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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.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Software stewardship and advancement of a high-performance computing scientific application: QMCPACK

Here, we provide an overview of the software engineering efforts and their impact in QMCPACK, a production-level ab-initio Quantum Monte Carlo open-source code targeting high-performance computing (HPC) systems. Aspects included are: (i) strategic expansion of continuous integration (CI) targeting CPUs, using GitHub Actions own runners, and NVIDIA and AMD GPUs used in pre-exascale systems, (ii) incremental reduction of memory leaks using sanitizers, (iii) incorporation of Docker containers for CI and reproducibility, and (iv) refactoring efforts to improve maintainability, testing coverage, and memory lifetime management. We quantify the value of these improvements by providing metrics to illustrate the shift towards a predictive, rather than reactive, maintenance approach. Our goal, in documenting the impact of these efforts on QMCPACK, is to contribute to the body of knowledge on the importance of research software engineering (RSE) for the stewardship and advancement of community HPC codes to enable scientific discovery at scale.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Efficient genetic code expansion tools enable in vivo study of lysine acetylation in non-model bacteria

Recent proteomic advancements have revealed widespread Nε-lysine acetylation in pathways governing pathogenicity, metabolism, and antibiotic resistance in bacteria. The spontaneous, non-specific nature of this modification in prokaryotes obscures its biological role, necessitating prokaryotic specific in vivo interrogation systems. Genetic Code Expansion (GCE) offers a powerful method to investigate the roles and regulation dynamics of acetyl-lysine in vivo with the precise incorporation of a suite of non-canonical amino acids, including acetyl-lysine analogs. However, its use has been largely restricted to E. coli strains due to challenges associated with implementation and optimization of the technology in more diverse bacterial strains. Here, we present a bacterial host-agnostic, readily optimizable GCE platform designed to site-specifically incorporate non-canonical amino acids into target proteins within living bacteria. We further demonstrate the versatility of this technology by showcasing, for the first time, the successful incorporation of acetyl-lysine in a non- E. coli bacterium.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Advances in 3D transient plasma dynamics and control through MHD and hybrid fluid-kinetic simulations with JOREK

Transient phenomena and their control are of high relevance in magnetic confinement fusion plasmas to guarantee a stable and safe plasma operation. Interpretative simulations can maximize the insights gained from experiments on present machines and predictive simulations can help in the preparation of design, mitigation techniques and operational scenarios for future devices. In this article, we provide an overview of recent advances and novel scientific results obtained with the 3D non-linear hybrid fluid-kinetic code JOREK, covering physics of plasma transients from the core to the scrape-off layer (SOL) both for tokamak and stellarator devices. Substantial progress was made in the physics understanding, model validation with experiments and experiment interpretation, thus, giving confidence for predictions to devices like DTT, ITER and DEMO. The topics addressed comprise a wide range: the edge physics of new operation scenarios and edge localized mode suppression; major disruptions with a focus on runaway electrons and vertical displacement events as well as disruption mitigation by shattered pellet injection; the physics mechanisms and operational limits of the flux pumping regime for sawtooth control; MHD limits of stellarators and work towards incorporating advanced edge/SOL/exhaust dynamics; continuing improvements of the code for more efficient hybrid simulations on conventional and accelerated high performance computing architectures.

disruptions↗
DOE OSTI2022

SPEL: Software tool for Porting E3SM Land Model with OpenACC in a Function Unit Test Framework

Most high-end computers adopt hybrid architecture, porting a large-scale scientific code onto accelerators is necessary. The paper presents a generic method for porting large-scale scientific code onto accelerators using compiler directives within a modularized function unit test platform. We have implemented the method and designed a software tool (SPEL) to port the E3SM Land Model (ELM) onto the GPUs in the Summit computer. SPEL automatically generates GPU-ready test modules for all ELM functions, such as CanopyFlux, SoilTemperature, and EcosystemDynamics. SPEL breaks the ELM into a collection of standalone unit test programs for easy code verification and further performance improvement. We further optimize several ELM test modules with advanced techniques, including memory reduction, reconstructed parallel loops, and asynchronous GPU kernel launch. We hope our study will inspire new toolkit developments that expedite large-scale scientific code porting with compiler directives.

Schwartz, Peter↗
DOE OSTI2020

Oak Ridge National Laboratory Technical Input for the Nuclear Regulatory Commission Review of the 2017 Edition of ASME Section III, Division 5, ‘High Temperature Reactors’

To assist the Nuclear Regulatory Commission in its decision making on endorsement of the American Society for Mechanical Engineers Boiler and Pressure Vessel Code Section III, Division 5 (2017 Edition) for development of advanced non-light water reactors, the following Division 5 portions were reviewed: Article HBB-2000 Material; Article HCB-2000 Material; Article HGB-2000 Material; Mandatory Appendix HBB-I-14 Tables and Figures; and, Nonmandatory Appendix HBB-U Guidelines for Restricted Material Specifications to Improve Performance in Certain Service Applications. In addition to the 2017 Edition, the same parts of the 2019 Edition have also been reviewed as indicated in various sections of the report. This review was conducted by a collaboration of national laboratory and private sector participants with significant industrial experience, including some heavy lifting and deep diving from Clarus Consulting, LLC., all intended to achieve an objective, independent, and practical perspective. The report provides recommendations, descriptions of the evaluation methods, and the source references for the data used. To build confidence required for endorsement of the Code, this review was conducted as a verification and validation of the above Code contents. The objective of verification is to ensure that the Code is free of error – direct or implied; contains the information needed for its use, including proper coverage of the Code-specified materials for the intended application, and completeness and adequacy of references to other portions of the Code. The objective of validation is to authenticate that the Code tabulations and graphs represent design inputs consistent with what are determined using rules and methods specified by the Code. The authentication process used data that were assembled and/or generated independent of Code development, while the methods of analysis followed Code-specified methods where appropriate. The designated portions for this review cover the five alloys codified for high temperature reactor applications in Division 5, i.e. 316 SS, 304 SS, 800H, 2¼Cr-1Mo, and 9Cr-1Mo-V, regarding their general requirements, permitted specifications and design stress intensity values for pressure-retaining applications, deterioration in service, fatigue acceptance test, permissible weld materials, tensile and yield strength, expected minimum stress-to-rupture values (including for Alloy 718), weld stress rupture factors, permissible materials for bolting use, and restricted specifications in certain service applications. Additionally, stress intensity values for bolting materials including 316 SS, 304 SS and alloy 718 were reviewed. Analysis and discussion are also provided on contents outside of these designated Code portions where it was deemed relevant and necessary to develop a technically sound understanding of issues relating to the designated portions. Due to unavailability of sufficient test data on welds during the review period, the weld stress rupture factors in Tables HBB-I-10.14A to E, which cover a total of ten tables for the five alloys welded with twenty-eight different weld metals (some with similar properties), have been deferred to a future review effort. The review identified mainly two types of issues. The first type includes instances where the Code is found factually incomplete or incorrect, such as obsolete materials specifications listings, missing tabulation of stresses for bolting. Changes to the Code are recommended in these cases. The second type of issue includes instances where the Code tabulations and graphs are found to be less conservative than the review analysis results. In these cases, recommendations are made for further review and consideration where the difference in conservatism exceeds 10%, which is our threshold for questioning technical adequacy, meriting a risk assessment by the Nuclear Regulatory Commission and/or reactor designers. It is noted that this effort has been executed using all available data and established methods of analysis, including methods and criteria specified and used by the Code. As such, the findings that are presented in quantitative detail, in a format for convenient comparison with the Code, and with identification of where further review is recommended, should provide a sound technical basis for decisions about quantifying the implications of the reduced design margins and technical adequacy/inadequacy to form a basis for conditioning specific Code tabulation values on endorsement. Recommendations for specific changes to the Code, however, entail design conservatism considerations beyond the scope of this review effort, and are not made in this report.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

As-Run Neutronics Evaluation for the CSM-10584 Experiment in the ATR

This engineering calculations and analysis report (ECAR) documents the results of the Advanced Test Reactor (ATR) detailed Monte Carlo N-Particle (MCNP) code full-core model as-run physics analysis performed to support the Colorado School of Mines (CSM) experiment in the B-5 position.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

The General Atomic and Molecular Electronic Structure System (GAMESS): Novel Methods on Novel Architectures

The primary focus of GAMESS over the last 5 years has been the development of new high-performance codes that are able to take effective and efficient advantage of the most advanced computer architectures, both CPU and accelerators. These efforts include employing density fitting and fragmentation methods to reduce the high scaling of well-correlated (e.g., coupled-cluster) methods as well as developing novel codes that can take optimal advantage of graphical processing units and other modern accelerators. Because accurate wave functions can be very complex, an important new functionality in GAMESS is the quasi-atomic orbital analysis, an unbiased approach to the understanding of covalent bonds embedded in the wave function. Finally, best practices for the maintenance and distribution of GAMESS are also discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Multi-scale fission product release model with comparison to AGR data

TRistructural ISOtropic (TRISO) particle fuel is central to several advanced, high-temperature reactor designs. Each particle consists of a fuel kernel encapsulated by three layers of carbon and ceramics that prevent the release of fission products and ensure physical integrity. Despite outstanding retention properties, fission product release has been observed from intact particles. To better understand and quantify fission product release from TRISO particles, a multiscale, mechanistic model of fission product transport is being developed by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. Previous work focused on silver (Ag) transport and improved Ag release predictions. The work described in this report builds on this experience to better understand cesium (Cs) transport in silicon carbide (SiC), the main barrier to the release of fission products. Atomistic simulations provide bulk and grain boundary (GB) Cs diffusivities in SiC, which are used by phase field simulations in the mesoscale code Marmot to determine the temperature, microstructure, and irradiation-dependent Cs diffusivity at the mesoscale in SiC. This approach attributes the different temperature regimes experimentally observed for Cs diffusivities in SiC to a transition from bulk-dominated diffusivity at high temperatures to a GB-dominated regime at low temperatures, providing new insight. The multiscale, mechanistic effective diffusivity is then implemented in the fuel performance code BISON and further validated by comparing Cs release predictions from Advanced Gas Reactor (AGR)-1 and AGR-2 post-irradiation measurements. The new model improves BISON’s predictability. This document also reports improvements made on Ag transport modeling by accounting for different GB types having different diffusivities. Moreover, this report details preliminary efforts to model palladium (Pd) attack of the SiC at the mesoscale using a phase field approach. Pd attack and its impact on accelerated Ag transport remains a misunderstood phenomenon, and we use the model to demonstrate that the formation of lamellae that has been observed in experiments can be explained by the reaction of Pd with SiC to form alternating layers of graphite and Pd 2 Si. This effort aims to improve our understanding of the reaction and eventually provide a model for BISON to account for Pd penetration and its effects on fission product release.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Worst Case Sabotage Consequence Modeling for Advanced Reactors

Under proposed rulemaking by the United States Nuclear Regulatory Commission, advanced reactor licensees may qualify for a reduction in onsite responders if the consequences from a sabotage attack do not exceed 25 rem at the reactor site boundary 2 hours after a release occurs. This work presents a preliminary assessment of the feasibility of meeting the 25 rem at the site boundary criteria. Using advanced reactor radionuclide inventories radiological release estimates created by collaborators at Oak Ridge National Laboratory, the MACCS consequence analysis code was used to investigate the distance at the dose from hypothetical sabotage events reaches 25 rem for different advanced reactor technologies. It was found that the distance to 25 rem depended heavily on sampled weather conditions and sabotage release fractions, and further refinement of release fractions and MACCS modeling parameters is recommended.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Code validation of SAM using natural-circulation experimental data from the compact integral effects test (CIET) facility

The primary objective of this study is to validate the system analysis code, SAM, using experimental data from the Compact Integral Effects Test (CIET) experimental loop. SAM is a modern system analysis code being developed at Argonne National Laboratory for safety analysis of designs for advanced non-light water reactors (non-LWRs), such as sodium-cooled fast reactors, high-temperature gas-cooled reactors, and fluoride salt-cooled high-temperature reactors (FHRs). To support SAM code development for the wide range of non-LWR applications, it is of paramount importance to validate the code against experiments highly relevant to these reactor concepts. Additionally, the CIET facility, which was designed to reproduce the thermal-hydraulics response of FHRs under both forced- and natural-circulation conditions, has been identified and selected as one of the benchmark test facilities for SAM code validation. In this study, two sets of available CIET tests were selected for SAM code validation purposes, namely, power step change transient tests and steady-state natural-circulation tests. For all selected tests, SAM-predicted results show very good agreement with experimental data. The successful validation of SAM against these selected CIET experiments demonstrates that the computer code is well suited for thermal-hydraulics analysis of FHR designs.

42 ENGINEERING↗
DOE OSTI2023

Compare predictions of transient fission gas release by empirical and mechanistic models to experiments in high burnup UO 2 fuel

Understanding and predicting fuel performance at high burnup require improving our understanding of transient fission gas release. High-burnup operations enable new mechanisms of fission gas release, which affect fuel performance. The Nuclear Regulatory Commission has recently published its interpretation of existing fuel fragmentation, relocation, and dispersal data in a research information letter. There, transient fission gas release was identified as one of the main factors that contributes to fuel fragmentation, relocation, and dispersal, and therefore limits fuel extension to high burnup. However, transient fission gas release is a complex phenomenon that cannot be fully described by simple empirical descriptions. This report summarizes the development of a mechanistic model for high-burnup transient fission gas release in the fuel performance code BISON. This research was supported by the Nuclear Energy Advanced Modeling and Simulation program during fiscal year 2023 to improve our understanding of high-burnup transient fission gas release and ability to predict it as a function of operation history. To support the development of a mechanistic transient fission gas release model, the existing Simple Integrated Fission Gas Release and Swelling (Sifgrs) model in BISON has been completely refactored to make it more modular and extensible. This effort supports the model's application to high-burnup conditions, its extension to other fuel forms, and the continuous improvement of its current features. Once refactoring was completed, models for high-burnup structure formation, fission gas transfer from non-restructured fuel to high-burnup structure, high-burnup structure intragranular and intergranular fission gas behavior, high-burnup structure bubble evolution, fuel pulverization, and the resulting transient fission gas release were tested and implemented in the Simple Integrated Fission Gas Release and Swelling (Sifgrs) model or tightly coupled to it. The new mechanistic model was then compared to an empirical model developed in parallel by a Nuclear Energy University Program project using a Studsvik high-burnup loss-of-coolant-accident assessment case. Finally, the report details the preliminary BISON results for a benchmark activity organized by the Nuclear Energy Agency to evaluate fuel performance codes' predictive capabilities for burst fission gas release. This work represents an important step toward a mechanistic understanding of fission gas release in high-burnup conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Advanced Modeling and Simulation Methods for Evaluation of Thermal Neutron Scattering Materials

With the rise of interest in thermal neutron scattering data for advanced reactor, criticality safety, and shielding applications, new experimental data are required for evaluation of new materials or for re-evaluation (or validations) of previously evaluated materials. New experimental data are evaluated in a three-step process: (1) computing the phonon characteristics, (2) computing the dynamic structure factor (DSF) from the data, and (3) using the experimental setup to simulate the experimental data. All three steps have challenges, ranging from the need for a sufficiently general material simulation code—a processing code that can compute the corresponding DSF—to having a detailed layout of the instrument/beamline/facility where the data were measured. Whereas phonon characteristics of materials can be computed using various methods (molecular dynamics, density functional theory, etc.), a high-fidelity computation of the DSF and the simulation of the experiment based on the DSF is vital to the accuracy of the evaluation. The latter two steps can be achieved by using the two corresponding code systems developed by instrument scientists at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory: (1) OCLIMAX, a program that calculates the dynamic structure factor from DFT and MD simulation results, and (2) MCViNE, a Monte Carlo neutron ray-tracing program designed to simulate neutron scattering experiments. Recently, polyethylene and yttrium hydride were measured at the Wide Angular-Range Chopper (ARCS) and SEQUOIA instrument stations of the SNS. These experiments are simulated using the density functional theory code, the Cambridge Serial Total Energy Package (CASTEP), to compute its phonon characteristics (eigenvalues/vectors and PDOS), which is then processed using OCLIMAX to yield the DSF, and finally the data at each instrument station are simulated by the MCViNE for comparison to the measured data for evaluation. For comparison to conventional evaluation methods, the scattering data processed from OCLIMAX are compared against those processed from the LEAPR module of NJOY, and the results from MCViNE simulations are compared against previously used simplified beamline models implemented in the Monte Carlo N-Particle (MCNP) code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

The Multiphysics on Advanced Platforms Project

In 2015, the Lawrence Livermore National Laboratory started development of next-generation multiphysics simulation capabilities for the National Nuclear Security Administration under the Advanced Technologies Development and Mitigation (ATDM) element of the Advanced Simulation and Computing program in collaboration with the Exascale Computing Project (ECP). A key driver for this effort across the NNSA tri-lab was the emergence of advanced high performance computing (HPC) architectures based on heterogeneous compute capabilities, including GPU based systems, as part of the national drive toward exascale computing platforms at multiple Department of Energy (DOE) facilities. Developing a multiphysics code capable of meeting the various simulation needs of the NNSA as defined by the current generation of integrated codes (or ICs), initially developed as part of the Accelerated Strategic Computing Initiative (ASCI) program beginning in 1996, and able to scale to the current 100 petaflop class pre-exascale systems, as well the forthcoming exaflop class computers, is a daunting challenge. To accomplish this ambitious goal, LLNL has embraced two key themes: use of high-order numerical methods and a modular approach to code development. The LLNL next generation effort is organized under the Multi-Physics on Advanced Platforms Project (MAPP). A foundational component of MAPP is the Axom computer science (CS) toolkit which provides infrastructure for the development of modular, performance portable, multi-physics application codes. MARBL is a next-generation application code built on the Axom base to address the modeling needs of the high energy density physics (HEDP) community for simulating high-explosive, magnetic or laser driven experiments such as inertial confinement fusion (ICF), pulsed-power magneto-hydrodynamics (MHD), equation of state (EOS) and material strength studies as part of the NNSA’s stockpile stewardship program (SSP).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Recommendations for Minimum Required Diagnostics Information

The rapid growth of electrified transportation, including light- and medium-duty electric vehicles (EVs) as a mobility solution requires a reliable EV-charging infrastructure. To advance charging reliability, the ChargeX Consortium reports “Recommendations for Minimum Required Error Codes for Electric Vehicle Charging Infrastructure” and “Implementation Guide for Minimum Required Error Codes in Electric Vehicle Charging Infrastructure” provided recommendations for a set of minimum required error codes (MRECs), their functional and responsibility classifications, and a guide for their implementation, using Open Charge Point Protocol (OCPP) versions 1.6J4 and 2.0.1.5 These reports outline a recommended practice for consistent error reporting and interpretation, which is essential for communicating issues uniformly across the complex and diverse EV-charging ecosystem. However, MRECs are just one part of diagnosing issues; another critical part is obtaining enough information about the current state and performance of the various charging components to identify root causes for each of the error codes. This additional diagnostics data can be used by technicians or automated systems to understand the context around an issue, allowing for timely resolution, decreased maintenance costs, and increased charging reliability. During everyday operations, data are regularly collected and analyzed across the ecosystem. Although sharing of all that available data would be great for diagnostics, concerns on data ownership, privacy, and original equipment manufacturer (OEM) intellectual property pose a challenge. To overcome this obstacle, this report proposes a set of minimum required diagnostic information (MRDI) and recommends that the industry implement these uniformly across the North American EV charging ecosystem. MRDI provides a means to exchange only data deemed necessary for root cause determination.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2021

Expanded Energy Credits in Energy Codes (Technical Brief)

This technical brief provides additional energy efficiency measures that go beyond the current prescriptive commercial energy codes. It demonstrates relative savings for multiple measures and shows a base cost effective package by building type and climate zone. An advanced savings package is also shown. Potential building savings for the base package for different building types across climate zones range from 3.9% to 22% of building energy cost, while the advanced package building savings range from 8.4% to 44%. In addition to measure descriptions, this technical brief includes code language that can be adopted by local jurisdictions to implement these measures for new buildings.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2021

Recent Updates in ETOE-2 and MC 2 -3

The MC 2 -3 code is a multigroup cross section generation code for fast reactor applications, developed by Argonne National Laboratory (ANL) under the DOE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. In this work, first, the cross section libraries for ENDF/B-VII.1 and ENDF/B-VIII.0 data were generated using the updated ETOE-2 code. Preliminary verification and validation tests of the ENDF/B-VII.1 MC 2 -3 library were performed with the selected fast reactor benchmark problems. Processing and verifying the libraries suggested that significant efforts would be required for thoroughly verifying the ENDF/B-VII.1 MC 2 -3 library and successfully processing the ENDF/B-VIII.0 MC 2 -3 library. Secondly, the cross section generation capability of MC 2 -3 was updated with the intermediate group lattice calculation and the equivalent Dancoff-factor cell (EDC) method to significantly improve the performance of a twodimensional assembly calculation using the method of characteristics (MOC). This effort was made useful in implementing and verifying the EDC method in the Griffin cross section API. Finally, we analyzed a SFR problem, for which unusually large deviations in core eigenvalues from Monte Carlo solutions were reported, by generating multigroup cross sections with MC 2 -3, performing core calculations with DIF3D-VARIANT, and analyzing cross section and eigenvalue results against Monte Carlo solutions. The analysis confirmed that the MC 2 -3/DIF3D solutions were in good agreement with Monte Carlo solutions, providing the correct process of accurately generating broad-group cross sections with MC 2 -3

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Numerical modeling of a proof-of-principle experiment on optical stochastic cooling at an electron storage ring

Cooling of beams circulating in storage rings is critical for many applications including particle colliders and synchrotron light sources. A method enabling unprecedented beam-cooling rates, optical stochastic cooling (OSC), was recently demonstrated in the Integrable Optics Test Accelerator (IOTA) electron storage ring at Fermilab [J. Jarvis , ]. This paper describes the numerical implementation of the OSC process in the particle-tracking program and discusses the validation of the developed model with available experimental data. The model is also employed to highlight some features associated with different modes of operation of OSC. The developed simulation tool should be valuable in guiding future configurations of optical stochastic cooling and, more broadly, modeling self-field-based beam manipulations. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗
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↗