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Testing New Programming Paradigms with NAS Parallel Benchmarks

Over the past decade, high performance computing has evolved rapidly, not only in hardware architectures but also with increasing complexity of real applications. Technologies have been developing to aim at scaling up to thousands of processors on both distributed and shared memory systems. Development of parallel programs on these computers is always a challenging task. Today, writing parallel programs with message passing (e.g. MPI) is the most popular way of achieving scalability and high performance. However, writing message passing programs is difficult and error prone. Recent years new effort has been made in defining new parallel programming paradigms. The best examples are: HPF (based on data parallelism) and OpenMP (based on shared memory parallelism). Both provide simple and clear extensions to sequential programs, thus greatly simplify the tedious tasks encountered in writing message passing programs. HPF is independent of memory hierarchy, however, due to the immaturity of compiler technology its performance is still questionable. Although use of parallel compiler directives is not new, OpenMP offers a portable solution in the shared-memory domain. Another important development involves the tremendous progress in the internet and its associated technology. Although still in its infancy, Java promisses portability in a heterogeneous environment and offers possibility to "compile once and run anywhere." In light of testing these new technologies, we implemented new parallel versions of the NAS Parallel Benchmarks (NPBs) with HPF and OpenMP directives, and extended the work with Java and Java-threads. The purpose of this study is to examine the effectiveness of alternative programming paradigms. NPBs consist of five kernels and three simulated applications that mimic the computation and data movement of large scale computational fluid dynamics (CFD) applications. We started with the serial version included in NPB2.3. Optimization of memory and cache usage was applied to several benchmarks, noticeably BT and SP, resulting in better sequential performance. In order to overcome the lack of an HPF performance model and guide the development of the HPF codes, we employed an empirical performance model for several primitives found in the benchmarks. We encountered a few limitations of HPF, such as lack of supporting the "REDISTRIBUTION" directive and no easy way to handle irregular computation. The parallelization with OpenMP directives was done at the outer-most loop level to achieve the largest granularity. The performance of six HPF and OpenMP benchmarks is compared with their MPI counterparts for the Class-A problem size in the figure in next page. These results were obtained on an SGI Origin2000 (195MHz) with MIPSpro-f77 compiler 7.2.1 for OpenMP and MPI codes and PGI pghpf-2.4.3 compiler with MPI interface for HPF programs.

Jin, H.↗

Charon Toolkit for Parallel, Implicit Structured-Grid Computations: Functional Design

In a previous report the design concepts of Charon were presented. Charon is a toolkit that aids engineers in developing scientific programs for structured-grid applications to be run on MIMD parallel computers. It constitutes an augmentation of the general-purpose MPI-based message-passing layer, and provides the user with a hierarchy of tools for rapid prototyping and validation of parallel programs, and subsequent piecemeal performance tuning. Here we describe the implementation of the domain decomposition tools used for creating data distributions across sets of processors. We also present the hierarchy of parallelization tools that allows smooth translation of legacy code (or a serial design) into a parallel program. Along with the actual tool descriptions, we will present the considerations that led to the particular design choices. Many of these are motivated by the requirement that Charon must be useful within the traditional computational environments of Fortran 77 and C. Only the Fortran 77 syntax will be presented in this report.

VanderWijngaart, Rob F.↗

Parallel Grid Manipulations in Earth Science Calculations

The National Aeronautics and Space Administration (NASA) Data Assimilation Office (DAO) at the Goddard Space Flight Center is moving its data assimilation system to massively parallel computing platforms. This parallel implementation of GEOS DAS will be used in the DAO's normal activities, which include reanalysis of data, and operational support for flight missions. Key components of GEOS DAS, including the gridpoint-based general circulation model and a data analysis system, are currently being parallelized. The parallelization of GEOS DAS is also one of the HPCC Grand Challenge Projects. The GEOS-DAS software employs several distinct grids. Some examples are: an observation grid- an unstructured grid of points at which observed or measured physical quantities from instruments or satellites are associated- a highly-structured latitude-longitude grid of points spanning the earth at given latitude-longitude coordinates at which prognostic quantities are determined, and a computational lat-lon grid in which the pole has been moved to a different location to avoid computational instabilities. Each of these grids has a different structure and number of constituent points. In spite of that, there are numerous interactions between the grids, e.g., values on one grid must be interpolated to another, or, in other cases, grids need to be redistributed on the underlying parallel platform. The DAO has designed a parallel integrated library for grid manipulations (PILGRIM) to support the needed grid interactions with maximum efficiency. It offers a flexible interface to generate new grids, define transformations between grids and apply them. Basic communication is currently MPI, however the interfaces defined here could conceivably be implemented with other message-passing libraries, e.g., Cray SHMEM, or with shared-memory constructs. The library is written in Fortran 90. First performance results indicate that even difficult problems, such as above-mentioned pole rotation- a sparse interpolation with little data locality between the physical lat-lon grid and a pole rotated computational grid- can be solved efficiently and at the GFlop/s rates needed to solve tomorrow's high resolution earth science models. In the subsequent presentation we will discuss the design and implementation of PILGRIM as well as a number of the problems it is required to solve. Some conclusions will be drawn about the potential performance of the overall earth science models on the supercomputer platforms foreseen for these problems.

Sawyer, W.↗

Implementing Multidisciplinary and Multi-Zonal Applications Using MPI

Multidisciplinary and multi-zonal applications are an important class of applications in the area of Computational Aerosciences. In these codes, two or more distinct parallel programs or copies of a single program are utilized to model a single problem. To support such applications, it is common to use a programming model where a program is divided into several single program multiple data stream (SPMD) applications, each of which solves the equations for a single physical discipline or grid zone. These SPMD applications are then bound together to form a single multidisciplinary or multi-zonal program in which the constituent parts communicate via point-to-point message passing routines. Unfortunately, simple message passing models, like Intel's NX library, only allow point-to-point and global communication within a single system-defined partition. This makes implementation of these applications quite difficult, if not impossible. In this report it is shown that the new Message Passing Interface (MPI) standard is a viable portable library for implementing the message passing portion of multidisciplinary applications. Further, with the extension of a portable loader, fully portable multidisciplinary application programs can be developed. Finally, the performance of MPI is compared to that of some native message passing libraries. This comparison shows that MPI can be implemented to deliver performance commensurate with native message libraries.

Fineberg, Samuel A.↗

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↗

A Comparison of Three Programming Models for Adaptive Applications

We study the performance and programming effort for two major classes of adaptive applications under three leading parallel programming models. We find that all three models can achieve scalable performance on the state-of-the-art multiprocessor machines. The basic parallel algorithms needed for different programming models to deliver their best performance are similar, but the implementations differ greatly, far beyond the fact of using explicit messages versus implicit loads/stores. Compared with MPI and SHMEM, CC-SAS (cache-coherent shared address space) provides substantial ease of programming at the conceptual and program orchestration level, which often leads to the performance gain. However it may also suffer from the poor spatial locality of physically distributed shared data on large number of processors. Our CC-SAS implementation of the PARMETIS partitioner itself runs faster than in the other two programming models, and generates more balanced result for our application.

Shan, Hong-Zhang↗

Development of Message Passing Routines for High Performance Parallel Computations

Computational Fluid Dynamics (CFD) calculations require a great deal of computing power for completing the detailed computations involved. In an effort shorten the time it takes to complete such calculations they are implemented on a parallel computer. In the case of a parallel computer some sort of message passing structure must be used to communicate between the computers because, unlike a single machine, each computer in a parallel computing cluster does not have access to all the data or run all the parts of the total program. Thus, message passing is used to divide up the data and send instructions to each machine. The nature of my work this summer involves programming the "message passing" aspect of the parallel computer. I am working on modifying an existing program, which was written with OpenMP, and does not use a multi-machine parallel computing structure, to work with Message Passing Interface (MPI) routines. The actual code is being written in the FORTRAN 90 programming language. My goal is to write a parameterized message passing structure that could be used for a variety of individual applications and implement it on Silicon Graphics Incorporated s (SGI) IRIX operating system. With this new parameterized structure engineers would be able to speed up computations for a wide variety of purposes without having to use larger and more expensive computing equipment from another division or another NASA center.

Summers, Edward K.↗

Framework for Extensible, Asynchronous Task Scheduling (FEATS) in Fortran

Most parallel scientific programs contain compiler directives (pragmas) such as those from OpenMP, explicit calls to runtime library procedures such as those implementing the Message Passing Interface (MPI), or compiler-specific language extensions such as those provided by CUDA. By contrast, the recent Fortran standards empower developers to express parallel algorithms without directly referencing lower-level parallel programming models. Fortran’s parallel features place the language within the Partitioned Global Address Space (PGAS) class of programming models. When writing programs that exploit data-parallelism, application developers often find it straightforward to develop custom parallel algorithms. Problems involving complex, heterogeneous, staged calculations, however, pose much greater challenges. Such applications require careful coordination of tasks in a manner that respects dependencies prescribed by a directed acyclic graph. When rolling one’s own solution proves difficult, extending a customizable framework becomes attractive. The paper presents the design, implementation, and use of the Framework for Extensible Asynchronous Task Scheduling (FEATS), which we believe to be the first task-scheduling tool written in modern Fortran. We describe the benefits and compromises associated with choosing Fortran as the implementation language, and we propose ways in which future Fortran standards can best support the use case in this paper.

Modern Fortran↗

MPIRUN: A Portable Loader for Multidisciplinary and Multi-Zonal Applications

Multidisciplinary and multi-zonal applications are an important class of applications in the area of Computational Aerosciences. In these codes, two or more distinct parallel programs or copies of a single program are utilized to model a single problem. To support such applications, it is common to use a programming model where a program is divided into several single program multiple data stream (SPMD) applications, each of which solves the equations for a single physical discipline or grid zone. These SPMD applications are then bound together to form a single multidisciplinary or multi-zonal program in which the constituent parts communicate via point-to-point message passing routines. One method for implementing the message passing portion of these codes is with the new Message Passing Interface (MPI) standard. Unfortunately, this standard only specifies the message passing portion of an application, but does not specify any portable mechanisms for loading an application. MPIRUN was developed to provide a portable means for loading MPI programs, and was specifically targeted at multidisciplinary and multi-zonal applications. Programs using MPIRUN for loading and MPI for message passing are then portable between all machines supported by MPIRUN. MPIRUN is currently implemented for the Intel iPSC/860, TMC CM5, IBM SP-1 and SP-2, Intel Paragon, and workstation clusters. Further, MPIRUN is designed to be simple enough to port easily to any system supporting MPI.

Fineberg, Samuel A.↗

NavP: Structured and Multithreaded Distributed Parallel Programming

We present Navigational Programming (NavP) -- a distributed parallel programming methodology based on the principles of migrating computations and multithreading. The four major steps of NavP are: (1) Distribute the data using the data communication pattern in a given algorithm; (2) Insert navigational commands for the computation to migrate and follow large-sized distributed data; (3) Cut the sequential migrating thread and construct a mobile pipeline; and (4) Loop back for refinement. NavP is significantly different from the current prevailing Message Passing (MP) approach. The advantages of NavP include: (1) NavP is structured distributed programming and it does not change the code structure of an original algorithm. This is in sharp contrast to MP as MP implementations in general do not resemble the original sequential code; (2) NavP implementations are always competitive with the best MPI implementations in terms of performance. Approaches such as DSM or HPF have failed to deliver satisfying performance as of today in contrast, even if they are relatively easy to use compared to MP; (3) NavP provides incremental parallelization, which is beyond the reach of MP; and (4) NavP is a unifying approach that allows us to exploit both fine- (multithreading on shared memory) and coarse- (pipelined tasks on distributed memory) grained parallelism. This is in contrast to the currently popular hybrid use of MP+OpenMP, which is known to be complex to use. We present experimental results that demonstrate the effectiveness of NavP.

navigational programming (NavP)↗

Development of a Grid-Independent Geos-Chem Chemical Transport Model (v9-02) as an Atmospheric Chemistry Module for Earth System Models

The GEOS-Chem global chemical transport model (CTM), used by a large atmospheric chemistry research community, has been re-engineered to also serve as an atmospheric chemistry module for Earth system models (ESMs). This was done using an Earth System Modeling Framework (ESMF) interface that operates independently of the GEOSChem scientific code, permitting the exact same GEOSChem code to be used as an ESM module or as a standalone CTM. In this manner, the continual stream of updates contributed by the CTM user community is automatically passed on to the ESM module, which remains state of science and referenced to the latest version of the standard GEOS-Chem CTM. A major step in this re-engineering was to make GEOS-Chem grid independent, i.e., capable of using any geophysical grid specified at run time. GEOS-Chem data sockets were also created for communication between modules and with external ESM code. The grid-independent, ESMF-compatible GEOS-Chem is now the standard version of the GEOS-Chem CTM. It has been implemented as an atmospheric chemistry module into the NASA GEOS- 5 ESM. The coupled GEOS-5-GEOS-Chem system was tested for scalability and performance with a tropospheric oxidant-aerosol simulation (120 coupled species, 66 transported tracers) using 48-240 cores and message-passing interface (MPI) distributed-memory parallelization. Numerical experiments demonstrate that the GEOS-Chem chemistry module scales efficiently for the number of cores tested, with no degradation as the number of cores increases. Although inclusion of atmospheric chemistry in ESMs is computationally expensive, the excellent scalability of the chemistry module means that the relative cost goes down with increasing number of cores in a massively parallel environment.

CTM↗

Simulated convective systems using a cloud resolving model: Impact of large-scale temperature and moisture forcing using observations and GEOS-3 reanalysis

The GCE (Goddard Cumulus Ensemble) model, which has been developed and improved at NASA Goddard Space Flight Center over the past two decades, is considered as one of the finer and state-of-the-art CRMs (Cloud Resolving Models) in the research community. As the chosen CRM for a NASA Interdisciplinary Science (IDS) Project, GCE has recently been successfully upgraded into an MPI (Message Passing Interface) version with which great improvement has been achieved in computational efficiency, scalability, and portability. By basically using the large-scale temperature and moisture advective forcing, as well as the temperature, water vapor and wind fields obtained from TRMM (Tropical Rainfall Measuring Mission) field experiments such as SCSMEX (South China Sea Monsoon Experiment) and KWAJEX (Kwajalein Experiment), our recent 2-D and 3-D GCE simulations were able to capture detailed convective systems typical of the targeted (simulated) regions. The GEOS-3 [Goddard EOS (Earth Observing System) Version-3] reanalysis data have also been proposed and successfully implemented for usage in the proposed/performed GCE long-term simulations (i.e., aiming at producing massive simulated cloud data -- Cloud Library) in compensating the scarcity of real field experimental data in both time and space (location). Preliminary 2-D or 3-D pilot results using GEOS-3 data have generally showed good qualitative agreement (yet some quantitative difference) with the respective numerical results using the SCSMEX observations. The first objective of this paper is to ensure the GEOS-3 data quality by comparing the model results obtained from several pairs of simulations using the real observations and GEOS-3 reanalysis data. The different large-scale advective forcing obtained from these two kinds of resources (i.e., sounding observations and GEOS-3 reanalysis) has been considered as a major critical factor in producing various model results. The second objective of this paper is therefore to investigate and present such an impact of large-scale forcing on various modeled quantities (such as hydrometeors, rainfall, and etc.). A third objective is to validate the overall GCE 3-D model performance by comparing the numerical results with sounding observations, as well as available satellite retrievals.

Shie, C.-L.↗

LEGION: Lightweight Expandable Group of Independently Operating Nodes

LEGION is a lightweight C-language software library that enables distributed asynchronous data processing with a loosely coupled set of compute nodes. Loosely coupled means that a node can offer itself in service to a larger task at any time and can withdraw itself from service at any time, provided it is not actively engaged in an assignment. The main program, i.e., the one attempting to solve the larger task, does not need to know up front which nodes will be available, how many nodes will be available, or at what times the nodes will be available, which is normally the case in a "volunteer computing" framework. The LEGION software accomplishes its goals by providing message-based, inter-process communication similar to MPI (message passing interface), but without the tight coupling requirements. The software is lightweight and easy to install as it is written in standard C with no exotic library dependencies. LEGION has been demonstrated in a challenging planetary science application in which a machine learning system is used in closed-loop fashion to efficiently explore the input parameter space of a complex numerical simulation. The machine learning system decides which jobs to run through the simulator; then, through LEGION calls, the system farms those jobs out to a collection of compute nodes, retrieves the job results as they become available, and updates a predictive model of how the simulator maps inputs to outputs. The machine learning system decides which new set of jobs would be most informative to run given the results so far; this basic loop is repeated until sufficient insight into the physical system modeled by the simulator is obtained.

Burl, Michael C.↗

Implementation of a Message Passing Interface into a Cloud-Resolving Model for Massively Parallel Computing

The capability for massively parallel programming (MPP) using a message passing interface (MPI) has been implemented into a three-dimensional version of the Goddard Cumulus Ensemble (GCE) model. The design for the MPP with MPI uses the concept of maintaining similar code structure between the whole domain as well as the portions after decomposition. Hence the model follows the same integration for single and multiple tasks (CPUs). Also, it provides for minimal changes to the original code, so it is easily modified and/or managed by the model developers and users who have little knowledge of MPP. The entire model domain could be sliced into one- or two-dimensional decomposition with a halo regime, which is overlaid on partial domains. The halo regime requires that no data be fetched across tasks during the computational stage, but it must be updated before the next computational stage through data exchange via MPI. For reproducible purposes, transposing data among tasks is required for spectral transform (Fast Fourier Transform, FFT), which is used in the anelastic version of the model for solving the pressure equation. The performance of the MPI-implemented codes (i.e., the compressible and anelastic versions) was tested on three different computing platforms. The major results are: 1) both versions have speedups of about 99% up to 256 tasks but not for 512 tasks; 2) the anelastic version has better speedup and efficiency because it requires more computations than that of the compressible version; 3) equal or approximately-equal numbers of slices between the x- and y- directions provide the fastest integration due to fewer data exchanges; and 4) one-dimensional slices in the x-direction result in the slowest integration due to the need for more memory relocation for computation.

Juang, Hann-Ming Henry↗

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.↗

Supercomputing Aspects for Simulating Incompressible Flow

The primary objective of this research is to support the design of liquid rocket systems for the Advanced Space Transportation System. Since the space launch systems in the near future are likely to rely on liquid rocket engines, increasing the efficiency and reliability of the engine components is an important task. One of the major problems in the liquid rocket engine is to understand fluid dynamics of fuel and oxidizer flows from the fuel tank to plume. Understanding the flow through the entire turbo-pump geometry through numerical simulation will be of significant value toward design. One of the milestones of this effort is to develop, apply and demonstrate the capability and accuracy of 3D CFD methods as efficient design analysis tools on high performance computer platforms. The development of the Message Passage Interface (MPI) and Multi Level Parallel (MLP) versions of the INS3D code is currently underway. The serial version of INS3D code is a multidimensional incompressible Navier-Stokes solver based on overset grid technology, INS3D-MPI is based on the explicit massage-passing interface across processors and is primarily suited for distributed memory systems. INS3D-MLP is based on multi-level parallel method and is suitable for distributed-shared memory systems. For the entire turbo-pump simulations, moving boundary capability and efficient time-accurate integration methods are built in the flow solver, To handle the geometric complexity and moving boundary problems, an overset grid scheme is incorporated with the solver so that new connectivity data will be obtained at each time step. The Chimera overlapped grid scheme allows subdomains move relative to each other, and provides a great flexibility when the boundary movement creates large displacements. Two numerical procedures, one based on artificial compressibility method and the other pressure projection method, are outlined for obtaining time-accurate solutions of the incompressible Navier-Stokes equations. The performance of the two methods is compared by obtaining unsteady solutions for the evolution of twin vortices behind a flat plate. Calculated results are compared with experimental and other numerical results. For an unsteady flow, which requires small physical time step, the pressure projection method was found to be computationally efficient since it does not require any subiteration procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy the incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in present computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive.

Kwak, Dochan↗

Use Computer-Aided Tools to Parallelize Large CFD Applications

Porting applications to high performance parallel computers is always a challenging task. It is time consuming and costly. With rapid progressing in hardware architectures and increasing complexity of real applications in recent years, the problem becomes even more sever. Today, scalability and high performance are mostly involving handwritten parallel programs using message-passing libraries (e.g. MPI). However, this process is very difficult and often error-prone. The recent reemergence of shared memory parallel (SMP) architectures, such as the cache coherent Non-Uniform Memory Access (ccNUMA) architecture used in the SGI Origin 2000, show good prospects for scaling beyond hundreds of processors. Programming on an SMP is simplified by working in a globally accessible address space. The user can supply compiler directives, such as OpenMP, to parallelize the code. As an industry standard for portable implementation of parallel programs for SMPs, OpenMP is a set of compiler directives and callable runtime library routines that extend Fortran, C and C++ to express shared memory parallelism. It promises an incremental path for parallel conversion of existing software, as well as scalability and performance for a complete rewrite or an entirely new development. Perhaps the main disadvantage of programming with directives is that inserted directives may not necessarily enhance performance. In the worst cases, it can create erroneous results. While vendors have provided tools to perform error-checking and profiling, automation in directive insertion is very limited and often failed on large programs, primarily due to the lack of a thorough enough data dependence analysis. To overcome the deficiency, we have developed a toolkit, CAPO, to automatically insert OpenMP directives in Fortran programs and apply certain degrees of optimization. CAPO is aimed at taking advantage of detailed inter-procedural dependence analysis provided by CAPTools, developed by the University of Greenwich, to reduce potential errors made by users. Earlier tests on NAS Benchmarks and ARC3D have demonstrated good success of this tool. In this study, we have applied CAPO to parallelize three large applications in the area of computational fluid dynamics (CFD): OVERFLOW, TLNS3D and INS3D. These codes are widely used for solving Navier-Stokes equations with complicated boundary conditions and turbulence model in multiple zones. Each one comprises of from 50K to 1,00k lines of FORTRAN77. As an example, CAPO took 77 hours to complete the data dependence analysis of OVERFLOW on a workstation (SGI, 175MHz, R10K processor). A fair amount of effort was spent on correcting false dependencies due to lack of necessary knowledge during the analysis. Even so, CAPO provides an easy way for user to interact with the parallelization process. The OpenMP version was generated within a day after the analysis was completed. Due to sequential algorithms involved, code sections in TLNS3D and INS3D need to be restructured by hand to produce more efficient parallel codes. An included figure shows preliminary test results of the generated OVERFLOW with several test cases in single zone. The MPI data points for the small test case were taken from a handcoded MPI version. As we can see, CAPO's version has achieved 18 fold speed up on 32 nodes of the SGI O2K. For the small test case, it outperformed the MPI version. These results are very encouraging, but further work is needed. For example, although CAPO attempts to place directives on the outer- most parallel loops in an interprocedural framework, it does not insert directives based on the best manual strategy. In particular, it lacks the support of parallelization at the multi-zone level. Future work will emphasize on the development of methodology to work in a multi-zone level and with a hybrid approach. Development of tools to perform more complicated code transformation is also needed.

Jin, H.↗