implementation of the new method for solving second order ODEs directly particularly when the step size becomes finer.

Load balanced parallel QR decomposition on shared memory multiprocessors

This paper introduces a new parallel QR decomposition algorithm with two key advantages over previous techniques. It is specifically designed to achieve high parallel efficiency on shared memory parallel computers with a modest number of processors, and the novel load balancing method described here considers total computational work as opposed to just balancing Givens rotations. This results in expected efficiencies which approach optimal as problem size grows relative to number of processors. The hybrid nature of the algorithm seeks to maximize computation between communication and synchronization. Implementation results on shared memory multiprocessors track expected performance well up to 12 processors, and initial performance results on a distributed shared memory machine are presented.

A hybrid approach for the modelling and simulation of a virtually shared memory parallel computer architecture

Modelling and simulation have been assigned crucial roles in the design, development, analysis and evaluation of computer architectures. The design of parallel architectures in particular is a complex and difficult endeavour that makes modelling and simulation essential tools. In this case, high simulation performance is a prerequisite since, large workloads need to be simulated for a realistic analysis of the parallel system. This paper presents the approach that has been followed for the modelling and simulation of PiSMA, a virtual shared memory parallel architecture, scaleable up to 100 s of processors.

A parallel Navier–Stokes solver for the rotating flow problem

AbstractIn this paper, we investigate the parallel solution of rotating internal flow problems, using the Navier–Stokes equations as proposed by Speziale and Thangam (in 1983) and Speziale (in 1985). A Runge–Kutta time‐stepping scheme was applied to the equations and both sequential and message‐passing implementations were developed, the latter using MPI, and were tested on a four‐processor SGI Origin200 distributed, global shared memory parallel computer and on a 32‐processor IBM 9076 SP/2 distributed memory parallel computer. The results show that our approach to parallelize the sequential implementation requires little effort whilst providing good results even for medium‐sized problems. Copyright © 2001 John Wiley & Sons, Ltd.

The Semi-Automatic Parallelisation of Scientific Application Codes Using a Computer Aided Parallelisation Toolkit

The shared-memory programming model can be an effective way to achieve parallelism on shared memory parallel computers. Historically however, the lack of a programming standard using directives and the limited scalability have affected its take-up. Recent advances in hardware and software technologies have resulted in improvements to both the performance of parallel programs with compiler directives and the issue of portability with the introduction of OpenMP. In this study, the Computer Aided Parallelisation Toolkit has been extended to automatically generate OpenMP-based parallel programs with nominal user assistance. We categorize the different loop types and show how efficient directives can be placed using the toolkit's in-depth interprocedural analysis. Examples are taken from the NAS parallel benchmarks and a number of real-world application codes. This demonstrates the great potential of using the toolkit to quickly parallelise serial programs as well as the good performance achievable on up to 300 processors for hybrid message passing-directive parallelisations.

Computation of Internal and External Compressible Flows Using EDICT

Results are presented for finite element computations involving high speed, viscous compressible internal and external flows. The stabilized finite-element formulations for the Navier-Stokes equations in the conservation law form are solved using the conservation variables. To improve the accuracy of the base method, especially in the regions of flow that are associated with shocks, boundary-layers and their interactions, the Enhanced-Discretization Interface-Capturing Technique (EDICT) is utilized. An error indicator is employed to identify the regions in the computational domain that need enhanced discretization for increased accuracy. The method is implemented on a shared-memory parallel computer and is used to study complex flows, that involve shock-wave/boundary-layer interactions, in supersonic diffusers and wind-tunnels. The start-up problem in supersonic wind-tunnels, caused by a narrow second throat in the diffuser section, is simulated. This computation brings out some of the very interesting features of the unsteady dynamics of the start-up shock.

Taming complexity in high-performance computing

Today’s high-performance computing environments, and the applications that must exploit them, have become much more complex than ever. We now build ensembles of large, shared-memory parallel computers, linked together with high-speed networks, in an attempt to achieve previously unheard-of speeds and still retain a ‘general-purpose’ capability for running diverse applications. Demands for greater precision and realism in today’s computer simulations of physical phenomena tax the imagination of the most aggressive system designers. Enhancing the accuracy of tomorrow’s simulations requires simultaneously accounting for more physical, chemical and biological components. Predictive simulation is essential for making informed, science-based decisions on questions of national importance, including stockpile stewardship, global climate change, wild-fires, earthquakes and epidemics. These applications are too massive and inter-related to be built, verified, tuned and maintained by conventional methods. Software teams in the Advanced Computing Laboratory (ACL) at Los Alamos National Laboratory, along with collaborators world-wide, are building an integrated software infrastructure for scientific simulation development. This paper describes the ACL projects now underway in object-oriented frameworks, scalable run-time software, scientific visualization, software component architecture, and high-end and experimental computer systems. We include achieved results and the status of projects.

A two colorable fourth-order compact difference scheme and parallel iterative solution of the 3D convection diffusion equation

A new fourth-order compact difference scheme for the three-dimensional (3D) convection diffusion equation with variable coefficients is presented. The novelty of this new difference scheme is that it only requires 15 grid points and that it can be decoupled with two colors. The entire computational grid can be updated in two parallel subsweeps with a Gauss–Seidel type iterative method. This is compared with the known 19-point fourth-order compact difference scheme which requires four colors to decouple the computational grid. Numerical results, with multigrid methods implemented on a shared memory parallel computer, are presented to compare the 15- and 19-point fourth-order compact schemes.

A new-generation parallel computer and its performance evaluation

An innovative design is proposed for an MIMD distributed shared-memory (DSM) parallel computer capable of achieving gracious performance with technology expected to become feasible/viable in less than a decade. This New Millennium Computing Point Design was chosen by NSF, DARPA, and NASA as having the potential to deliver 100 TeraFLOPS and 1 PetaFLOPS performance by the year 2005 and 2007, respectively. Its scalability guarantees a lifetime extending well into the next century. Our design takes advantage of free-space optical technologies, with simple guided-wave concepts, to produce a 1D building block (BB) that implements efficiently a large, fully connected system of processors. Designing fully connected, large systems of electronic processors could be a very beneficial impact of optics on massively parallel processing. A 2D structure is proposed for the complete system, where the aforementioned 1D BB is extended into two dimensions. This architecture behaves like a 2D generalized hypercube, which is characterized by outstanding performance and extremely high wiring complexity that prohibits its electronics-only implementation. With readily available technology, a mesh of clear plastic/glass bars in our design facilitate point-to-point bit-parallel transmissions that utilize wavelength-division multiplexing (WDM) and follow dedicated optical paths. Each processor is mounted on a card. Each card contains eight processors interconnected locally via an electronic crossbar. Taking advantage of higher-speed optical technologies, all eight processors share the same communications interface to the optical medium using time-division multiplexing (TDM). A case study for 100 TeraFLOPS performance by the year 2005 is investigated in detail; the characteristics of chosen hardware components in the case study conform to SIA (Semiconductor Industry Association) projections. An impressive property of our system is that its bisection bandwidth matches, within an order of magnitude, the performance of its computation engine. Performance results based on the implementation of various important algorithmic kernels show that our design could have a tremendous, positive impact on massively parallel computing. 2D and 3D implementations of our design could achieve gracious (i.e., sustained) PetaFLOPS performance before the end of the next decade.