Search NASA⌕ Search

SEARCH · Search NASA

Results for “Computer performance”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,171 records · Page 65
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Probabilistic Look-ahead Contingency Analysis Integration with Commercial Tool and Practical Data

This paper presents an initial effort of integrating a smart sampling-based probabilistic look-ahead contingency analysis algorithm with General Electric (GE) Grid Solutions’ commercial energy management system (EMS) tool as a proof-of-concept for a seamless research tool integration using real world large-scale grid data. With the increasing impact of random forces such as variable generation and load, their stochastic behaviors cannot be ignored. However, the current practices are still dominated by deterministic tools. They are becoming increasingly inadequate for the future grid. The developed look-ahead contingency analysis algorithm incorporates forecast errors of variable energy and load to address the challenges brought by the increasing uncertainty of power system. The algorithm can reveal the potential violations caused by the variance of variable energy and load that are not normally detected by traditional deterministic approaches. To test its performance under practical environments ( real data with real commercial tool), significant efforts have been made to prepare test cases, modify GE EMS tool, and adapt an extreme value distribution algorithm to analyze the GE EMS’s violation-only outputs. The test results clearly demonstrate the effectiveness of the developed algorithm as new transformer violations that were not previously detected have been identified. This performance provides better situational awareness to engineers for their decision-making process under uncertainty. Moreover, with the discussion of computational performance and future work, this paper has shown a clear path for integrating the probabilistic algorithm with commercial tools to make us better equipped for the changing power system.

Modeling and simulation of power systems, constrai↗
DOE OSTI2015

Using ASCEM modeling and visualization to inform stakeholders of contaminant plume evolution and remediation efficacy at F-Basin Savannah river, SC - 15156

Communication with stakeholders, regulatory agencies, and the public is an essential part of implementing different remediation and monitoring activities, and developing site closure strategies at contaminated sites. Modeling of contaminant plume evolution plays a critical role in estimating the benefit, cost, and risk of particular options. At the same time, effective visualization of monitoring data and modeling results are particularly important for conveying the significance of the results and observations. In this paper, we present the results of the Advanced Simulation Capability for Environmental Management (ASCEM) project, including the discussion of the capabilities of newly developed ASCEM software package, along the its application to the F-Area Seepage Basins located in the U.S. Department of Energy Savannah River Site (SRS). ASCEM software includes state-of-the-art numerical methods for simulating complex flow and reactive transport, as well as various tool-sets such as a graphical user interface (GUI), visualization, data management, uncertainty quantification, and parameter estimation. Using this software, we have developed an advanced visualization of tritium plume migration coupled with a data management system, and simulated a three-dimensional model of flow and plume evolution on a high-performance computing platform. We evaluated the effect of engineered flow barriers on a nonreactive tritium plume, through advanced plume visualization and modeling of tritium plume migration. In addition, we developed a geochemical reaction network to describe complex geochemical processes at the site, and evaluated the impact of coupled hydrological and geochemical heterogeneity. These results are expected to support SRS's monitoring activities and operational decisions. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Pass-efficient methods for compression of high-dimensional turbulent flow data

The future of high-performance computing, specifically on future Exascale computers, will presumably see memory capacity and bandwidth fail to keep pace with data generated, for instance, from massively parallel partial differential equation (PDE) systems. Current strategies proposed to address this bottleneck entail the omission of large fractions of data, as well as the incorporation of in situ compression algorithms to avoid overuse of memory. To ensure that post-processing operations are successful, this must be done in a way that a sufficiently accurate representation of the solution is stored. Moreover, in situations where the input/output system becomes a bottleneck in analysis, visualization, etc., or the execution of the PDE solver is expensive, the number of passes made over the data must be minimized. In the interest of addressing this problem, this work focuses on the utility of pass-efficient, parallelizable, low-rank, matrix decomposition methods in compressing high-dimensional simulation data from turbulent flows. Additionally, a particular emphasis is placed on using coarse representation of the data – compatible with the PDE discretization grid – to accelerate the construction of the low-rank factorization. This includes the presentation of a novel single-pass matrix decomposition algorithm for computing the so-called interpolative decomposition. The methods are described extensively and numerical experiments on two turbulent channel flow data are performed. In the first (unladen) channel flow case, compression factors exceeding 400 are achieved while maintaining accuracy with respect to first- and second-order flow statistics. In the particle-laden case, compression factors of 100 are achieved and the compressed data is used to recover particle velocities. These results show that these compression methods can enable efficient computation of various quantities of interest in both the carrier and disperse phases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Simulating the Effect of Fracture Connectivity on Repository Performance with GDSA Framework - 18589

This work examines the possible migration of radionuclides from a deep geologic nuclear waste repository sited in fractured crystalline host rock. The key safety concern is the potential effect on waste isolation of the inter-connectivity of the fracture network, which is primarily established by the temporal evolution of the temperature and stress fields at the time of original rock intrusion and cooling. Two end members are considered in these simulations, one with a high degree of connectivity to the biosphere, such that advective transport through the fracture and fault network controls radionuclide migration, and the other with a low degree of connectivity, such that slow diffusive transport through the crystalline rock matrix is the controlling process for radionuclide migration to the biosphere. Both end members have several areally extensive, high-transmissivity deformation zones, whose distance to the repository is an important factor for waste isolation capability. Uncertainties in fracture properties (transmissivity, orientation, radius) and fracture distribution also give rise to uncertainty in waste isolation capability (i.e., the overall connectivity of the repository with the surface biosphere). These types of natural system uncertainties are generally present in any geologic site-characterization program and thus represent an important factor in assessing repository performance in hard rock environments. The waste considered in these simulations are spent fuel rod assemblies from the U.S. commercial nuclear reactor fleet. Thermal output of the waste must be considered in the simulations and can influence the rate and timing of waste package failure, waste form degradation, and fluid flux due to thermal expansion around the repository horizon. To achieve a high-fidelity representation of radionuclide transport in fractures and rock matrix, combined with thermal energy transport and fluid flow in fractures and matrix, the mathematical model is solved numerically in a parallel high-performance computing (HPC) environment on a finite volume unstructured grid consisting of approximately 5 million cells, using Geologic Disposal Safety Assessment (GDSA) Framework (https://pa.sandia.gov), an open-source performance assessment tool for deep underground disposal of nuclear waste. GDSA Framework uses PFLOTRAN to solve the balance equations on a three-dimensional grid with heterogeneous properties, using multiple processors in a parallel configuration based on domain decomposition. The fracture networks in these simulations are originally generated as discrete fracture networks (DFNs), which are sets of two-dimensional planes distributed in a three-dimensional domain. The method used in GDSA Framework maps the stochastically generated DFN to an equivalent continuous porous medium (ECPM) domain that allows for the simulation of coupled heat flow, fluid flow, and radionuclide transport, including heat conduction through the matrix of the fractured rock, which is a process not easily modeled in a DFN representation. Computational efficiency is also greatly enhanced using the ECPM method, allowing for a realistic representation and analysis of uncertainties in a multi-realization performance assessment of a deep geologic repository. The effect of fracture connectivity on the waste isolation safety function, as brought to light by these GDSA Framework simulations, points to the importance of including a realistic representation of uncertainties in fracture properties and distribution (effectively, uncertainty in spatial heterogeneity) in repository safety assessment simulations. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2015

Havery Mudd 2014-2015 Computer Science Conduit Clinic. Final Report

Conduit, a new open-source library developed at Lawrence Livermore National Laboratories, provides a C++ application programming interface (API) to describe and access scientific data. Conduit’s primary use is for inmemory data exchange in high performance computing (HPC) applications. Our team tested and improved Conduit to make it more appealing to potential adopters in the HPC community. We extended Conduit’s capabilities by prototyping four libraries: one for parallel communication using MPI, one for I/O functionality, one for aggregating performance data, and one for data visualization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Numerical Simulation and Model Analyses of In-situ Biogeochemical Remediation of Chromium at the LANL - 18306

Environmental management problems associated with contamination of groundwater resources with heavy metals (such as chromium) typically require complex biogeochemical model simulations and analysis of in situ remediation. Frequently, the in situ remediation is the only viable treatment option. In these cases, a three-dimensional reactive transport model of relevant biogeochemical processes is invaluable. Recently, we have developed a novel unique biogeochemical simulator called CHROTRAN (http://chrotran.lanl.gov; Hansen et al. 2017, Vesselinov et al. 2018a) capable to represent the full three-dimensional dynamics of processes associated with in situ biogeochemical remediation of heavy metals in heterogeneous aquifers. CHROTRAN accounts for spatial and temporal transients of (1) the heavy metal to be remediated, (2) introduced amendments (e.g., through well injection), and (3) biomass growth and decay. The introduced amendments can include (1) an electron donor (e.g., molasses), (2) a nontoxic-conservative bio-inhibitor (e.g., ethanol), and (3) a biocide (e.g., dithionite). In addition, direct abiotic reduction by donor-metal interaction as well as donor-driven biomass growth and bio-reduction are modeled in CHROTRAN. Other critical processes, such as donor sorption, bio-fouling and biomass death are also modeled. CHROTRAN can simulate the groundwater flow dynamics introduced due a series of injection and extraction wells and account for reduction of aquifer permeability near the wells due bio clogging. CHROTRAN is based on the existing PFLOTRAN (http://pflotran.org; Lichtner et al, 2017a) code framework, taking advantage of the reaction interface allowing for implementation of complex model features and leverage other facets of PFLOTRAN, such as multi-component geochemistry and high-performance computing. Here, we present numerical simulations and model analyses related to the Los Alamos National Laboratory (LANL) chromium site. The analyses are performed by coupling of CHROTRAN with MADS (Model Analysis and Decision Support; http://mads.lanl.gov; Vesselinov et al., 2018b). We present analyses related to uncertainty quantification of model predictions, sensitivity of model parameters and remedial decision support. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

The SONATA data format for efficient description of large-scale network models

Increasing availability of comprehensive experimental datasets and of high-performance computing resources are driving rapid growth in scale, complexity, and biological realism of computational models in neuroscience. To support construction and simulation, as well as sharing of such large-scale models, a broadly applicable, flexible, and high-performance data format is necessary. To address this need, we have developed the Scalable Open Network Architecture TemplAte (SONATA) data format. It is designed for memory and computational efficiency and works across multiple platforms. The format represents neuronal circuits and simulation inputs and outputs via standardized files and provides much flexibility for adding new conventions or extensions. SONATA is used in multiple modeling and visualization tools, and we also provide reference Application Programming Interfaces and model examples to catalyze further adoption. SONATA format is free and open for the community to use and build upon with the goal of enabling efficient model building, sharing, and reproducibility.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Ensembles of Networks Produced from Neural Architecture Search

Neural architecture search (NAS) is a popular topic at the intersection of deep learning and high performance computing. NAS focuses on optimizing the architecture of neural networks along with their hyperparameters in order to produce networks with superior performance. Much of the focus has been on how to produce a single best network to solve a machine learning problem, but as NAS methods produce many networks that work very well, this affords the opportunity to ensemble these networks to produce an improved result. Additionally, the diversity of network structures produced by NAS drives a natural bias towards diversity of predictions produced by the individual networks. This results in an improved ensemble over simply creating an ensemble that contains duplicates of the best network architecture retrained to have unique weights.

Herron, Emily↗
DOE OSTI2015

Performance upgrades to the MCNP6 burnup capability for large scale depletion calculations

The first MCNP based inline Monte Carlo depletion capability was officially released from the Radiation Safety Information and Computational Center as MCNPX 2.6.0. With the merger of MCNPX and MCNP5, MCNP6 combined the capability of both simulation tools, as well as providing new advanced technology, in a single radiation transport code. The new MCNP6 depletion capability was first showcased at the International Congress for Advancements in Nuclear Power Plants (ICAPP) meeting in 2012. At that conference the new capabilities addressed included the combined distributive and shared memory parallel architecture for the burnup capability, improved memory management, physics enhancements, and new predictability as compared to the H.B Robinson Benchmark. At Los Alamos National Laboratory, a special purpose cluster named “tebow,” was constructed such to maximize available RAM per CPU, as well as leveraging swap space with solid state hard drives, to allow larger scale depletion calculations (allowing for significantly more burnable regions than previously examined). As the MCNP6 burnup capability was scaled to larger numbers of burnable regions, a noticeable slowdown was realized.This paper details two specific computational performance strategies for improving calculation speedup: (1) retrieving cross sections during transport; and (2) tallying mechanisms specific to burnup in MCNP. To combat this slowdown new performance upgrades were developed and integrated into MCNP6 1.2.

42 ENGINEERING↗
DOE OSTI2018

Analysis Report for Exascale Storage Requirements for Scientific Data.

Over the next 10 years, the Department of Energy will be transitioning from Petascale to Exascale Computing resulting in data storage, networking, and infrastructure requirements to increase by three orders of magnitude. The technologies and best practices used today are the result of a relatively slow evolution of ancestral technologies developed in the 1950s and 1960s. These include magnetic tape, magnetic disk, networking, databases, file systems, and operating systems. These technologies will continue to evolve over the next 10 to 15 years on a reasonably predictable path. Experience with the challenges involved in transitioning these fundamental technologies from Terascale to Petascale computing systems has raised questions about how these will scale another 3 or 4 orders of magnitude to meet the requirements imposed by Exascale computing systems. This report is focused on the most concerning scaling issues with data storage systems as they relate to High Performance Computing- and presents options for a path forward. Given the ability to store exponentially increasing amounts of data, far more advanced concepts and use of metadata will be critical to managing data in Exascale computing systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Fibre Channel Development Final Report CRADA No. TC-0340-92-D

The Fibre Channel (FC) Development project was designed to enhance U.S. industrial competitiveness by accelerating the standardization and subsequent industrial acceptance of the American National Standards Institute’s (AIW) Fibre Channel Standard (now X3T1 1). It was also intended to give the principal U.S. participants a one- to two-year lead in developing heterogeneous high-speed computer networks, dktibuted computing through clustering, scientific visualization techniques, and high speed channels. The project was proposed to benefit U.S. industry as these high performance computing methods became generally available. In 1992-93, during the initial project phases, Fibre Channel PC) was emerging as a new ANSI standard. It was envisioned as becoming the mechanism for data transfer between the next generation of computers, and between these computers and their peripherals. Using this channel standard, U.S. computer vendors were expecting to be able to provide high-speed interoperability between heterogeneous computers and their storage devices, with data transfer rates greater than a GBit/sec. Our project was composed of key principal players in the FC standardization effort from both U.S. industry and the Department of Energy’s (DOES) Lawrence Liverrnore National Laboratory (LLNL). The industial participants were developing individual FC interfaces to operate with their platform products. LLNL’s role was to be a neutral testing site and a facilitator for helping to resolve conflicting interpretations of the embryonic Fibre Channel specification. LLNL anticipated that conflicts in the interpretation of such a standard would arise and require neutral resolution and that such resolutions would best be achieved in cooperation with the ANSI FC Working Group. Project plans included transferring to U.S. industry any resilient FC testing capabilities at the project conclusion.

42 ENGINEERING↗
DOE OSTI2018

Fibre Channel Development Final Report CRADA No. TC-0340-92-C

The Fibre Channel (FC) Development project was designed to enhance U.S. industrial competitiveness by accelerating the standardization and subsequent industrial acceptance of the American National Standards Institute’s (ANSI) Fibre Channel Standard (now X3T1 1). It was also intended to give the principal U.S. participants a one-to two-year lead in developing heterogeneous high-speed computer networks, distributed computing through clustering, scientific visualization techniques, and high speed channels. The project was proposed to benefit U.S. industry as these high performance computing methods became generally available. In 1992-93, during the initial project phases, Fibre Channel (FC) was emerging as a new ANSI standard. It was envisioned as becoming the mechanism for data transfer between the next generation of computers, and between these computers and their peripherals. Using this channel standard, U.S. computer vendors were expecting to be able to provide high-speed interoperatillity between heterogeneous computers and their storage devices, with data transfer rates greater than a GBit/sec. Our project was composed of key principal players in the FC standardization effort from both U.S. industry and the Department of Energy’s@OEs) Lawrence Liverrnore National Laboratory (LLNL). The industrial participants were developing individual FC interfaces to operate with their platform products. LLNL’s.role was to be a neutral testing site and a facilitator for helping to resolve conflicting interpretations of the embryonic Fibre Channel specification. LLNL anticipated that conflicts in the interpretation of such a standard would arise and require neutral resolution and that such resolutions would best be achieved in cooperation with the ANSI FC Working Group. Project plans included transferring to U.S. industry any resilient FC testing capabilities at the project conclusion.

42 ENGINEERING↗
DOE OSTI2020

Optimizing Bifacial PV Systems (Q3 FY2020 Project Report)

This project has four main technical objectives. Develop and improve bifacial performance models by adding the capability to evaluate electrical behavior and performance of bifacial modules and arrays under realistic field conditions including irradiance variability caused by racking, module frame, and position in the array. Instrument and monitor performance of fielded bifacial systems to validate performance models and to measure, analyze and publish on bifacial energy gain. These should include both research and commercial bifacial systems and cover a variety of deployment applications. Evaluate optimal bifacial system designs using simulations leveraging high performance computing, and also using full sized and miniaturized experimental field deployments. Establish and contribute to international test standards for bifacial system performance, testing, and safety, and work with the community to establish installation and siting best practices.

14 SOLAR ENERGY↗
DOE OSTI2026

A time-parallel method for scalable heat transfer simulations of additive manufacturing

Here, a major challenge in simulating the thermal behavior in additive manufacturing processes is the disparate length and time scales between transport phenomena occurring in the melt pool and the component. A common simulation approach relies on spatial decomposition for parallel computing, but due to the nature of heat transfer in AM, where most of the computational expenditure is localized near the melt pool, the computational speedup from spatial parallelization saturates quickly. Therefore, additional parallelism by means of time-domain decomposition is needed to fully take advantage of high-performance computing (HPC) resources. This work introduces a time-parallel method to improve the computational scalability of additive manufacturing simulations on HPC systems, while maintaining high temporal resolution of heat transfer near the melt pool. The method, inspired by the nonlinear paraexp formalism, performs an iterative superposition of nonlinear solutions to the initial value problem, integrating the heat equation across overlapping time-parallel intervals. For a single layer of the NIST AMB2018–01 L7 benchmark problem, the method achieves a 38.51x speedup in wall-clock time with a maximum error in the global temperature solution of 0.99%. This reduces the total solution time from 196.72 min to 5.11 min on 128 nodes of the ORNL Frontier supercomputer. The tradeoff between accuracy and total wall-clock time is investigated and recommendations for time-parallel deployment for AM problems are made.

Additive manufacturing↗
DOE OSTI2022

SMALE: Enhancing Scalability of Machine Learning Algorithms on Extreme-Scale Computing Platforms

Deployment and execution of machine learning tasks on extreme-scale computing platforms face several significant technical challenges: 1) High computing cost incurred by dense networks – The computing workload of deep networks with densely-connected topology increases rapidly with the network size, imposing a non-scalable computing model of extreme-scale computing platforms; 2) Non-optimized workload distribution – Many advanced deep learning algorithms, e.g., sparsification and irregular net-work topology, produce very unbalanced workload distribution on extreme-scale computing platforms. The computation efficiency is greatly hindered by the incurred data and computation redundancies as well as long tails of the node with extensive workload; 3) Constraints in data movement and I/O bottle-neck – Inter-node data movement in extreme-scale computing platforms are associated with high energy and latency costs, and subject to the constraints of I/O bandwidth; and 4) Generalization of algorithm realization and acceleration on computing platforms – The large varieties of machine learning algorithms and structures of extreme-scale computing platforms make the derivation of a generalized algorithm realization and acceleration method very challenging, which, however, is the requirement by domain scientists and interested users. We call the above challenges Smale’s Problems in Machine Learning and Understanding for High-Performance Computing Scientific Discovery. The objective of our three-year research project is to develop a holistic innovation set at structure, assembly, and acceleration layers of machine learning algorithms to address the above challenges in algorithm deployment and execution. Three tasks are particularly performed, including: At the algorithm structure level, we investigate the techniques that can structurally sparsify on the topology of deep networks for computing workload reduction. We also study clustering and pruning techniques that can optimize the workload distributions over the extreme-scale computing platforms; At the algorithm assembly level, we derive a unified learning framework for unsupervised transfer learning and dynamic growing capabilities. Novel training methods are also exploited to enhance the training efficiency of the proposed framework; At the algorithm acceleration level, we will develop a series of techniques that can accelerate the computation of sparse matrix operations, which are one of the core executions in deep learning and optimize memory access of the concerned platforms. Our proposed techniques attack the fundamental problems in machine learning algorithms running on extreme-scale computing platforms by vertically integrating the solutions at three closely entangled layers, paving the long-term scaling path of machine learning applications under DOE context. Three tasks corresponding to the above respective research orientations are performed during the three-year project period with our collaborators at ORNL. The outcome of the proposed project is anticipated to form a holistic solution set of novel algorithms and network topologies, efficient training techniques, and fast acceleration methods to promote the computing scalability of the machine learning applications of particular interest to DOE.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Graphics processing unit accelerated phase field dislocation dynamics: Application to bi-metallic interfaces

We present the first high-performance computing implementation of the meso-scale phase field dislocation dynamics (PFDD) model on a graphics processing unit (GPU)-based platform. The implementation takes advantage of the portable OpenACC standard directive pragmas along with Nvidia's compute unified device architecture (CUDA) fast Fourier transform (FFT) library called CUFFT to execute the FFT computations within the PFDD formulation on the same GPU platform. The overall implementation is termed ACCPFDD-CUFFT. The package is entirely performance portable due to the use of OPENACC-CUDA inter-operability, in which calls to CUDA functions are replaced with the OPENACC data regions for a host central processing unit (CPU) and device (GPU). A comprehensive benchmark study has been conducted, which compares a number of FFT routines, the Numerical Recipes FFT (FOURN), Fastest Fourier Transform in the West (FFTW), and the CUFFT. The last one exploits the advantages of the GPU hardware for FFT calculations. The novel ACCPFDD-CUFFT implementation is verified using the analytical solutions for the stress field around an infinite edge dislocation and subsequently applied to simulate the interaction and motion of dislocations through a bi-phase copper-nickel (Cu–Ni) interface. It is demonstrated that the ACCPFDD-CUFFT implementation on a single TESLA K80 GPU offers a 27.6X speedup relative to the serial version and a 5X speedup relative to the 22-multicore Intel Xeon CPU E5-2699 v4 @ 2.20 GHz version of the code.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Machine Learning for First Principles Calculations of Material Properties for Ferromagnetic Materials

The investigation of finite temperature properties using Monte-Carlo (MC) methods requires a large number of evaluations of the system’s Hamiltonian to sample the phase space needed to obtain physical observables as function of temperature. DFT calculations can provide accurate evaluations of the energies, but they are too computationally expensive for routine simulations. To circumvent this problem, machine-learning (ML) based surrogate models have been developed and implemented on high-performance computing (HPC) architectures. In this paper, we describe two ML methods (linear mixing model and HydraGNN) as surrogates for first principles density functional theory (DFT) calculations with classical MC simulations. These two surrogate models are used to learn the dependence of target physical properties from complex compositions and interactions of their constituents. We present the predictive performance of these two surrogate models with respect to their complexity while avoiding the danger of overfitting the model. An important aspect of our approach is the periodic retraining with newly generated first principles data based on the progressive exploration of the system’s phase space by the MC simulation. The numerical results show that HydraGNN model attains superior predictive performance compared to the linear mixing model for magnetic alloy materials.

Eisenbach, Markus↗
DOE OSTI2023

PETSc/TAO Users Manual (Rev. 3.19)

This manual describes the use of the Portable, Extensible Toolkit for Scientific Computation (PETSc) and the Toolkit for Advanced Optimization (TAO) for the numerical solution of partial differential equations and related problems on high-performance computers. PETSc/TAO is a suite of data structures and routines that provide the building blocks for the implementation of large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all distributed memory communication. PETSc/TAO includes a large suite of parallel linear solvers, nonlinear solvers, time integrators, and opti mization that may be used in application codes written in Fortran, C, C++, and Python (via petsc4py; see Getting Started). PETSc provides many of the mechanisms needed within parallel application codes, such as parallel matrix and vector assembly routines. The library is organized hierarchically, enabling users to employ the level of abstraction that is most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous flexibility for users. PETSc is a sophisticated set of software tools; as such, for some users it initially has a much steeper learning curve than packages such as MATLAB or a simple subroutine library. In particular, for individuals without some computer science background, experience programming in C, C++, python, or Fortran and experience using a debugger such as gdb or lldb, it may require a significant amount of time to take full advantage of the features that enable efficient software use. However, the power of the PETSc design and the algorithms it incorporates may make the efficient implementation of many application codes simpler than “rolling them” yourself. For many tasks a package such as MATLAB is often the best tool; PETSc is not intended for the classes of problems for which effective MATLAB code can be written. There are several packages, built on PETSc, that may satisfy your needs without requiring directly using PETSc. We recommend reviewing these packages functionality before starting to code directly with PETSc. PETSc can be used to provide a “MPI parallel linear solver” in an otherwise sequential, or OpenMP parallel code. This approach cannot provide extremely large improvements in the application time by utilizing large numbers of MPI processes but can still improve the performance. Certainly all parts of a previously sequential code need not be parallelized but the matrix generation portion must be parallelized to expect true scalability to large numbers of MPI processes. See PCMPI for details on how to utilize the PETSc MPI linear solver server. Since PETSc is under continued development, small changes in usage and calling sequences of routines will occur. PETSc has been supported for twenty-five years; see mailing list information on our website for information on contacting support.

97 MATHEMATICS AND COMPUTING↗