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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Atom-resolved imaging with a silicon tip integrated into an on-chip scanning tunneling microscope

Limited throughput is a shortcoming of the Scanning Tunneling Microscope (STM), particularly when used for atomically precise lithography. To address this issue, we have developed an on-chip STM based on Microelectromechanical-Systems (MEMS) technology. The device reported here has one degree of freedom, replacing the Z axis in a conventional STM. The small footprint of the on-chip STM provides a great opportunity to increase STM throughput by incorporating a number of on-chip STMs in an array to realize parallel STM. The tip methodology adopted for the on-chip STM presented here, which is a batch-fabricated Si tip, makes our design conducive to this goal. In this work, we investigate the capability of this on-chip STM with an integrated Si tip for STM imaging. We integrate the on-chip STM into a commercial ultrahigh-vacuum STM system and perform imaging with atomic resolution on par with conventional STMs but at higher scan speeds due to the higher sensitivity of the MEMS actuator relative to a piezotube. The results attest that it is possible to achieve a parallel and high-throughput STM platform, which is a fully batch-fabricated MEMS STM nanopositioner capable of performing atomic-resolution STM imaging.

Instruments & Instrumentation↗
DOE OSTI2024

Scaling neural simulations in STACS

Abstract As modern neuroscience tools acquire more details about the brain, the need to move towards biological-scale neural simulations continues to grow. However, effective simulations at scale remain a challenge. Beyond just the tooling required to enable parallel execution, there is also the unique structure of the synaptic interconnectivity, which is globally sparse but has relatively high connection density and non-local interactions per neuron. There are also various practicalities to consider in high performance computing applications, such as the need for serializing neural networks to support potentially long-running simulations that require checkpoint-restart. Although acceleration on neuromorphic hardware is also a possibility, development in this space can be difficult as hardware support tends to vary between platforms and software support for larger scale models also tends to be limited. In this paper, we focus our attention on Simulation Tool for Asynchronous Cortical Streams (STACS), a spiking neural network simulator that leverages the Charm++ parallel programming framework, with the goal of supporting biological-scale simulations as well as interoperability between platforms. Central to these goals is the implementation of scalable data structures suitable for efficiently distributing a network across parallel partitions. Here, we discuss a straightforward extension of a parallel data format with a history of use in graph partitioners, which also serves as a portable intermediate representation for different neuromorphic backends. We perform scaling studies on the Summit supercomputer, examining the capabilities of STACS in terms of network build and storage, partitioning, and execution. We highlight how a suitably partitioned, spatially dependent synaptic structure introduces a communication workload well-suited to the multicast communication supported by Charm++. We evaluate the strong and weak scaling behavior for networks on the order of millions of neurons and billions of synapses, and show that STACS achieves competitive levels of parallel efficiency.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Porting hypre to heterogeneous computer architectures: Strategies and experiences

We report that linear systems are occurring in many applications, and solving them can take a large amount of the total simulation time. The high performance library hypre provides a variety of interfaces and linear solvers, including various multigrid methods, that have achieved good scalability on a variety of homogeneous parallel computer architectures. Heterogeneous architectures with nodes that have both CPUs and accelerators provide new challenges, since they require more fine-grained parallelism and reduced data movement between different memories on a single node as well as across nodes. We will discuss our experiences and strategies to port hypre to heterogeneous computers with accelerators, including the design of a new memory model, the use of abstractions, the BoxLoop macros in the structured and semi-structured interfaces, and the restructuring of algebraic multigrid (AMG) into modular components. We present numerical experiments comparing CPU and GPU performance for several test problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

The sweeper spectrometer for neutron invariant-mass spectroscopy at FRIB

Neutron invariant-mass spectroscopy (NIMS) is a key technique for studying unbound and weakly bound nuclei at the limits of stability. At the Facility for Rare Isotope Beams (FRIB), such measurements are performed using the Sweeper spectrometer, a large-gap, high-rigidity dipole system coupled to the MoNA-LISA neutron detector arrays. To meet the demands imposed by higher beam energies (>130 MeV/u) and the broad cocktail-beam selection available at FRIB, the spectrometer has recently been upgraded to improve particle-identification and detection performance. Upstream of the reaction target, a plastic scintillator with Silicon photomultiplier (SiPM) readout provides the global trigger and time reference, two parallel plate avalanche counters (PPACs) track the trajectories of incoming beam particles, and a silicon PIN detector measures the energy loss, ΔE, for charge (Z) identification. After the Sweeper magnet, the trajectories of the reaction products are tracked by two micro-pattern drift chambers (MPDCs), their charge (Z) is identified by a Frisch-grid ionization chamber (FG-IC), and their mass-to-charge ratio (A/Q) is deduced by time-of-flight measurement using a fast plastic scintillator read out by an array of photomultiplier tubes (PMTs). The detection system also incorporates the Modular Neutron Array (MoNA) for neutron detection and the CAESium-iodide scintillator ARray (CAESAR) for high-efficiency γ-ray measurements to enable full kinematic reconstruction. Performance was evaluated using a cocktail beam around 37 Al accelerated at E ≈ 130 MeV/u during the first FRIB campaign, demonstrating the readiness of the upgraded system for future studies of nuclei at and beyond the neutron drip line.

Particle identification methods↗
DOE OSTI2024

Impact of Reordering on the LU Factorization Performance of Bordered Block-Diagonal Sparse Matrix

Power engineers rely on computer-based simulation tools to assess grid performance and ensure security. At the core of these tools are solvers for sparse linear equations. When transformed into a bordered block-diagonal (BBD) structure, part of the sparse linear equation solving can be parallelized. This work focuses on using the Schur-complement-based method for LU factorization on BBD matrices, specifically, Jacobian matrices from large-scale systems. Our findings show that the natural ordering method outperforms the default ordering method in computational performance for each block of the BBD matrix. This observation is validated using synthetic 25k-bus and 70k-bus cases, showing a speedup of up to 38% when using natural ordering without permutation. Additionally, the impact of the number of partitions is studied, and the result shows that computational performance improves with more, smaller partitions in the BBD matrices.

BBD matrix↗
DOE OSTI2025

Priority-BF: A Task Manager for Priority-Based Scheduling

The increasing demand for computational resources, particularly in High-Performance Computing environments, necessitates to rethink how we handle job scheduling strategies. This work addresses the challenge of managing concurrent jobs with differing priorities on overloaded parallel systems, where strict QoS constraints are often difficult for users to define. Our solution relies on a qualitative description of priorities and pulls from two key approaches: the Easy-BF algorithm and the Conservative Backfilling algorithms. This solution improves the response time for high-priority jobs by 50% without affecting the overall system utilization. We show its applicability in several critical scenarios such as High-Performance Computing (HPC) resource management and in-situ computing.

Gainaru, Ana [ORNL]↗
DOE OSTI2025

Optimizing Management of Persistent Data Structures in High-Performance Analytics

Large-scale data analytics workflows ingest massive input data into various data structures, including graphs and key-value datastores. These data structures undergo multiple transformations and computations and are typically reused in incremental and iterative analytics workflows. Persisting in-memory views of these data structures enables reusing them beyond the scope of a single program run while avoiding repetitive raw data ingestion overheads. Memory-mapped I/O enables persisting in-memory data structures without data serialization and deserialization overheads. However, memory-mapped I/O lacks the key feature of persisting consistent snapshots of these data structures for incremental ingestion and processing. The obstacles to efficient virtual memory snapshots using memory-mapped I/O include background writebacks outside the application’s control, and the significantly high storage footprint of such snapshots. To address these limitations, we present Privateer, a memory and storage management tool that enables storage-efficient virtual memory snapshotting while also optimizing snapshot I/O performance. Here, we integrated Privateer into Metall, a state-of-the-art persistent memory allocator for C++, and the Lightning Memory-Mapped Database (LMDB), a widely-used key-value datastore in data analytics and machine learning. Privateer optimized application performance by 1.22× when storing data structure snapshots to node-local storage, and up to 16.7× when storing snapshots to a parallel file system. Privateer also optimizes storage efficiency of incremental data structure snapshots by up to 11× using data deduplication and compression.

Computer science↗
DOE OSTI2022

Perovskite superlattices with efficient carrier dynamics

Compared with their three-dimensional (3D) counterparts, low-dimensional metal halide perovskites (2D and quasi-2D; B 2 A n-1 M n X 3n+1 , such as B = R-NH 3 + , A = HC(NH 2 ) 2 + , Cs + ; M = Pb 2+ , Sn 2+ ; X = Cl - , Br - , I - ) with periodic inorganic-organic structures have shown promising stability and hysteresis-free electrical performance. However, their unique multiple-quantum-well structure limits the device efficiencies because of the grain boundaries and randomly oriented quantum wells in polycrystals. In single crystals, the carrier transport through the thickness direction is hindered by the layered insulating organic spacers. Furthermore, the strong quantum confinement from the organic spacers limits the generation and transport of free carriers. Also, lead-free metal halide perovskites have been developed but their device performance is limited by their low crystallinity and structural instability 11 . Here, in this paper, we report a low-dimensional metal halide perovskite BA 2 MA n-1 Sn n I 3n+1 (BA, butylammonium; MA, methylammonium; n = 1, 3, 5) superlattice by chemical epitaxy. The inorganic slabs are aligned vertical to the substrate and interconnected in a criss-cross 2D network parallel to the substrate, leading to efficient carrier transport in three dimensions. A lattice-mismatched substrate compresses the organic spacers, which weakens the quantum confinement. The performance of a superlattice solar cell has been certified under the quasi-steady state, showing a stable 12.36% photoelectric conversion efficiency. Moreover, an intraband exciton relaxation process may have yielded an unusually high open-circuit voltage (V OC ).

36 MATERIALS SCIENCE↗
DOE OSTI2024

Single-Shot Decoding of Good Quantum LDPC Codes

Abstract Quantum Tanner codes constitute a family of quantum low-density parity-check codes with good parameters, i.e., constant encoding rate and relative distance. In this article, we prove that quantum Tanner codes also facilitate single-shot quantum error correction (QEC) of adversarial noise, where one measurement round (consisting of constant-weight parity checks) suffices to perform reliable QEC even in the presence of measurement errors. We establish this result for both the sequential and parallel decoding algorithms introduced by Leverrier and Zémor. Furthermore, we show that in order to suppress errors over multiple repeated rounds of QEC, it suffices to run the parallel decoding algorithm for constant time in each round. Combined with good code parameters, the resulting constant-time overhead of QEC and robustness to (possibly time-correlated) adversarial noise make quantum Tanner codes alluring from the perspective of quantum fault-tolerant protocols.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

$\mathrm{Perturbo}$: A software package for ab initio electron–phonon interactions, charge transport and ultrafast dynamics

We report Perturbo is a software package for first-principles calculations of charge transport and ultrafast carrier dynamics in materials. The current version focuses on electron–phonon interactions and can compute phonon-limited transport properties such as the conductivity, carrier mobility and Seebeck coefficient. It can also simulate the ultrafast nonequilibrium electron dynamics in the presence of electron–phonon scattering. Perturbo uses results from density functional theory and density functional perturbation theory calculations as input, and employs Wannier interpolation to reduce the computational cost. It supports norm-conserving and ultrasoft pseudopotentials, spin–orbit coupling, and polar electron–phonon interactions for bulk and 2D materials. Hybrid MPI plus OpenMP parallelization is implemented to enable efficient calculations on large systems (up to at least 50 atoms) using high-performance computing. Taken together, Perturbo provides efficient and broadly applicable ab initio tools to investigate electron–phonon interactions and carrier dynamics quantitatively in metals, semiconductors, insulators, and 2D materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

ROOT RNTuple and EOS: The Next Generation of Event Data I/O

For several years, the ROOT team is developing the new RNTuple I/O subsystem in preparation of the next generation of collider experiments. Both HL-LHC and DUNE are expected to start data taking by the end of this decade. They pose unprecedented challenges to event data I/O in terms of data rates, event sizes, and event complexity. At the same time, the I/O landscape is becoming more diverse. HPC cluster file systems and object stores, NVMe disk cache layers in analysis facilities, and S3 storage on cloud resources are mixing with traditional XRootD-managed spinning disk pools.The ROOT team will finalize a first production version of the RNTuple binary format by the end of 2024. After this point, ROOT will provide backward compatibility for RNTuple data. This contribution provides an overview of the RNTuple feature set, the related R&D activities and the long-term vision for RNTuple. We report on performance, interface design, tooling, robustness, integration with experiment frameworks, and validation results, as well as recent R&D on parallel reading and writing and exploitation of modern hardware and storage systems. We will give an outlook on possible future features after a first production release.Collaboratively, the IT and EP departments at CERN have launched a formal project within the Research and Computing sector to evaluate the novel data format for physics analysis data utilized in LHC experiments and other fields. This part of the project focuses on validating the scalability of the EOS storage backend during the transition from the over 25 years old TTree production format to the newly developed RNTuple format, using both replicated and erasure-coded storage profiles.

Blomer, Jakob [CERN]↗
DOE OSTI2022

Multiphysics analysis system for heat pipe cooled micro-reactors employing PRAGMA-OpenFOAM-ANLHTP

A multiphysics analysis system for neutronics/thermo-mechanical/heat-pipe analysis of heat pipe cooled micro-reactors was developed using the PRAGMA code as the neutronics engine. PRAGMA, which used to be a GPU-based continuous-energy MC code for power reactor applications, now has an extended geometry package to handle geometries with unstructured meshes generated by the ANSYS Design-Modeler and Meshing. The NVIDIA ray tracing engine OptiX was exploited for efficient neutron transport on unstructured geometry. On the multiphysics side, the open-source CFD tool OpenFOAM and one-dimensional heat pipe analysis code ANLHTP were adopted. The manager-worker system based on the MPI dynamic process management (DPM) model enables efficient coupling of codes employing different parallelization schemes. With all the features, the multiphysics analysis of the one-sixth symmetrical MegaPower 2D core was performed and it demonstrated the benefit of the tight integration of the three-way coupling system and one-to-one geometry coupling strategy. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Effects of drifts on scrape-off layer transport in W7-X

Abstract Drifts affect particle, momentum, and energy transport in the scrape-off layer (SOL) of tokamaks and stellarators, altering plasma flows and creating asymmetries between divertors. To understand how drifts affect SOL transport in the W7-X island divertor, an experiment was performed to compare plasmas with matched core parameters but opposite magnetic field directions, and therefore opposite drift transport directions. Parallel flow measurements made with coherence imaging spectroscopy are interpreted with the aid of a diagnostic forward model and a 1D simple SOL model that includes the E × B drift. In low-density plasmas ( n ‾ e < 2 × 10 19 m −3 ), the poloidal E × B drift induces a large poloidal density asymmetry within the island SOL, as measured by divertor Langmuir probes. This in turn causes the parallel flow stagnation point to shift from the position halfway between targets to the X-point in the drift direction, leading to near-unidirectional flow throughout the SOL. As density increases, the effects of the poloidal E × B drift decrease substantially, resulting in a smaller density asymmetry and the development of a counter-streaming flow pattern. For the entire density range probed in this experiment ( n ‾ e = 1.5 − 6 × 10 19 m −3 ), the experimental observations are more consistent with the effects of the poloidal E × B drift than the radial E × B drift.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Transferring predictions of formation energy across lattices of increasing size*

In this study, we show the transferability of graph convolutional neural network (GCNN) predictions of the formation energy of the nickel-platinum solid solution alloy across atomic structures of increasing sizes. The original dataset was generated with the large-scale atomic/molecular massively parallel simulator using the second nearest-neighbor modified embedded-atom method empirical interatomic potential. Geometry optimization was performed on the initially randomly generated face centered cubic crystal structures and the formation energy has been calculated at each step of the geometry optimization, with configurations spanning the whole compositional range. Using data from various steps of the geometry optimization, we first trained our open-source, scalable implementation of GCNN called HydraGNN on a lattice of 256 atoms, which accounts well for the short-range interactions. Using this data, we predicted the formation energy for lattices of 864 atoms and 2048 atoms, which resulted in lower-than-expected accuracy due to the long-range interactions present in these larger lattices. We accounted for the long-range interactions by including a small amount of training data representative for those two larger sizes, whereupon the predictions of HydraGNN scaled linearly with the size of the lattice. Therefore, our strategy ensured scalability while reducing significantly the computational cost of training on larger lattice sizes.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A deep learning model for automatic analysis of cavities in irradiated materials

Transmission electron microscopy (TEM) is a commonly used technique in materials science for defect investigation. Quantitative analysis of defects is important for understanding the properties of a material, but manual analysis of TEM micrographs can be time-consuming and prone to error, especially when the defects have irregular shapes rather than spherical shapes. Many existing methods or deep learning models do not handle a wide range of sizes for the same object type within a single image. In this work, we present a framework that enables users to train an instance segmentation model called Mask R- CNN on any microstructure dataset, perform multi-detection on the same image at different scales, and obtain properties (e.g., size, area) of the objects based on the desired shape (e.g., circle, ellipse, rectangle). Additionally, we have developed a parallel detection module that uses multiple GPUs to increase the efficiency of the object detection process. We demonstrate the capabilities of our framework using a set of TEM images of cavities with different shapes, size distributions, and background contrasts. Finally, we show that the performance of our model in terms of density, size, and swelling of the cavities is comparable to the human average and that our model achieves the highest recall value compared to existing methods due to the use of image multi-rescaling.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Model-parallel Fourier neural operators as learned surrogates for large-scale parametric PDEs

Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep learning approaches. Once trained, FNOs can achieve speed-ups of multiple orders of magnitude over conventional numerical PDE solvers. However, due to the high dimensionality of their input data and network weights, FNOs have so far only been applied to two-dimensional or small three-dimensional problems. To remove this limited problem-size barrier, we propose a model-parallel version of FNOs based on domain-decomposition of both the input data and network weights. Here, we demonstrate that our model-parallel FNO is able to predict time-varying PDE solutions of over 2.6 billion variables on Perlmutter using up to 512 A100 GPUs and show an example of training a distributed FNO on the Azure cloud for simulating multiphase CO 2 dynamics in the Earth’s subsurface.

58 GEOSCIENCES↗
DOE OSTI2021

Development of NDE/NDT Tools for High-Volume & High-Speed Inspection of CFRP Structures in Automotive Manufacturing

Main advantages of the air-coupled ultrasound testing (ACUT) and electromagnetic testing (EMT) techniques for NDE of CFRP composites were non-contact sensing, scalability for high-speed inspection, cost-effectiveness, and non-hazardous operation. Despite these advantages, no systems that would satisfy the project requirements were commercially available. Hence, one of the major efforts of the Michigan State University (MSU) team at the initial stage of the project was to close this technological gap by developing, optimizing, and validating array sensors that would provide sufficient sensitivity, spatial coverage, and resolution for robust defect detection. Optimization of the ACUT and EMT sensor designs was performed using experimentally validated finite element models. Initial experiments using array probes were conducted on relatively flat CFRP samples. In parallel, the MSU team designed and assembled a portable platform with two robotic arms. The robots were equipped with newly designed sensors that enabled high-speed NDE of curved CFRP parts. Presently, the developed robotic platform can be used as a demo/template NDE system, which is easily adaptable to manufacturing environments and in-line NDE. The ACUT NDE system developed by the MSU team used a high-power 4-channel pulser receiver for parallel data acquisition. The array probes were designed by stacking commercially available ACUT transducers, which operated in the frequency range between 100 kHz and 500 kHz. MSU optimized the excitation procedure and developed wave focusing cones so as to reduce the crosstalk between the transducers and to provide higher pulse repletion frequency (PRF). The through-transmission (TT) and single-side access (SSA) inspection modes were successfully implemented. In the TT-ACUT, structural defects in CFRP were detected by passing ultrasonic waves through the test part. Hence, the ACUT transmitters and receivers needed to be placed on the opposite sides of the test part. In the SSA-ACUT, guided waves (GW) were excited in the test part using the transmitters and were sensed by the receivers from the same side. Multi-channel TT-ACUT and SSA-ACUT provided high-speed NDE, and were successfully validated on CFRP test samples with interlaminar delaminations and other embedded defects The EM techniques developed by the MSU team included: 1) eddy current testing (ECT), 2) capacitive imaging (CI) and hybrid dual-mode imaging. In ECT, structural damage was detected in CFRP using coils sensor arrays. In ECT, the excitation magnetic field is generated by passing an alternating current through a coil, which is placed above the test sample. The excitation field penetrates the conductive sample and induces the eddy currents in its transect. In turn, the eddy currents generate the reaction field, which affects the total field sensed by a coil. Hence, the presence of structural flaws will alter the eddy current flow and the picked-up signal. ECT is mostly sensitive to local changes of the electric conductivity of the test sample, and CFRPs are mostly conductive in the direction of carbon fibers. Hence, ECT was well suited for the detection of fiber damage/fiber irregularities. The MSU team developed printed circuit boards (PCB) with coil sensor arrays optimized for NDE of CFRP. Unlike most commercial probes designed for ECT of metallic structures, the MSU array probes were designed for operation in [1-10] MHz frequency range, which was optimal for low-conductive CFRP. Multiple sensing topologies (coil groups excitation/sensing arrangements) were implemented and successfully validated. Capacitive Imaging (CI) technique developed by MSU was complementary to ECT. In contrast to ECT, which was sensitive to local changes of the electrical conductivity, the CI was sensitive to local changes of the dielectric constant. Therefore, CI could provide information about matrix damage/matrix irregularities in CFRP. The MSU CI sensor arrays were made of multiple circular or rectangular open-plate capacitors printed on PCB. Sensors of this type are not commercially available. In addition to ECT and CI, the MSU team developed a hybrid (dual-mode) inductive/capacitive measurement technique that synergistically combined the benefits of inductive and capacitive sensing for rapid NDE of fiber reinforced polymer (FRP) composite structures. Fiber damage and fiber irregularities in FRPs were detected by configuring hybrid sensors as coil sensors. Similarly, matrix damage, matrix irregularities and interlaminar delaminations were detected by configuring hybrid sensors as capacitive sensors. ECT and CI were performed sequentially by means of electronic switching. Hence, eliminating the need for mounting two separate sensor arrays on the probe. Portable robotic platform was developed by MSU for multi-technique high-speed NDE of CFRP test parts. The platform had two 6-axis robots, which enabled inspection of curved parts in approximately a 6×6×6 ft 3 active scan area. On the software side, the MSU team integrated scripts for NDE hardware control with scripts for robot motion control. MSU also implemented automated path planning for the robots, reconstruction of part’s surfaces via stereovision, 3D rendering of inspection data, and image processing algorithms for enhanced defect detection. Automotive composite parts manufactured by Plasan Composites from Phase I were used to validate the ACUT and EMT techniques on representative testbeds. Among those parts were three X-braces for a Dodge Viper, one composite calibration plaque with known defects at known locations, and four other test sections, including sections from a front splitter, a corner section from a composite hood, and a high-pressure RTM panel made using non crimp fabric. Other test samples included CFRP and GFRP calibration plates with fiber/matrix defects fabricated at MSU/CVRC.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Analyzing the Performance Trade-Off in Implementing User-Level Threads

User-level threads have been widely adopted as a means of achieving lightweight concurrent execution without the costs of OS-level threads. Nevertheless, the costs of managing user-level threads represent a performance barrier that dictates how fine grained the concurrency exposed by an application can be without incurring significant overheads; this in turn may translate into insufficient parallelism to exploit highly parallel systems. This article is a deep dive into the fundamental costs in implementing user-level threads. We first identify that one of the highest sources of fork-join overheads stems from deviations, events that incur context switching during the execution of a thread and disrupt a run-to-completion execution. We then conduct an in-depth investigation of a wide spectrum of methods with respect to how they handle deviations while covering both parent- and child-first scheduling policies. Our methodology involves a comprehensive instruction- and cache-level analysis of all methods on several modern CPU architectures. Finally, the primary finding of our evaluation is that dynamic promotion methods that assume the absence of deviation and dynamically provide context-switching support offer the best trade-off between performance and capability when the likelihood of deviation is low.

97 MATHEMATICS AND COMPUTING↗