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NASA NTRS2017

Parallel Computation of the Jacobian Matrix for Nonlinear Equation Solvers Using MATLAB

Demonstrating speedup for parallel code on a multicore shared memory PC can be challenging in MATLAB due to underlying parallel operations that are often opaque to the user. This can limit potential for improvement of serial code even for the so-called embarrassingly parallel applications. One such application is the computation of the Jacobian matrix inherent to most nonlinear equation solvers. Computation of this matrix represents the primary bottleneck in nonlinear solver speed such that commercial finite element (FE) and multi-body-dynamic (MBD) codes attempt to minimize computations. A timing study using MATLAB's Parallel Computing Toolbox was performed for numerical computation of the Jacobian. Several approaches for implementing parallel code were investigated while only the single program multiple data (spmd) method using composite objects provided positive results. Parallel code speedup is demonstrated but the goal of linear speedup through the addition of processors was not achieved due to PC architecture.

Rose, Geoffrey K.↗

DOE OSTI2021

Improving I/O Performance for Exascale Applications through Online Data Layout Reorganization

The applications being developed within the U.S. Exascale Computing Project (ECP) to run on imminent Exascale computers will generate scientific results with unprecedented fidelity and record turn-around time. Many of these codes are based on particle-mesh methods and use advanced algorithms, especially dynamic load-balancing and mesh-refinement, to achieve high performance on Exascale machines. Yet, as such algorithms improve parallel application efficiency, they raise new challenges for I/O logic due to their irregular and dynamic data distributions. Thus, while the enormous data rates of Exascale simulations already challenge existing file system write strategies, the need for efficient read and processing of generated data introduces additional constraints on the data layout strategies that can be used when writing data to secondary storage. We review these I/O challenges and introduce two online data layout reorganization approaches for achieving good tradeoffs between read and write performance. We demonstrate the benefits of using these two approaches for the ECP particle-in-cell simulation WarpX, which serves as a motif for a large class of important Exascale applications. Here, we show that by understanding application I/O patterns and carefully designing data layouts we can increase read performance by more than 80 percent.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2000

Incremental Parallelization of Non-Data-Parallel Programs Using the Charon Message-Passing Library

Message passing is among the most popular techniques for parallelizing scientific programs on distributed-memory architectures. The reasons for its success are wide availability (MPI), efficiency, and full tuning control provided to the programmer. A major drawback, however, is that incremental parallelization, as offered by compiler directives, is not generally possible, because all data structures have to be changed throughout the program simultaneously. Charon remedies this situation through mappings between distributed and non-distributed data. It allows breaking up the parallelization into small steps, guaranteeing correctness at every stage. Several tools are available to help convert legacy codes into high-performance message-passing programs. They usually target data-parallel applications, whose loops carrying most of the work can be distributed among all processors without much dependency analysis. Others do a full dependency analysis and then convert the code virtually automatically. Even more toolkits are available that aid construction from scratch of message passing programs. None, however, allows piecemeal translation of codes with complex data dependencies (i.e. non-data-parallel programs) into message passing codes. The Charon library (available in both C and Fortran) provides incremental parallelization capabilities by linking legacy code arrays with distributed arrays. During the conversion process, non-distributed and distributed arrays exist side by side, and simple mapping functions allow the programmer to switch between the two in any location in the program. Charon also provides wrapper functions that leave the structure of the legacy code intact, but that allow execution on truly distributed data. Finally, the library provides a rich set of communication functions that support virtually all patterns of remote data demands in realistic structured grid scientific programs, including transposition, nearest-neighbor communication, pipelining, gather/scatter, and redistribution. At the end of the conversion process most intermediate Charon function calls will have been removed, the non-distributed arrays will have been deleted, and virtually the only remaining Charon functions calls are the high-level, highly optimized communications. Distribution of the data is under complete control of the programmer, although a wide range of useful distributions is easily available through predefined functions. A crucial aspect of the library is that it does not allocate space for distributed arrays, but accepts programmer-specified memory. This has two major consequences. First, codes parallelized using Charon do not suffer from encapsulation; user data is always directly accessible. This provides high efficiency, and also retains the possibility of using message passing directly for highly irregular communications. Second, non-distributed arrays can be interpreted as (trivial) distributions in the Charon sense, which allows them to be mapped to truly distributed arrays, and vice versa. This is the mechanism that enables incremental parallelization. In this paper we provide a brief introduction of the library and then focus on the actual steps in the parallelization process, using some representative examples from, among others, the NAS Parallel Benchmarks. We show how a complicated two-dimensional pipeline-the prototypical non-data-parallel algorithm- can be constructed with ease. To demonstrate the flexibility of the library, we give examples of the stepwise, efficient parallel implementation of nonlocal boundary conditions common in aircraft simulations, as well as the construction of the sequence of grids required for multigrid.

VanderWijngaart, Rob F.↗

NASA NTRS2007

Reusable, Extensible High-Level Data-Distribution Concept

A framework for high-level specification of data distributions in data-parallel application programs has been conceived. [As used here, distributions signifies means to express locality (more specifically, locations of specified pieces of data) in a computing system composed of many processor and memory components connected by a network.] Inasmuch as distributions exert a great effect on the performances of application programs, it is important that a distribution strategy be flexible, so that distributions can be adapted to the requirements of those programs. At the same time, for the sake of productivity in programming and execution, it is desirable that users be shielded from such error-prone, tedious details as those of communication and synchronization. As desired, the present framework enables a user to refine a distribution type and adjust it to optimize the performance of an application program and conceals, from the user, the low-level details of communication and synchronization. The framework provides for a reusable, extensible, data-distribution design, denoted the design pattern, that is independent of a concrete implementation. The design pattern abstracts over coding patterns that have been found to be commonly encountered in both manually and automatically generated distributed parallel programs. The following description of the present framework is necessarily oversimplified to fit within the space available for this article. Distributions are among the elements of a conceptual data-distribution machinery, some of the other elements being denoted domains, index sets, and data collections (see figure). Associated with each domain is one index set and one distribution. A distribution class interface (where "class" is used in the object-oriented-programming sense) includes operations that enable specification of the mapping of an index to a unit of locality. Thus, "Map(Index)" specifies a unit, while "LocalLayout(Index)" specifies the local address within that unit. The distribution class can be extended to enable specification of commonly used distributions or novel user-defined distributions. A data collection can be defined over a domain. The term "data collection" in this context signifies, more specifically, an abstraction of mappings from index sets to variables. Since the index set is distributed, the addresses of the variables are also distributed.

James, Mark↗

NASA NTRS1993

Distributed Virtual System (DIVIRS) project

As outlined in the continuation proposal 92-ISI-50R (revised) on NASA cooperative agreement NCC 2-539, the investigators are developing software, including a system manager and a job manager, that will manage available resources and that will enable programmers to develop and execute parallel applications in terms of a virtual configuration of processors, hiding the mapping to physical nodes; developing communications routines that support the abstractions implemented; continuing the development of file and information systems based on the Virtual System Model; and incorporating appropriate security measures to allow the mechanisms developed to be used on an open network. The goal throughout the work is to provide a uniform model that can be applied to both parallel and distributed systems. The authors believe that multiprocessor systems should exist in the context of distributed systems, allowing them to be more easily shared by those that need them. The work provides the mechanisms through which nodes on multiprocessors are allocated to jobs running within the distributed system and the mechanisms through which files needed by those jobs can be located and accessed.

Schorr, Herbert↗

NASA NTRS1993

Distributed Virtual System (DIVIRS) Project

As outlined in our continuation proposal 92-ISI-50R (revised) on contract NCC 2-539, we are (1) developing software, including a system manager and a job manager, that will manage available resources and that will enable programmers to program parallel applications in terms of a virtual configuration of processors, hiding the mapping to physical nodes; (2) developing communications routines that support the abstractions implemented in item one; (3) continuing the development of file and information systems based on the virtual system model; and (4) incorporating appropriate security measures to allow the mechanisms developed in items 1 through 3 to be used on an open network. The goal throughout our work is to provide a uniform model that can be applied to both parallel and distributed systems. We believe that multiprocessor systems should exist in the context of distributed systems, allowing them to be more easily shared by those that need them. Our work provides the mechanisms through which nodes on multiprocessors are allocated to jobs running within the distributed system and the mechanisms through which files needed by those jobs can be located and accessed.

Schorr, Herbert↗

NASA NTRS1994

DIstributed VIRtual System (DIVIRS) project

As outlined in our continuation proposal 92-ISI-. OR (revised) on NASA cooperative agreement NCC2-539, we are (1) developing software, including a system manager and a job manager, that will manage available resources and that will enable programmers to develop and execute parallel applications in terms of a virtual configuration of processors, hiding the mapping to physical nodes; (2) developing communications routines that support the abstractions implemented in item one; (3) continuing the development of file and information systems based on the Virtual System Model; and (4) incorporating appropriate security measures to allow the mechanisms developed in items 1 through 3 to be used on an open network. The goal throughout our work is to provide a uniform model that can be applied to both parallel and distributed systems. We believe that multiprocessor systems should exist in the context of distributed systems, allowing them to be more easily shared by those that need them. Our work provides the mechanisms through which nodes on multiprocessors are allocated to jobs running within the distributed system and the mechanisms through which files needed by those jobs can be located and accessed.

Schorr, Herbert↗

NASA NTRS1995

DIstributed VIRtual System (DIVIRS) project

As outlined in our continuation proposal 92-ISI-50R (revised) on NASA cooperative agreement NCC2-539, we are (1) developing software, including a system manager and a job manager, that will manage available resources and that will enable programmers to develop and execute parallel applications in terms of a virtual configuration of processors, hiding the mapping to physical nodes; (2) developing communications routines that support the abstractions implemented in item one; (3) continuing the development of file and information systems based on the Virtual System Model; and (4) incorporating appropriate security measures to allow the mechanisms developed in items 1 through 3 to be used on an open network. The goal throughout our work is to provide a uniform model that can be applied to both parallel and distributed systems. We believe that multiprocessor systems should exist in the context of distributed systems, allowing them to be more easily shared by those that need them. Our work provides the mechanisms through which nodes on multiprocessors are allocated to jobs running within the distributed system and the mechanisms through which files needed by those jobs can be located and accessed.

Schorr, Herbert↗

DOE OSTI2024

Distributed-Memory Sparse Deep Neural Network Inference Using Global Arrays

Partitioned Global Address Space (PGAS) models exhibit tremendous promise in developing efficient and productive distributed-memory parallel applications. They have been used extensively in scientific computations due to conveniently offering a ``shared-memory''-like model and convenient interfaces that separate communication with synchronization. Traditionally, PGAS communication models have been applied to dense/contiguously distributed data, but most modern applications depict varied levels of sparsity. Existing PGAS models require certain adaptations to support distributed sparse computations, since associated computations often require matrix arithmetic, in addition to data movement. The Global Arrays toolkit from Pacific Northwest National Laboratory (PNNL) is one of the earliest PGAS models to combine one-sided data communication and distributed matrix operations and is still used in the popular NWChem quantum chemistry suite. Recently, we have expanded the Global Arrays toolkit to support common sparse operations, like sparse matrix-dense matrix multiplies (SpMM), sparse matrix-sparse matrix multiplication (SpGEMM) and Sampled Dense-Dense Matrix Multiplication (SDDMM). As it turns out, these operations are the bedrock of sparse Deep Learning (DL); sparse deep neural networks and Graph Neural Networks (GNNs) have gained increasing attention recently in achieving speedups on training and inference with reduced memory footprints. Unlike scientific applications in High Performance Computing (HPC), modern (distributed-memory capable) DL toolkits often rely on non-standardized and closed-source vendor software optimizations, creating challenges in software-hardware co-design at scale. Our goal is to support a variety of distributed-memory sparse matrix operations and helper functions in the newly created Sparse Global Arrays (SGA), such that it is possible to build portable and productive Machine Learning scenarios for algorithm/software and hardware codesign purposes. Contemporary data-parallel schemes for training/inference are undergoing a major overhaul since model replication limits scalability and causes resource inefficiencies. As such, we have adopted tensor parallelism in decomposing the model and inputs, to mitigate memory issues. Current implementation is built on top of MPI and uses CPUs to maximize the portability across the platforms.

Distributed computing, machine learning↗

NASA NTRS1995

NAS Experiences of Porting CM Fortran Codes to HPF on IBM SP2 and SGI Power Challenge

Current Connection Machine (CM) Fortran codes developed for the CM-2 and the CM-5 represent an important class of parallel applications. Several users have employed CM Fortran codes in production mode on the CM-2 and the CM-5 for the last five to six years, constituting a heavy investment in terms of cost and time. With Thinking Machines Corporation's decision to withdraw from the hardware business and with the decommissioning of many CM-2 and CM-5 machines, the best way to protect the substantial investment in CM Fortran codes is to port the codes to High Performance Fortran (HPF) on highly parallel systems. HPF is very similar to CM Fortran and thus represents a natural transition. Conversion issues involved in porting CM Fortran codes on the CM-5 to HPF are presented. In particular, the differences between data distribution directives and the CM Fortran Utility Routines Library, as well as the equivalent functionality in the HPF Library are discussed. Several CM Fortran codes (Cannon algorithm for matrix-matrix multiplication, Linear solver Ax=b, 1-D convolution for 2-D datasets, Laplace's Equation solver, and Direct Simulation Monte Carlo (DSMC) codes have been ported to Subset HPF on the IBM SP2 and the SGI Power Challenge. Speedup ratios versus number of processors for the Linear solver and DSMC code are presented.

Saini, Subhash↗

NASA NTRSDate not supplied

Performance Optimization Methods for a Memory-Bound, Unstructured-Grid CFD Application on Massively Parallel GPU Platforms

Computational performance of the FUN3D unstructured-grid computational fluid dynamics (CFD) application on massively parallel GPU environments is memory-bound and highly dependent upon efficient reads from and atomic updates to the irregular cell-, edge-, and node-based data structures. In this talk, we present recent efforts into optimizing select performance-critical kernels on NVIDIA Tesla V100 and A100 GPUs and AMD CDNA MI100 GPUs. A novel use of L2 cache residency controls and asynchronous loads into on-chip shared memory are explored on the A100 GPU for the sparse iterative solver, which is dominated by mixed-precision, sparse matrix vector multiplication. Demonstrations show that these methods improve global memory bandwidth utilization by 13.5% on the A100 GPU. Several techniques are also presented that use registers and/or shared memory to facilitate array transposition and aggregation which combine to reduce the frequency and increase the cache efficiency of floating-point atomic updates to the irregular data structures. These methods are demonstrated to improve the kernel throughput by nearly 500% on select kernels on the AMD MI100 over atomic updates directly to global memory. Overall, both V100 and A100 GPUs outperformed the MI100 GPU on kernels dominated by double-precision atomic updates; however, the techniques demonstrated here reduced the performance gap and improved the MI100 performance.

GPU CPU unstructured CFD memory↗

NASA NTRS1997

The Automated Instrumentation and Monitoring System (AIMS): Design and Architecture

Whether a researcher is designing the 'next parallel programming paradigm', another 'scalable multiprocessor' or investigating resource allocation algorithms for multiprocessors, a facility that enables parallel program execution to be captured and displayed is invaluable. Careful analysis of such information can help computer and software architects to capture, and therefore, exploit behavioral variations among/within various parallel programs to take advantage of specific hardware characteristics. A software tool-set that facilitates performance evaluation of parallel applications on multiprocessors has been put together at NASA Ames Research Center under the sponsorship of NASA's High Performance Computing and Communications Program over the past five years. The Automated Instrumentation and Monitoring Systematic has three major software components: a source code instrumentor which automatically inserts active event recorders into program source code before compilation; a run-time performance monitoring library which collects performance data; and a visualization tool-set which reconstructs program execution based on the data collected. Besides being used as a prototype for developing new techniques for instrumenting, monitoring and presenting parallel program execution, AIMS is also being incorporated into the run-time environments of various hardware testbeds to evaluate their impact on user productivity. Currently, the execution of FORTRAN and C programs on the Intel Paragon and PALM workstations can be automatically instrumented and monitored. Performance data thus collected can be displayed graphically on various workstations. The process of performance tuning with AIMS will be illustrated using various NAB Parallel Benchmarks. This report includes a description of the internal architecture of AIMS and a listing of the source code.

Yan, Jerry C.↗

NASA NTRS2001

A Simple XML Producer-Consumer Protocol

There are many different projects from government, academia, and industry that provide services for delivering events in distributed environments. The problem with these event services is that they are not general enough to support all uses and they speak different protocols so that they cannot interoperate. We require such interoperability when we, for example, wish to analyze the performance of an application in a distributed environment. Such an analysis might require performance information from the application, computer systems, networks, and scientific instruments. In this work we propose and evaluate a standard XML-based protocol for the transmission of events in distributed systems. One recent trend in government and academic research is the development and deployment of computational grids. Computational grids are large-scale distributed systems that typically consist of high-performance compute, storage, and networking resources. Examples of such computational grids are the DOE Science Grid, the NASA Information Power Grid (IPG), and the NSF Partnerships for Advanced Computing Infrastructure (PACIs). The major effort to deploy these grids is in the area of developing the software services to allow users to execute applications on these large and diverse sets of resources. These services include security, execution of remote applications, managing remote data, access to information about resources and services, and so on. There are several toolkits for providing these services such as Globus, Legion, and Condor. As part of these efforts to develop computational grids, the Global Grid Forum is working to standardize the protocols and APIs used by various grid services. This standardization will allow interoperability between the client and server software of the toolkits that are providing the grid services. The goal of the Performance Working Group of the Grid Forum is to standardize protocols and representations related to the storage and distribution of performance data. These standard protocols and representations must support tasks such as profiling parallel applications, monitoring the status of computers and networks, and monitoring the performance of services provided by a computational grid. This paper describes a proposed protocol and data representation for the exchange of events in a distributed system. The protocol exchanges messages formatted in XML and it can be layered atop any low-level communication protocol such as TCP or UDP Further, we describe Java and C++ implementations of this protocol and discuss their performance. The next section will provide some further background information. Section 3 describes the main communication patterns of our protocol. Section 4 describes how we represent events and related information using XML. Section 5 describes our protocol and Section 6 discusses the performance of two implementations of the protocol. Finally, an appendix provides the XML Schema definition of our protocol and event information.

Smith, Warren↗

NASA NTRS1996

Effective Boundary Treatment for the Biharmonic Dirichlet Problem

The biharmonic equation can be rewritten as a system of two Poisson equations. Multigrid solution of this system is expected to converge with the same amount of work as solving two Poisson equations, requiring less than 70 floating point operations (scalar multiply or addition) per fine grid point to reach a solution using an FMG algorithm. For periodic boundary conditions, this goal is attained by simple, straightforward application of multigrid. For Dirichlet boundary conditions, however, convergence is impeded by poor interaction with the boundaries. Attempts to overcome the slowness without specifically addressing the boundaries have resulted in multigrid algorithms not attaining the Poisson convergence rate. We present three methods of boundary treatment with which full multigrid efficiency can be obtained. All implement an approach described by Brandt, concentrating some additional effort near the boundary. The first approach simply adds a number of relaxation sweeps over points close to the boundary. The second uses joint relaxation on near-boundary points. The third method takes something from each of the first two methods, resulting in a solver more suitable for highly parallel applications.

Brandt, A.↗

NASA NTRS2017

Single Degree-of-Freedom Modeling of SLS Liquid Hydrogen Pre-Valve Flow Guide to Enable Rapid Transient Analysis

A unique single degree-of-freedom approximation technique has been developed to enable rapid application of a temporally-defined multi-spectral semi-narrow-band loading for generation of realistic stress/cycle values compared to a resonant analysis. The technique uses the harmonic analysis at resonance of a high-fidelity finite element model to produce a transfer function, which is then used to calibrate the response of the SDOF model. A standard numerical ordinary differential equation solver is then used to obtain the temporal response, and its histogram is used in a fatigue/fracture model. This technique is related to other SDOF methods used widely in industry, such as Miles' Equation and the Shock Response Spectra, but it is unique in that it produces a realistic time history of the response. The most obvious error in the process, which is the effect of closely-spaced modes, was also assessed using the parallel application of several SDOF models, and the error is shown to be small. The application of this unique and tractable reduced-order methodology has enabled the SLS program to avoid substantial cost and schedule penalties if a redesign or change of material were required. It has also enabled quick analysis of a number of other structures undergoing the same or similar excitation fields, and quick assessment when the excitation and structural configuration has been altered due to design changes in the system.

Brown, Andrew M.↗

DOE OSTI2023

Optimizing Irregular Communication with Neighborhood Collectives and Locality-Aware Parallelism

Irregular communication often limits both the performance and scalability of parallel applications. Typically, applications individually implement irregular communication as point-to-point, and any optimizations are integrated directly into the application. As a result, these optimizations lack portability. It is difficult to optimize point-to-point messages within MPI, as the interface for single messages provides no information on the collection of all communication to be performed. However, the persistent neighbor collective API, released in the MPI 4 standard, provides an interface for portable optimizations of irregular communication within MPI libraries. This paper presents methods for implementing existing optimizations for irregular communication within neighborhood collectives, analyzes the impact of replacing point-to-point communication in existing codebases such as Hypre BoomerAMG with neighborhood collectives, and finally shows up to a 1.38x speedup on sparse matrix-vector multiplication communication within a BoomerAMG solve through the use of our optimized neighbor collectives. Here, the authors analyze three implementations of persistent neighborhood collectives for Alltoallv: an unoptimized wrapper of standard point-to-point communication, and two locality-aware aggregating methods. The second locality-aware implementation exposes an non-standard interface to perform additional optimization, and the authors present the additional 0.07x speedup from the extended interface. All optimizations are available in an open-source codebase, MPI Advance, which sits on top of MPI, allowing for optimizations to be added into existing codebases regardless of the system MPI install.

AMG↗

DOE OSTI2024

A survey on checkpointing strategies: Should we always checkpoint à la Young/Daly?

The Young/Daly formula provides an approximation of the optimal checkpointing period for a parallel application executing on a supercomputing platform. It was originally designed to handle fail-stop errors for preemptible tightly-coupled applications, but has been extended to other application and resilience frameworks. Here, we provide some background and survey various scenarios to assess the usefulness and limitations of the formula, both for preemptible applications and workflow applications represented as a graph of tasks. We also discuss scenarios with uncertainties, and extend the study to silent errors. We exhibit cases where the optimal period is of a different order than that dictated by the Young/Daly formula, and finally we explain how checkpointing can be further combined with replication.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A Feynman-Kac based numerical method for the exit time probability of a class of transport problems

The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems. In this work, we present an accurate and efficient numerical method for computing this probability for systems described by non-autonomous (time-dependent) stochastic differential equations (SDEs) or their equivalent Fokker-Planck partial differential equations. The method is based on the direct approximation of the Feynman-Kac formula that establishes a link between the adjoint Fokker-Planck equation and the forward SDE. The Feynman-Kac formula is approximated using the Gauss-Hermite quadrature rules and piecewise cubic Hermite interpolating polynomials, and a GPU accelerated matrix representation is used to compute the entire time evolution of the exit time probability using a single pass of the algorithm. The method is unconditionally stable, exhibits second order convergence in space, first order convergence in time, and it is straightforward to parallelize. Applications are presented to the advection diffusion of a passive tracer in a fluid flow exhibiting chaotic advection, and to the runaway acceleration of electrons in a plasma in the presence of an electric field, collisions, and radiation damping. Benchmarks against analytical solutions as well as comparisons with explicit and implicit finite difference standard methods for the adjoint Fokker-Planck equation are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗