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High-Performance Computing Optimization for Aladyn – Adaptive Neural Network Molecular Dynamics Mini-Application

This report provides a description and performance evaluation of the optimization techniques for high performance computing (HPC) implementation of the open source Computational Materials mini-application Aladyn (https://github.com/nasa/aladyn). Aladyn is a basic molecular dynamics code written in FORTRAN 2003, which is designed to demonstrate the use of adaptive neural networks (ANNs) in atomistic simulations. The role of ANNs is to efficiently reproduce the very complex energy landscape resulting from the atomic interactions in materials with the accuracy of the more expensive quantum mechanics-based calculations. The ANN is trained on a large set of atomic structures calculated using the density functional theory (DFT) method. While achieving orders of magnitude faster computational performance than DFT, the ANN-based approach was still very computationally demanding compared to the conventional approach of using empirically fitted energy functions. After its initial development, Aladyn was evaluated and optimized by experts at the NASA Advanced Supercomputing (NAS) division to exploit modern supercomputer architectures. The code has been optimized for execution on multicore central processing units (CPUs), including Intel® Skylake microarchitecture, and on graphic accelerators, such as Nvidia® V100 graphic processing units (GPUs), using Open Multi-Processing (OpenMP) and Open Accelerators (OpenACC) programming interfaces. The optimization achieved a speedup of 4.7 times the baseline version on CPU performance and an additional 2.4 times on CPU+GPU performance. Atomistic computer simulations are a fundamental tool in materials research to model material properties form physics-based first principles. Atomic interaction, governed by Quantum Mechanics (QM) require sophisticated and highly computationally demanding mathematical models to calculate [1]. Classical methods use approximate functional forms, empirically fitted through a set of variable parameters to emulate atomic energies as direct functions of atomic coordinates [2]. While empirical potentials are computationally much simpler, allowing simulations of large-scale systems of up to a trillion (1012) atoms [3], they are substantially less accurate compared to quantum calculations and applicable only to very specific atomic configurations or predefined crystallographic phases. A recently suggested approach is to use heuristic machine learning methods [4], such as those based on Adaptive Neural Networks (ANNs) to predict atomic energies, after being trained on a sufficiently large database of QM-calculated structures [5,6]. This approach reduces significantly the computational complexity, allowing for simulations of orders of magnitude larger systems compared to QM-based methods without compromising accuracy. Still, compared to classical methods using empirical energy functions, ANN methods remain two- to three orders of magnitude more computationally demanding. Hence, the computational cost of simulations, together with the need for extensive training of ANNs, still makes the practical implementation of ANN-based methods quite challenging. The purpose of the Aladyn mini-application software [7], available as open source at https://github.com/nasa/aladyn, is to be a testbed for exploring possible optimization strategies to develop highly scalable parallel algorithms for ANN-based atomistic simulations. Aladyn is aimed at utilizing the architecture of the high-end modern highperformance computing (HPC) hardware based on multicore central processing units (CPUs) equipped with graphic processing unit (GPU) accelerators. Specifically, the goal is to optimize the performance on a single HPC compute node, before implementing scaling to multi-node parallelization using message passing interface (MPI). At the same time, the open source code of Aladyn can serve as a training model for students and professors in academia.

Yamakov, Vesselin I.↗

Parallel Simulation of Unsteady Turbulent Flames

Time-accurate simulation of turbulent flames in high Reynolds number flows is a challenging task since both fluid dynamics and combustion must be modeled accurately. To numerically simulate this phenomenon, very large computer resources (both time and memory) are required. Although current vector supercomputers are capable of providing adequate resources for simulations of this nature, the high cost and their limited availability, makes practical use of such machines less than satisfactory. At the same time, the explicit time integration algorithms used in unsteady flow simulations often possess a very high degree of parallelism, making them very amenable to efficient implementation on large-scale parallel computers. Under these circumstances, distributed memory parallel computers offer an excellent near-term solution for greatly increased computational speed and memory, at a cost that may render the unsteady simulations of the type discussed above more feasible and affordable.This paper discusses the study of unsteady turbulent flames using a simulation algorithm that is capable of retaining high parallel efficiency on distributed memory parallel architectures. Numerical studies are carried out using large-eddy simulation (LES). In LES, the scales larger than the grid are computed using a time- and space-accurate scheme, while the unresolved small scales are modeled using eddy viscosity based subgrid models. This is acceptable for the moment/energy closure since the small scales primarily provide a dissipative mechanism for the energy transferred from the large scales. However, for combustion to occur, the species must first undergo mixing at the small scales and then come into molecular contact. Therefore, global models cannot be used. Recently, a new model for turbulent combustion was developed, in which the combustion is modeled, within the subgrid (small-scales) using a methodology that simulates the mixing and the molecular transport and the chemical kinetics within each LES grid cell. Finite-rate kinetics can be included without any closure and this approach actually provides a means to predict the turbulent rates and the turbulent flame speed. The subgrid combustion model requires resolution of the local time scales associated with small-scale mixing, molecular diffusion and chemical kinetics and, therefore, within each grid cell, a significant amount of computations must be carried out before the large-scale (LES resolved) effects are incorporated. Therefore, this approach is uniquely suited for parallel processing and has been implemented on various systems such as: Intel Paragon, IBM SP-2, Cray T3D and SGI Power Challenge (PC) using the system independent Message Passing Interface (MPI) compiler. In this paper, timing data on these machines is reported along with some characteristic results.

Menon, Suresh↗

Aerodynamic Shape Optimization of Supersonic Aircraft Configurations via an Adjoint Formulation on Parallel Computers

This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations. In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that this basic methodology could be ported to distributed memory parallel computing architectures. In this paper, our concern will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.

Reuther, James↗

A Loader for Executing Multi-Binary Applications on the Thinking Machines CM-5: It's Not Just for SPMD Anymore

The Thinking Machines CM-5 platform was designed to run single program, multiple data (SPMD) applications, i.e., to run a single binary across all nodes of a partition, with each node possibly operating on different data. Certain classes of applications, such as multi-disciplinary computational fluid dynamics codes, are facilitated by the ability to have subsets of the partition nodes running different binaries. In order to extend the CM-5 system software to permit such applications, a multi-program loader was developed. This system is based on the dld loader which was originally developed for workstations. This paper provides a high level description of dld, and describes how it was ported to the CM-5 to provide support for multi-binary applications. Finally, it elaborates how the loader has been used to implement the CM-5 version of MPIRUN, a portable facility for running multi-disciplinary/multi-zonal MPI (Message-Passing Interface Standard) codes.

Becker, Jeffrey C.↗

Aerodynamic Shape Optimization of Supersonic Aircraft Configurations via an Adjoint Formulation on Parallel Computers

This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods (13, 12, 44, 38). The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method (19, 20, 21, 23, 39, 25, 40, 41, 42, 43, 9) was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations (39, 25). In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that the basic methodology could be ported to distributed memory parallel computing architectures [241. In this paper, our concem will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.

Reuther, James↗

Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers

An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat complete configuration designs subject to multiple design points and geometric constraints. Examples are presented for both transonic and supersonic configurations ranging from wing alone designs to complex configuration designs involving wing, fuselage, nacelles and pylons.

Reuther, James↗

CFD Analysis and Design Optimization Using Parallel Computers

A versatile and efficient multi-block method is presented for the simulation of both steady and unsteady flow, as well as aerodynamic design optimization of complete aircraft configurations. The compressible Euler and Reynolds Averaged Navier-Stokes (RANS) equations are discretized using a high resolution scheme on body-fitted structured meshes. An efficient multigrid implicit scheme is implemented for time-accurate flow calculations. Optimum aerodynamic shape design is achieved at very low cost using an adjoint formulation. The method is implemented on parallel computing systems using the MPI message passing interface standard to ensure portability. The results demonstrate that, by combining highly efficient algorithms with parallel computing, it is possible to perform detailed steady and unsteady analysis as well as automatic design for complex configurations using the present generation of parallel computers.

Martinelli, Luigi↗

An Efficient Multiblock Method for Aerodynamic Analysis and Design on Distributed Memory Systems

The work presented in this paper describes the application of a multiblock gridding strategy to the solution of aerodynamic design optimization problems involving complex configurations. The design process is parallelized using the MPI (Message Passing Interface) Standard such that it can be efficiently run on a variety of distributed memory systems ranging from traditional parallel computers to networks of workstations. Substantial improvements to the parallel performance of the baseline method are presented, with particular attention to their impact on the scalability of the program as a function of the mesh size. Drag minimization calculations at a fixed coefficient of lift are presented for a business jet configuration that includes the wing, body, pylon, aft-mounted nacelle, and vertical and horizontal tails. An aerodynamic design optimization is performed with both the Euler and Reynolds Averaged Navier-Stokes (RANS) equations governing the flow solution and the results are compared. These sample calculations establish the feasibility of efficient aerodynamic optimization of complete aircraft configurations using the RANS equations as the flow model. There still exists, however, the need for detailed studies of the importance of a true viscous adjoint method which holds the promise of tackling the minimization of not only the wave and induced components of drag, but also the viscous drag.

Reuther, James↗

Parallel PAB3D: Experiences with a Prototype in MPI

PAB3D is a three-dimensional Navier Stokes solver that has gained acceptance in the research and industrial communities. It takes as computational domain, a set disjoint blocks covering the physical domain. This is the first report on the implementation of PAB3D using the Message Passing Interface (MPI), a standard for parallel processing. We discuss briefly the characteristics of tile code and define a prototype for testing. The principal data structure used for communication is derived from preprocessing "patching". We describe a simple interface (COMMSYS) for MPI communication, and some general techniques likely to be encountered when working on problems of this nature. Last, we identify levels of improvement from the current version and outline future work.

Guerinoni, Fabio↗

I/O Parallelization for the Goddard Earth Observing System Data Assimilation System (GEOS DAS)

The National Aeronautics and Space Administration (NASA) Data Assimilation Office (DAO) at the Goddard Space Flight Center (GSFC) has developed the GEOS DAS, a data assimilation system that provides production support for NASA missions and will support NASA's Earth Observing System (EOS) in the coming years. The GEOS DAS will be used to provide background fields of meteorological quantities to EOS satellite instrument teams for use in their data algorithms as well as providing assimilated data sets for climate studies on decadal time scales. The DAO has been involved in prototyping parallel implementations of the GEOS DAS for a number of years and is now embarking on an effort to convert the production version from shared-memory parallelism to distributed-memory parallelism using the portable Message-Passing Interface (MPI). The GEOS DAS consists of two main components, an atmospheric General Circulation Model (GCM) and a Physical-space Statistical Analysis System (PSAS). The GCM operates on data that are stored on a regular grid while PSAS works with observational data that are scattered irregularly throughout the atmosphere. As a result, the two components have different data decompositions. The GCM is decomposed horizontally as a checkerboard with all vertical levels of each box existing on the same processing element(PE). The dynamical core of the GCM can also operate on a rotated grid, which requires communication-intensive grid transformations during GCM integration. PSAS groups observations on PEs in a more irregular and dynamic fashion.

Lucchesi, Rob↗

I/O Parallelization for the Goddard Earth Observing System Data Assimilation System (GEOS DAS)

The National Aeronautics and Space Administration (NASA) Data Assimilation Office (DAO) at the Goddard Space Flight Center (GSFC) has developed the GEOS DAS, a data assimilation system that provides production support for NASA missions and will support NASA's Earth Observing System (EOS) in the coming years. The DAO's support of the EOS project along with the requirement of producing long-term reanalysis datasets with an unvarying system levy a large I/O burden on the future system. The DAO has been involved in prototyping parallel implementations of the GEOS DAS for a number of years and is now converting the production version from shared-memory parallelism to distributed-memory parallelism using the portable Message-Passing Interface (MPI). If the MPI-based GEOS DAS is to meet these production requirements, we must make I/O from the parallel system efficient. We have designed a scheme that allows efficient I/O processing while retaining portability, reducing the need for post-processing, and producing data formats that are required by our users, both internal and external. The first phase of the GEOS DAS Parallel I/O System (GPIOS) will expand upon the common method of gathering global data to a Single PE for output. Instead of using a PE also tasked with primary computation, a number of PEs will be dedicated to I/O and its related tasks. This allows the data transformations and formatting required prior to output to take place asynchronously with respect to the GEOS DAS assimilation cycle, improving performance and generating output data sets in a format convenient for our users. I/O PEs can be added as needed to handle larger data volumes or to meet user file specifications. We will show I/O performance results from a prototype MPI GCM integrated with GPIOS. Phase two of GPIOS development will examine ways of integrating new software technologies to further improve performance and build scalability into the system. The maturing of MPI-IO implementations and other supporting libraries such as parallel HDF should provide performance gains while retaining portability.

Lucchesi, R.↗

Simulations of the Unsteady Flow through the Fastrac Supersonic Turbine

Analysis of the unsteady aerodynamic environment in the Fastrac supersonic turbine is presented. Modal analysis of the turbine blades indicated possible resonance in crucial operating ranges of the turbopump. Unsteady computational fluid dynamics (CFD) analysis was conducted to support the aerodynamic and structural dynamic assessments of the turbine. Before beginning the analysis, two major problems with current unsteady analytical capabilities had to be addressed: modeling a straight centerline nozzle with the turbine blades and exit guide vanes (EGVs), and reducing run times significantly while maintaining physical accuracy. Modifications were made to the CFD code used in this study to allow the coupled nozzle/blade/EGV analysis and to incorporate Message Passing Interface (MPI) software. Because unsteadiness is a key issue for the Fastrac turbine [and future rocket engine turbines such as for the Reusable Launch Vehicle (RI.V)], calculations were performed for two nozzle-to-blade axial gaps. Calculations were also performed for the nozzle alone, and the results were imposed as an inlet boundary condition for a blade/EGV calculation for the large gap case. These results are compared to the nozzle/blade/EGV results.

Griffin, Lisa W.↗

Computation of an Underexpanded 3-D Rectangular Jet by the CE/SE Method

Recently, an unstructured three-dimensional space-time conservation element and solution element (CE/SE) Euler solver was developed. Now it is also developed for parallel computation using METIS for domain decomposition and MPI (message passing interface). The method is employed here to numerically study the near-field of a typical 3-D rectangular under-expanded jet. For the computed case-a jet with Mach number Mj = 1.6. with a very modest grid of 1.7 million tetrahedrons, the flow features such as the shock-cell structures and the axis switching, are in good qualitative agreement with experimental results.

Loh, Ching Y.↗

Simulation of Transonic Limit Cycle Oscillations Using a CFD Time-marching Method

CFD-based aeroelastic computations are performed to investigate the effect of nonlinear aerodynamics on transonic LCO (Limit Cycle Oscillations) characteristics of a two-dimensional supercritical wing with the NLR 7301section. It is found that the presentation of the viscous effects, including turbulence modeling, plays an important role on the accurate prediction of shock and LCO; and a small initial perturbation appears to produce large amplitude LCO at small mean pitch angle and plunge while a large amplitude initial perturbation produces small (or negligible) amplitude LCO at larger mean values. Also addressed in the paper is the issues related to multiblock MPI (Message Passing Interface) parallel computation.

Tang, L.↗

Efficient Tracing for On-the-Fly Space-Time Displays in a Debugger for Message Passing Programs

In this work we describe the implementation of a practical mechanism for collecting and displaying trace information in a debugger for message passing programs. We introduce a trace format that is highly compressible while still providing information adequate for debugging purposes. We make the mechanism convenient for users to access by incorporating the trace collection in a set of wrappers for the MPI (message passing interface) communication library. We implement several debugger operations that use the trace display: consistent stoplines, undo, and rollback. They all are implemented using controlled replay, which executes at full speed in target processes until the appropriate position in the computation is reached. They provide convenient mechanisms for getting to places in the execution where the full power of a state-based debugger can be brought to bear on isolating communication errors.

Hood, Robert↗

Efficiency Improvements to the Displacement Based Multilevel Structural Optimization Algorithm

Multilevel Structural Optimization (MSO) continues to be an area of research interest in engineering optimization. In the present project, the weight optimization of beams and trusses using Displacement based Multilevel Structural Optimization (DMSO), a member of the MSO set of methodologies, is investigated. In the DMSO approach, the optimization task is subdivided into a single system and multiple subsystems level optimizations. The system level optimization minimizes the load unbalance resulting from the use of displacement functions to approximate the structural displacements. The function coefficients are then the design variables. Alternately, the system level optimization can be solved using the displacements themselves as design variables, as was shown in previous research. Both approaches ensure that the calculated loads match the applied loads. In the subsystems level, the weight of the structure is minimized using the element dimensions as design variables. The approach is expected to be very efficient for large structures, since parallel computing can be utilized in the different levels of the problem. In this paper, the method is applied to a one-dimensional beam and a large three-dimensional truss. The beam was tested to study possible simplifications to the system level optimization. In previous research, polynomials were used to approximate the global nodal displacements. The number of coefficients of the polynomials equally matched the number of degrees of freedom of the problem. Here it was desired to see if it is possible to only match a subset of the degrees of freedom in the system level. This would lead to a simplification of the system level, with a resulting increase in overall efficiency. However, the methods tested for this type of system level simplification did not yield positive results. The large truss was utilized to test further improvements in the efficiency of DMSO. In previous work, parallel processing was applied to the subsystems level, where the derivative verification feature of the optimizer NPSOL had been utilized in the optimizations. This resulted in large runtimes. In this paper, the optimizations were repeated without using the derivative verification, and the results are compared to those from the previous work. Also, the optimizations were run on both, a network of SUN workstations using the MPICH implementation of the Message Passing Interface (MPI) and on the faster Beowulf cluster at ICASE, NASA Langley Research Center, using the LAM implementation of UP]. The results on both systems were consistent and showed that it is not necessary to verify the derivatives and that this gives a large increase in efficiency of the DMSO algorithm.

Plunkett, C. L.↗

Applications Performance Under MPL and MPI on NAS IBM SP2

On July 5, 1994, an IBM Scalable POWER parallel System (IBM SP2) with 64 nodes, was installed at the Numerical Aerodynamic Simulation (NAS) Facility Each node of NAS IBM SP2 is a "wide node" consisting of a RISC 6000/590 workstation module with a clock of 66.5 MHz which can perform four floating point operations per clock with a peak performance of 266 Mflop/s. By the end of 1994, 64 nodes of IBM SP2 will be upgraded to 160 nodes with a peak performance of 42.5 Gflop/s. An overview of the IBM SP2 hardware is presented. The basic understanding of architectural details of RS 6000/590 will help application scientists the porting, optimizing, and tuning of codes from other machines such as the CRAY C90 and the Paragon to the NAS SP2. Optimization techniques such as quad-word loading, effective utilization of two floating point units, and data cache optimization of RS 6000/590 is illustrated, with examples giving performance gains at each optimization step. The conversion of codes using Intel's message passing library NX to codes using native Message Passing Library (MPL) and the Message Passing Interface (NMI) library available on the IBM SP2 is illustrated. In particular, we will present the performance of Fast Fourier Transform (FFT) kernel from NAS Parallel Benchmarks (NPB) under MPL and MPI. We have also optimized some of Fortran BLAS 2 and BLAS 3 routines, e.g., the optimized Fortran DAXPY runs at 175 Mflop/s and optimized Fortran DGEMM runs at 230 Mflop/s per node. The performance of the NPB (Class B) on the IBM SP2 is compared with the CRAY C90, Intel Paragon, TMC CM-5E, and the CRAY T3D.

Saini, Subhash↗

NAS Parallel Benchmark. Results 11-96: Performance Comparison of HPF and MPI Based NAS Parallel Benchmarks

High Performance Fortran (HPF), the high-level language for parallel Fortran programming, is based on Fortran 90. HALF was defined by an informal standards committee known as the High Performance Fortran Forum (HPFF) in 1993, and modeled on TMC's CM Fortran language. Several HPF features have since been incorporated into the draft ANSI/ISO Fortran 95, the next formal revision of the Fortran standard. HPF allows users to write a single parallel program that can execute on a serial machine, a shared-memory parallel machine, or a distributed-memory parallel machine. HPF eliminates the complex, error-prone task of explicitly specifying how, where, and when to pass messages between processors on distributed-memory machines, or when to synchronize processors on shared-memory machines. HPF is designed in a way that allows the programmer to code an application at a high level, and then selectively optimize portions of the code by dropping into message-passing or calling tuned library routines as 'extrinsics'. Compilers supporting High Performance Fortran features first appeared in late 1994 and early 1995 from Applied Parallel Research (APR) Digital Equipment Corporation, and The Portland Group (PGI). IBM introduced an HPF compiler for the IBM RS/6000 SP/2 in April of 1996. Over the past two years, these implementations have shown steady improvement in terms of both features and performance. The performance of various hardware/ programming model (HPF and MPI (message passing interface)) combinations will be compared, based on latest NAS (NASA Advanced Supercomputing) Parallel Benchmark (NPB) results, thus providing a cross-machine and cross-model comparison. Specifically, HPF based NPB results will be compared with MPI based NPB results to provide perspective on performance currently obtainable using HPF versus MPI or versus hand-tuned implementations such as those supplied by the hardware vendors. In addition we would also present NPB (Version 1.0) performance results for the following systems: DEC Alpha Server 8400 5/440, Fujitsu VPP Series (VX, VPP300, and VPP700), HP/Convex Exemplar SPP2000, IBM RS/6000 SP P2SC node (120 MHz) NEC SX-4/32, SGI/CRAY T3E, SGI Origin2000.

Saini, Subash↗