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This is a bibliography on numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are also listed.
This is a bibliography on numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are also listed.
NASA's Office of Space Science and Applications (OSSA) gave a select group of scientists the opportunity to test and implement their computational algorithms on the Massively Parallel Processor (MPP) located at Goddard Space Flight Center, beginning in late 1985. One year later, the Working Group presented its report, which addressed the following: algorithms, programming languages, architecture, programming environments, the way theory relates, and performance measured. The findings point to a number of demonstrated computational techniques for which the MPP architecture is ideally suited. For example, besides executing much faster on the MPP than on conventional computers, systolic VLSI simulation (where distances are short), lattice simulation, neural network simulation, and image problems were found to be easier to program on the MPP's architecture than on a CYBER 205 or even a VAX. The report also makes technical recommendations covering all aspects of MPP use, and recommendations concerning the future of the MPP and machines based on similar architectures, expansion of the Working Group, and study of the role of future parallel processors for space station, EOS, and the Great Observatories era.
A data parallel mesh-vertex upwind finite-volume scheme for solving the Euler equations on triangular unstructured meshes is described. A novel vertex-based partitioning of the problem is introduced which minimizes the computation and communication costs associated with distributing the computation to the processors of a massively parallel computer. Finally, the performance of this unstructured computation on 8K processors of the Connection Machine CM-2 is compared with one processor of a Cray-YMP. The experiments show that 8K processors of the CM-2 achieve approximately 70 percent of the performance of one processor of the Cray-YMP on the unstructured mesh computations described here.
The fast adaptive composite (FAC) grid method is compared with the adaptive composite method (AFAC) under variety of conditions including vectorization and parallelization. Results are given for distributed memory multiprocessor architectures (SUPRENUM, Intel iPSC/2 and iPSC/860). It is shown that the good performance of AFAC and its superiority over FAC in a parallel environment is a property of the algorithm and not dependent on peculiarities of any machine.
Unlike traditional 'serial' processing computers in which one central processing unit performs one instruction at a time, parallel processing computers contain several processing units, thereby, performing several instructions at once. Many of today's fastest supercomputers achieve their speed by employing thousands of processing elements working in parallel. Few institutions can afford these state-of-the-art parallel processors, but many already have the makings of a modest parallel processing system. Workstations on existing high-speed networks can be harnessed as nodes in a parallel processing environment, bringing the benefits of parallel processing to many. While such a system can not rival the industry's latest machines, many common tasks can be accelerated greatly by spreading the processing burden and exploiting idle network resources. We study several aspects of this approach, from algorithms to select nodes to speed gains in specific tasks. With ever-increasing volumes of astronomical data, it becomes all the more necessary to utilize our computing resources fully.
In many flowfield computations, accuracy of the turbulence model employed is frequently a limiting factor in the overall accuracy of the computation. This is particularly true for complex flowfields such as those around full aircraft configurations. Free shear layers such as wakes, impinging jets (in V/STOL applications), and mixing layers over cavities are often part of these flowfields. Although flowfields have been computed for full aircraft, the memory and CPU requirements for these computations are often excessive. Additional computer power is required for multidisciplinary computations such as coupled fluid dynamics and conduction heat transfer analysis. Massively parallel computers show promise in alleviating this situation, and the purpose of this effort was to adapt and optimize CFD codes to these new machines. The objective of this research effort was to compute the flowfield and heat transfer for a two-dimensional jet impinging normally on a cool plate. The results of this research effort were summarized in an AIAA paper titled 'Parallel Implementation of the k-epsilon Turbulence Model'. Appendix A contains the full paper.
The code RITRACKS (Relativistic Ion Tracks) was developed to simulate detailed stochastic radiation track structures of ions of different types and energies. Many new capabilities were added to the code during the recent years. Several options were added to specify the times at which the tracks appear in the irradiated volume, allowing the simulation of dose-rate effects. The code has been used to simulate energy deposition in several targets: spherical, ellipsoidal and cylindrical. More recently, density changes as well as a spherical shell were implemented for spherical targets, in order to simulate energy deposition in walled tissue equivalent proportional counters. RITRACKS is used as a part of the new program BDSTracks (Biological Damage by Stochastic Tracks) to simulate several types of chromosome aberrations in various irradiation conditions. The simulation of damage to various DNA structures (linear and chromatin fiber) by direct and indirect effects has been improved and is ongoing. Many improvements were also made to the graphic user interface (GUI), including the addition of several labels allowing changes of units. A new GUI has been added to display the electron ejection vectors. The parallel calculation capabilities, notably the pre- and post-simulation processing on Windows and Linux machines have been reviewed to make them more portable between different systems. The calculation part is currently maintained in an Atlassian Stash® repository for code tracking and possibly future collaboration.
Research on the Goodyear Massively Parallel Processor (MPP) suggests that high-level parallel languages are practical and can be designed with powerful new semantics that allow algorithms to be efficiently mapped to the real machines. For the MPP these semantics include parallel/associative array selection for both dense and sparse matrices, variable precision arithmetic to trade accuracy for speed, micro-pipelined train broadcast, and conditional branching at the processing element (PE) control unit level. The preliminary design of a FORTRAN-like parallel language for the MPP has been completed and is being used to write programs to perform sparse matrix array selection, min/max search, matrix multiplication, Gaussian elimination on single bit arrays and other generic algorithms. A description is given of the MPP design. Features of the system and its operation are illustrated in the form of charts and diagrams.
This paper presents a methodology for debugging the performance of message-passing programs on both tightly coupled and loosely coupled distributed-memory machines. The AIMS (Automated Instrumentation and Monitoring System) toolkit, a suite of software tools for measurement and analysis of performance, is introduced and its application illustrated using several benchmark programs drawn from the field of computational fluid dynamics. AIMS includes (i) Xinstrument, a powerful source-code instrumentor, which supports both Fortran77 and C as well as a number of different message-passing libraries including Intel's NX Thinking Machines' CMMD, and PVM; (ii) Monitor, a library of timestamping and trace -collection routines that run on supercomputers (such as Intel's iPSC/860, Delta, and Paragon and Thinking Machines' CM5) as well as on networks of workstations (including Convex Cluster and SparcStations connected by a LAN); (iii) Visualization Kernel, a trace-animation facility that supports source-code clickback, simultaneous visualization of computation and communication patterns, as well as analysis of data movements; (iv) Statistics Kernel, an advanced profiling facility, that associates a variety of performance data with various syntactic components of a parallel program; (v) Index Kernel, a diagnostic tool that helps pinpoint performance bottlenecks through the use of abstract indices; (vi) Modeling Kernel, a facility for automated modeling of message-passing programs that supports both simulation -based and analytical approaches to performance prediction and scalability analysis; (vii) Intrusion Compensator, a utility for recovering true performance from observed performance by removing the overheads of monitoring and their effects on the communication pattern of the program; and (viii) Compatibility Tools, that convert AIMS-generated traces into formats used by other performance-visualization tools, such as ParaGraph, Pablo, and certain AVS/Explorer modules.
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.
A simple shallow water equations model used to test numerical weather prediction schemes is presented. The spherical geometry is transformed into a formally doubly periodic configuration which can be implemented on a massively parallel computer at 100% parallelism. A nonstaggered grid with all variables defined at the grid points (circles) is used. The parallel structure was simulated by performing step 1 in a FORTRAN array, on an Amdahl serial machine, changing the signs of the winds on the dark side.
TEKLIB is a library of procedures written in TI PASCAL to perform basic graphic tasks. TEKLIB was written to provide an interface between a graphics terminal and the TI 990. The TI 990 is used as a controller for the Finite Element Machine which is an array of microprocessors designed to solve problems by finite element methods in parallel. The use of TEKLIB provides a means of inputting data graphically and displaying output.
Research in cognitive science suggests that much of cognition involves the rapid manipulation of complex data structures. However, it is very unclear how this could be realized in neural networks or connectionist systems. A core question is: how could the interconnectivity of items in an abstract-level data structure be neurally encoded? The answer appeals mainly to positional relationships between activity patterns within neural arrays, rather than directly to neural connections in the traditional way. The new method was initially devised to account for abstract symbolic data structures, but it also supports cognitively useful spatial analogue, image-like representations. As the neural model is based on massive, uniform, parallel computations over 2D arrays, the massively parallel processor is a convenient tool for simulation work, although there are complications in using the machine to the fullest advantage. An MPP Pascal simulation program for a small pilot version of the model is running.
The overhead of interprocessor communication is a major factor in limiting the performance of parallel computer systems. The complete exchange is the severest communication pattern in that it requires each processor to send a distinct message to every other processor. This pattern is at the heart of many important parallel applications. On hypercubes, multiphase complete exchange has been developed and shown to provide optimal performance over varying message sizes. Most commercial multicomputer systems do not have a hypercube interconnect. However, they use special purpose hardware and dedicated communication processors to achieve very high performance communication and can be made to emulate the hypercube quite well. Multiphase complete exchange has been implemented on three contemporary parallel architectures: the Intel Paragon, IBM SP2 and Meiko CS-2. The essential features of these machines are described and their basic interprocessor communication overheads are discussed. The performance of multiphase complete exchange is evaluated on each machine. It is shown that the theoretical ideas developed for hypercubes are also applicable in practice to these machines and that multiphase complete exchange can lead to major savings in execution time over traditional solutions.
A 3D multistage simulation of each component of the GE90 Turbofan engine has been made. This includes 49 blade rows. A coupled simulation of all blade rows will be made very soon. The simulation is running using two levels of parallelism. The first level is on a blade row basis with information shared using files. The second level is using a grid domain decomposition with information shared using MPI. Timings will be shown for running on the SP2, an SGI Origin and a distributed system of HP workstations. On the HP workstations, the CHIMP version of MPI is used, with queuing supplied by LSF (Load Sharing Facility). A script-based control system is used to ensure reliability. An MPEG movie illustrating the flow simulation of the engine has been created using PV3, a parallel visualization library created by Bob Haimes of MIT. PVM is used to create a virtual machine from 10 HP workstations and display on an SGI workstation. A representative component simulation will be compared to rig data to demonstrate its usefulness in turbomachinery design and analysis.
The overset grid methodology has significantly reduced time-to-solution of high-fidelity computational fluid dynamics (CFD) simulations about complex aerospace configurations. The solution process resolves the geometrical complexity of the problem domain by using separately generated but overlapping structured discretization grids that periodically exchange information through interpolation. However, high performance computations of such large-scale realistic applications must be handled efficiently on state-of-the-art parallel supercomputers. This paper analyzes the effects of various performance enhancement techniques on the parallel efficiency of an overset grid Navier-Stokes CFD application running on an SGI Origin2000 machine. Specifically, the role of asynchronous communication, grid splitting, and grid grouping strategies are presented and discussed. Results indicate that performance depends critically on the level of latency hiding and the quality of load balancing across the processors.
Atmospheric chemistry models are a central tool to study and forecast the impact of air pollution on the environment, vegetation, and human health. However, the numerical simulation of chemical kinetics is computationally expensive due to the stiffness of the system of ordinary differential equations that describes atmospheric chemistry. Here we present an alternative approach to the computation of atmospheric chemistry based on machine learning. Our training data set is produced using the NASA Goddard Earth Observing System (GEOS) model with GEOS-Chem chemistry, run on the NASA Center for Climate Simulation (NCCS) Discover supercomputing cluster on 384 Intel Xeon Haswell cores. This model spends more than 50% of total run time on solving atmospheric chemistry. The data set contains as input features the air pollution concentrations before solving the differential equations, together with some key physical parameters such as temperature and sun intensity. As target variables we define the air pollution concentrations after solving the differential equations. Using Dask-cuDF and Dask-XGBoost on the NVIDIA RAPIDS platform on 8 Tesla V100 GPUs, we generate from this training set gradient boosted decision tree models that can reproduce the simulation of chemical kinetics. We do this on the NCCS Advanced Data Analytics Platform (ADAPT) science cloud environment. Our application takes full advantage of recent advances in Dask-XGBoost, such as multi-node and multi-GPU scaling for distributed training with large data sets. The increase in training data size enabled by this is critical to capture the full range of chemical environments encountered across the globe and all annual seasons.The boosted tree models offer good predictability and show many of the features of the full chemistry reference simulation. Further improvements can be achieved through mass balance considerations and by accounting for error correlations. We incorporate the boosted tree models into the GEOS reference model using XGBoost's C API. This enables a seamless integration of the GPU trained models into GEOS-Chem, which is written in Fortran and optimized for use in a massively parallel CPU environment. We show the benefits of this approach and discuss the potential speedup of this machine learning accelerated atmospheric chemistry model.