Cray YMP Research Articles

The computational accelerator physics conference series: From its origins to the present day

The first conference in what would become the International Computational Accelerator Physics (ICAP) series was held in 1988. At that time the most powerful computer in the world was a Cray YMP with 8 processors and a peak performance of 2 gigaflops. Today the fastest computer in the world has more than 2 million cores and a theoretical peak performance of nearly 200 petaflops. Compared to 1988, performance has increased by a factor of 100 million, accompanied by huge advances in memory, networking, big data management and analytics. By the time of the next ICAP in 2021 we will be at the dawn of the Exascale era. In this talk I will describe the advances in Computational Accelerator Physics that brought us to this point and describe trends in regard to large-scale accelerator simulation in the future.

Dynamics of very rich open clusters

The oldest open clusters in our Galaxy set the lower limit to the age of the Galactic Disk (9–10 Gyr). Although they appear to be very rich now, it is clear that their primordial populations were much larger. Often considered as transitional objects, these populous open clusters show structural differences with respect to globular clusters so their dynamics and characteristic evolutionary time scales can also be different. On the other hand, their large membership lead to different dynamical evolution as compared with average open clusters. In this paper, the differential features of the evolution of rich open clusters are studied using N-body simulations, including several of the largest (104 stars) published direct collisional N-body calculations so far, which were performed on a CRAY YMP. The disruption rate of rich open clusters is analysed in detail and the effect of the initial spatial distribution of the stars in the cluster on its dynamics is studied. The results show that cluster life-time depends on this initial distribution, decreasing when it is more concentrated. The effect of stellar evolution on the dynamical evolution of rich clusters is an important subject that also has been considered here. We demonstrate that the cluster's life-expectancy against evaporation increases because of mass loss by evolving high-mass stars.

Fast eigensolver for dense real-symmetric matrices

A new eigensolver for dense real-symmetric matrices resulting from upgrading and combining previous programs is tested for matrices of orders 100 to 2000 on Cray YMP, Pentium, Mips R1×000 and Dec Alpha 21×64 single processors. Comparisons of execution times with the latest versions (November 1999) of LAPACK routines are quite favorable, by a factor of two in most cases, while requiring only one half as much memory and no special installation.

Performance of Scientific Computing Platforms with MCNP4B

Several computing platforms were evaluated with the MCNP4B Monte Carlo radiation transport code. The DEC AlphaStation 500/500 was the fastest to run MCNP4B. Compared to the HP 9000-735, the fastest platform 4 yr ago, the AlphaStation is 335% faster, the HP C180 is 133% faster, the SGI Origin 2000 is 82% faster, the Sun UltraSparc-1 200E is 54% faster, the Micron Millennia Pro personal computer is 10% faster, the Cray T94/4128 is 1% faster, the IBM RS/6000-590 is 93% as fast, the DEC 3000/600 is 81% as fast, the Sun Sparc20 is 57% as fast, the Cray YMP 8/8128 is 57% as fast, the Sun Sparc5 is 33% as fast, and the Sun Sparc2 is 13% as fast. All results presented are reproducible and allow for comparison to computer platforms not included in this study. Timing studies are seen to be very problem dependent. The performance gains resulting from advances in software were also investigated. Various compilers and operating systems were seen to have a modest impact on performance, whereas hardware improvements have resulted in a factor of 4 improvement. MCNP4B also ran approximately as fast as MCNP4A.

Robust Parallel Algorithms for Solution of Riccati Equation

Robust and efficient parallel-vector algorithms are presented for the solution of the Riccati equations encountered in optimal control problems on shared-memory multiprocessor machines. The algorithms have been implemented on a Cray YMP 8/8128 and applied to three large problems resulting from a continuous bridge structure, a 21-story space truss structure, and a 12-story space moment-resisting building structure. Efficiency of the algorithms is presented in terms of millions of floating point operations per second (MFLOPS) and the speedup. The MFLOPS for the largest example resulting from the 12-story space frame structure is a high 206.0. The speedup due to parallel processing only (for the same example) using seven processors, is 6.33. When vectorization is combined with parallel processing a very significant speedup of 54.4 is obtained using seven processors. The algorithms developed in this research find applications in the complex integrated control/structural optimization problem. Further, the writers are currently using them to develop large adaptive/smart structures.

Direct collisional simulation of 10 000 particles past core collapse

A collisional $N$-body simulation using NBODY5 on a single CRAY YMP processor is followed well into the post-collapse regime. This is presently one of the largest particle numbers of all such models published, but some data for an even larger $N$ produced by using special-purpose computers have recently been presented. In contrast to previous ensemble-averaged $N$-body simulations the noise here is low enough to just compare this one single run with the expectations from statistical models based on the Fokker-Planck approximation. Agreement is as good as could be expected for the case of the evolution of the Lagrangian radii, radial and tangential velocity dispersions and various core quantities. We briefly discuss approximate models to understand number and energy of escapers and the question of gravothermal core oscillations; although the system exhibits post-collapse oscillations they turn out to be directly binary driven and we cannot prove the existence of a gravothermal expansion at this particle number. Finally in a detailed examination of the wandering of the density centre we find in contrast to some previous studies a clear long-time period of the order of about 14 half-mass crossing times.

Parallel Eigenvalue Algorithms for Large-Scale Control-Optimization Problems

In a recent article, the authors presented the formulation and outline of parallel algorithms for the integrated structural/control optimization problem. The solutions of the Riccati equation, open-loop system of equations, and closed loop system of equations encountered in this problem require repeated solution of the complex eigenvalue problem of a general unsymmetric matrix. This is the bottleneck for simultaneous optimization of structural and control systems and its application to design of large adaptive/smart structures. In this paper, robust parallel-vector algorithms are presented for the solution of the eigenvalue problem of a general unsymmetric real matrix employing the architecture of shared memory supercomputers such as Cray YMP 8/8128. Judicious combination of vectorization, microtasking, and macrotasking is explored in order to achieve maximum efficiency. The algorithms are applied to large matrices including one resulting from a 21-story space truss structure. It is shown that the speedup due to both vectorization and parallel processing increases with the size of the problem, thus making the algorithms particularly attractive for integrated structural/control optimization of large adaptive structures.

Dependency-based algorithms for vector processing of sparse matrix forward/backward substitutions [power system stability analysis

Recent efforts to improve the execution speed of steady-state and transient analysis of power systems are focused on exploiting parallel and vector processing. In this paper, two algorithms for forward/backward substitutions and their implementation on vector computers are considered. A dependency-based substitution algorithm (DBSA) is proposed and compared with the well known W-matrix method. According to DBSA, the nonzero entries of the factor matrices are rearranged in groups of elements (slices) leading to independent operations. In the implementation of the W-matrix method, the nonzero elements of the inverse factors are grouped in sets (pseudocolumns) to overcome the problem of dependency between addition operations. Test cases, performed on a CRAY X-MP2/216 and a CRAY Y-MP8/464 vector computer, are taken from real-life power system problems and consist in the solution of linear systems with up to 12000 equations. The maximum speed-ups achieved (with respect to a code based on standard sparsity programming) are near to 7 for complex arithmetic and to 11 for real arithmetic.

Weather forecasting on parallel architectures

Global forecasting at the National Meteorological Center is performed using a spherical harmonics spectral model. The model is used in global data assimilation, and in the aviation and medium range forecast production suites. In this presentation, the major numerical and physical aspects of the model are highlighted, and parallelization considerations are analyzed and applied to three parallel computer architectures. The first parallelization is on a parallel vector processor shared memory platform such as Cray YMP or C90. The other two are on distributed memory platforms: a data parallel implementation on Connection Machines and a single program multiple data (SPMD) adaptation to a Cray T3D machine.

Dynamic levelwise scheduling for sparse matrix factorization on vector computers

In this paper the problem of the efficient implementation of sparse matrix factorization on vector computers is considered. A fine-grain dynamic levelwise scheduling algorithm (DLSA) is proposed. DLSA takes into account the dependences between update operations, thus avoiding the recurrence problem. A simplified version of the algorithm (S-DLSA) can be employed to produce a suboptimal scheduling of the factorization operations. DLSA and S-DLSA are also applicable to all sparse matrix operations resulting in the modification of one-dimensional arrays. The scheduling procedures and the resulting vectorization-oriented numerical factorization have been implemented on a CRAY X-MP2/216 and a CRAY Y-MP8/464 computer. Test cases refer to real-life power systems with up to 12 000 buses. The maximum speed-ups achieved (with respect to a code based on standard sparsity programming) are close to 7 for complex matrices and 13 for real matrices.

Round-Up

The Numerical Algorithms Group Ltd (NAG) has increased the range of hardware platforms supporting the IRIS Explorer 2.1 scientific visualization and application builder software. The company has completed new ports to Hewlett-Packard HP9000/700, IBM RS/6000 and Sun Solaris workstations. In addition to Silicon Graphics workstations, IRIS Explorer is also now implemented on both the Sun operating system and Cray YMP range of computers. A DEC Alpha OSF/1 and 64-bit SGI port are scheduled for the next release of IRIS Explorer.

Supercomputer algorithms for efficient linear octree encoding of three-dimensional brain images

We designed and implemented algorithms for three-dimensional (3-D) reconstruction of brain images from serial sections using two important supercomputer architectures, vector and parallel. These architectures were represented by the Cray YMP and Connection Machine CM-2, respectively. The programs operated on linear octree representations of the brain data sets, and achieved 500–800 times acceleration when compared with a conventional laboratory workstation. As the need for higher resolution data sets increases, supercomputer algorithms may offer a means of performing 3-D reconstruction well above current experimental limits.

Parallel-Vector Algorithms for Analysis of Large Structures

In analysis of large space structures, the major computational steps are evaluation and assembly of the structure stiffness matrix and solution of the resulting simultaneous linear equations. In this paper we present efficient parallel-vector algorithms for these steps of structural analysis. The goal is to optimize the performance of the algorithms through judicious combination of parallel processing and vectorization. Parallel-vector algorithms are presented for solution of linear simultaneous equations using Cholesky decomposition and preconditioned conjugate gradient approaches. The algorithms are applied to three large space structures modeling the exterior envelope of high-rise and super high-rise building structures in the range of 50–162 stories with up to 6,136 members. Performance results are presented in terms of central-processing-unit time on a Cray Y-MP8/864 supercomputer, MFLOPS (millions of floating point operations per second), and speedup.

Collisions of microdrops of water

In this paper, collisions of microdrops of water were studied. Experimental studies of microdrops become very difficult as the drop dimensions become extremely small, particularly when the drops are so small that they contain only a few thousand molecules. To overcome these physical limitations, we produced a model for the H 2O molecule using molecular and atomic interaction forces. We then placed these molecules together to produce drops. Hence, using this new technique, we could study drops with no lower size limitations. To study the motions of these drops, large systems of second order nonlinear ordinary differential equations had to be solved numerically. The system of equations were solved using a CRAY Y-MP8/864 computer. To observe the motion of the drops, output data was transferred to a SGI IRIS 4D-70/GT graphics computer which drew three-dimensional pictures of the data.

Design optimization of large structural systems with substructuring in a parallel computational environment

Design optimization of large structural systems can be attempted through a substructure strategy when difficulties are encountered with convergence of such problems. In this strategy the large structure is divided into several smaller substructures, and a subproblem is defined for each substructure. Solution of the large problem can be obtained iteratively through repeated solutions of the modest subproblems. Substructure strategies, in sequential as well as in parallel computational modes on a CRAY YMP multiprocessor computer, have been incorporated into the code CometBoards, which is an acronym for Comparative Evaluation Test Bed of Optimization and Analysis Routines for Design of Structures. Three issues, intensive computation, convergence of the iterative process, and analytically superior optimum, encountered during the implementation of substructure optimization into CometBoards have been solved. Coupling between subproblems as well as local and global constraints grouping are essential for convergence of the iterative process. The substructure strategy can produce an analytically superior optimum different from what can be obtained by regular optimization. For the problems solved, substructure optimization in a parallel computational mode made effective use of all assigned processors.

Parallel Algorithms for Integrated Structural/Control Optimization

Optimization of combined structural and control systems is a complex problem requiring an inordinate amount of computer-processing time, especially the solution of the eigenvalue problem of a general unsymmetric square real matrix with complex eigenvalues and eigenvectors, which is frequently used in such problem. The few algorithms presented in the literature thus far have been applied to small structures with a few members and controllers only. Parallel processing on new-generation multiprocessor computers provides an opportunity to solve large-scale problems. In this paper, the integrated structural and control optimization problem is formulated by including constraints on displacements, stresses, and closed-loop eigenvalues and the corresponding damping factors. Then, parallel algorithms are presented for integrated optimization of structures on shared-memory multiprocessors such as the CRAY YMP 8/864 supercomputer. In particular, parallel algorithms are presented for the solution of complex eigenvalue problems encountered in structural control problems using the method of matrix iteration for dominant eigenvalue(s). The solution is divided into two parts. The first part is the iteration for dominant eigenvalue(s) and the corresponding eigenvector(s) and the second part is the reduction of the matrix to obtain the smaller eigenvalue(s) and the corresponding eigenvector(s).

Processor preallocation and load balancing of DOALL loops

Load balance is important because it may affect the speedup attained through the concurrent execution of loop iterations on a parallel processor. We study loop load balance in the context of the well-known Perfect benchmarks. Several static and dynamic characteristics of the Perfect benchmark DOALL loops are observed and interpreted. Thelate arrival of processors is noted as a major source of load imbalance. This observation suggested the idea ofprocessor preallocation. An analytic cost model is presented and the advantages of processor preallocation are demonstrated by experimental evaluation on a CRAY Y-MP8 under the Unicos operating system.

Relaxation-Newton methods for transient stability analysis on a vector/parallel computer

In this paper, the implementation of transient stability analysis programs on a vector/parallel computer is considered. The windowing technique is adopted. The parallelism-in-time is exploited by using the Gauss-Jacobi or the Gauss-Seidel methods to relax the dependency between time steps within a time window; the Newton method is employed to solve the discretized equations corresponding to each time step exploiting the parallelism-in-space. The computation of the bus voltage and state variables pertaining to different time steps is carried out in parallel by the processors available. A reordering of the operations relative to the synchronous machine equations is introduced to obtain an efficient use of the vector hardware of the computer. The W-matrix method is employed to solve the network equations. Test case simulations are performed for the IEEE 118 bus system and two US networks with 662 and 904 buses using a 4-processor CRAY Y-MP8/464 computer. The proposed vector/parallel programs achieve substantial speed-ups over a scalar reference program based on the Very Dishonest Newton method. The synergy between vector and parallel processing allows speed-ups in excess of 22 to be attained for the US 904 bus network; run times are always shorter than the simulation interval. Best results are obtained by implementing the proposed travelling window approach. Thanks to a suitable task partitioning, the apparently sequential Gauss-Seidel approach is demonstrated to be an effective alternative to the Gauss-Jacobi relaxation scheme. >

Comparison of Scientific Computing Platforms for MCNP4A Monte Carlo Calculations

The performance of seven computer platforms is evaluated with the widely used and internationally available MCNP4A Monte Carlo radiation transport code. All results are reproducible and are presented in such a way as to enable comparison with computer platforms not in the study. The authors observed that the HP/9000-735 workstation runs MCNP 50% faster than the Cray YMP 8/64. Compared with the Cray YMP 8/64, the IBM RS/6000-560 is 68% as fast, the Sun Sparc10 is 66% as fast, the Silicon Graphics ONYX is 90% as fast, the Gateway 2000 model 4DX2-66V personal computer is 27% as fast, and the Sun Sparc2 is 24% as fast. In addition to comparing the timing performance of the seven platforms, the authors observe that changes in compilers and software over the past 2 yr have resulted in only modest performance improvements, hardware improvements have enhanced performance by less than a factor of [approximately]3, timing studies are very problem dependent, MCNP4Q runs about as fast as MCNP4.

Density functional methods as computational tools in materials design

This article gives a brief overview of density functional theory and discusses two specific implementations: a numerical localized basis approach (DMol) and the pseudopotential plane-wave method. Characteristic examples include Cu, clusters, CO and NO dissociation on copper surfaces, Li-, K-, and O-endohedral fullerenes, tris-quaternary ammonium cations as zeolite template, and oxygen defects in bulk SiO2. The calculations reveal the energetically favorable structures (estimated to be within ± 0.02 A of experiment), the energetics of geometric changes, and the electronic structures underlying the bonding mechanisms. A characteristic DMo1 calculation on a 128-node nCUBE 2 parallel computer shows a speedup of about 107 over a single processor. A plane-wave calculation on a unit cell with 64 silicon atoms using 1024 nCUBE 2 processors runs about five times faster than on a single-processor CRAY YMP.