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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 1,063 records · Page 59
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Implementing Multidisciplinary and Multi-Zonal Applications Using MPI

Multidisciplinary and multi-zonal applications are an important class of applications in the area of Computational Aerosciences. In these codes, two or more distinct parallel programs or copies of a single program are utilized to model a single problem. To support such applications, it is common to use a programming model where a program is divided into several single program multiple data stream (SPMD) applications, each of which solves the equations for a single physical discipline or grid zone. These SPMD applications are then bound together to form a single multidisciplinary or multi-zonal program in which the constituent parts communicate via point-to-point message passing routines. Unfortunately, simple message passing models, like Intel's NX library, only allow point-to-point and global communication within a single system-defined partition. This makes implementation of these applications quite difficult, if not impossible. In this report it is shown that the new Message Passing Interface (MPI) standard is a viable portable library for implementing the message passing portion of multidisciplinary applications. Further, with the extension of a portable loader, fully portable multidisciplinary application programs can be developed. Finally, the performance of MPI is compared to that of some native message passing libraries. This comparison shows that MPI can be implemented to deliver performance commensurate with native message libraries.

Fineberg, Samuel A.↗
NASA NTRS1999

I/O Parallelization for the Goddard Earth Observing System Data Assimilation System (GEOS DAS)

The National Aeronautics and Space Administration (NASA) Data Assimilation Office (DAO) at the Goddard Space Flight Center (GSFC) has developed the GEOS DAS, a data assimilation system that provides production support for NASA missions and will support NASA's Earth Observing System (EOS) in the coming years. The DAO's support of the EOS project along with the requirement of producing long-term reanalysis datasets with an unvarying system levy a large I/O burden on the future system. The DAO has been involved in prototyping parallel implementations of the GEOS DAS for a number of years and is now converting the production version from shared-memory parallelism to distributed-memory parallelism using the portable Message-Passing Interface (MPI). If the MPI-based GEOS DAS is to meet these production requirements, we must make I/O from the parallel system efficient. We have designed a scheme that allows efficient I/O processing while retaining portability, reducing the need for post-processing, and producing data formats that are required by our users, both internal and external. The first phase of the GEOS DAS Parallel I/O System (GPIOS) will expand upon the common method of gathering global data to a Single PE for output. Instead of using a PE also tasked with primary computation, a number of PEs will be dedicated to I/O and its related tasks. This allows the data transformations and formatting required prior to output to take place asynchronously with respect to the GEOS DAS assimilation cycle, improving performance and generating output data sets in a format convenient for our users. I/O PEs can be added as needed to handle larger data volumes or to meet user file specifications. We will show I/O performance results from a prototype MPI GCM integrated with GPIOS. Phase two of GPIOS development will examine ways of integrating new software technologies to further improve performance and build scalability into the system. The maturing of MPI-IO implementations and other supporting libraries such as parallel HDF should provide performance gains while retaining portability.

Lucchesi, R.↗
NASA NTRS1999

Hydrazine Detection with a Tunable Diode Laser Spectrometer

Several instruments have been developed to measure low concentrations of hydrazine but none completely meet the sensitivity requirements while satisfying additional criteria such as quick response, stable calibration, interference free operation, online operation, reasonable cost, etc. A brief review is presented of the current technology including the electrochemical cell, the ion mobility spectrometer, the mass spectrometer, and the gas chromatograph. A review of the advantages and disadvantages of these instruments are presented here. The review also includes commercially unavailable technology such as the electronic nose and the Tunable Diode Laser (TDL) IR Spectrometer. It was found that the TDL could meet the majority of these criteria including fast response, minimum maintenance, portability, and reasonable cost. An experiment was conducted to demonstrate the feasibility of such a system using an existing (non-portable) instrument. A lead-salt tunable diode laser, cooled to 85 degrees Kelvin was used to record direct absorption and second-derivative spectra of Hydrazine at several pressures to study the sensitivity to low levels of Hydrazine. Spectra of NH3 and CO2 were used for wavelength identification of the scanned region. With a pathlength of 80 m, detection sensitivities of about 1 ppb were achieved for hydrazine in dry nitrogen at a cell pressure of 100 mbar. For spectroscopic detection of Hydrazine, spectral regions including strong Ammonia or Carbon Dioxide lines must be avoided. Strong Hydrazine absorption features were identified at 940/cm showing minimal contribution from Ammonia interferences as suitable candidates for Hydrazine gas detection. For the studies reported here, the particular laser diode could only cover the narrow regions near 962/cm and 965/cm where strong Ammonia interferences were expected. However, the high resolution (0.001/cm) of the TDL spectrometer allowed individual lines of Hydrazine to be identified away from interferences from either Ammonia or Carbon Dioxide, especially at lower pressures. A Hydrazine line was identified at 961.75/cm which was free from Ammonia absorption and would be suitable to monitor hydrazine levels. This paper also shows data on the degradation of the detectivity of Hydrazine with increasing pressure. Several design options for a portable unit are presented, including designs with near IR and Quantum Cascade laser components which do not require liquid nitrogen cooling.

Houseman, John↗
NASA NTRS1998

On the Efficacy of Source Code Optimizations for Cache-Based Systems

Obtaining high performance without machine-specific tuning is an important goal of scientific application programmers. Since most scientific processing is done on commodity microprocessors with hierarchical memory systems, this goal of "portable performance" can be achieved if a common set of optimization principles is effective for all such systems. It is widely believed, or at least hoped, that portable performance can be realized. The rule of thumb for optimization on hierarchical memory systems is to maximize temporal and spatial locality of memory references by reusing data and minimizing memory access stride. We investigate the effects of a number of optimizations on the performance of three related kernels taken from a computational fluid dynamics application. Timing the kernels on a range of processors, we observe an inconsistent and often counterintuitive impact of the optimizations on performance. In particular, code variations that have a positive impact on one architecture can have a negative impact on another, and variations expected to be unimportant can produce large effects. Moreover, we find that cache miss rates - as reported by a cache simulation tool, and confirmed by hardware counters - only partially explain the results. By contrast, the compiler-generated assembly code provides more insight by revealing the importance of processor-specific instructions and of compiler maturity, both of which strongly, and sometimes unexpectedly, influence performance. We conclude that it is difficult to obtain performance portability on modern cache-based computers, and comment on the implications of this result.

VanderWijngaart, Rob F.↗
NASA NTRS1998

On the Efficacy of Source Code Optimizations for Cache-Based Systems

Obtaining high performance without machine-specific tuning is an important goal of scientific application programmers. Since most scientific processing is done on commodity microprocessors with hierarchical memory systems, this goal of "portable performance" can be achieved if a common set of optimization principles is effective for all such systems. It is widely believed, or at least hoped, that portable performance can be realized. The rule of thumb for optimization on hierarchical memory systems is to maximize temporal and spatial locality of memory references by reusing data and minimizing memory access stride. We investigate the effects of a number of optimizations on the performance of three related kernels taken from a computational fluid dynamics application. Timing the kernels on a range of processors, we observe an inconsistent and often counterintuitive impact of the optimizations on performance. In particular, code variations that have a positive impact on one architecture can have a negative impact on another, and variations expected to be unimportant can produce large effects. Moreover, we find that cache miss rates-as reported by a cache simulation tool, and confirmed by hardware counters-only partially explain the results. By contrast, the compiler-generated assembly code provides more insight by revealing the importance of processor-specific instructions and of compiler maturity, both of which strongly, and sometimes unexpectedly, influence performance. We conclude that it is difficult to obtain performance portability on modern cache-based computers, and comment on the implications of this result.

VanderWijngaart, Rob F.↗
NASA NTRS2010

Biosensors for EVA: Improved Instrumentation for Ground-based Studies

During lunar excursions in the EVA suit, real-time measurement of metabolic rate is required to manage consumables and guide activities to ensure safe return to the base. Metabolic rate, or oxygen consumption (VO2), is normally measured from pulmonary parameters but cannot be determined with standard techniques in the oxygen-rich environment of a spacesuit. Our group has developed novel near infrared spectroscopic (NIRS) methods to calculate muscle oxygen saturation (SmO 2), hematocrit, and pH, and we recently demonstrated that we can use our NIRS sensor to measure VO 2 on the leg during cycling. Our NSBRI project has 4 objectives: (1) increase the accuracy of the metabolic rate calculation through improved prediction of stroke volume; (2) investigate the relative contributions of calf and thigh oxygen consumption to metabolic rate calculation for walking and running; (3) demonstrate that the NIRS-based noninvasive metabolic rate methodology is sensitive enough to detect decrement in VO 2 in a space analog; and (4) improve instrumentation to allow testing within a spacesuit. Over the past year we have made progress on all four objectives, but the most significant progress was made in improving the instrumentation. The NIRS system currently in use at JSC is based on fiber optics technology. Optical fiber bundles are used to deliver light from a light source in the monitor to the patient, and light reflected back from the patient s muscle to the monitor for spectroscopic analysis. The fiber optic cables are large and fragile, and there is no way to get them in and out of the test spacesuit used for ground-based studies. With complimentary funding from the US Army, we undertook a complete redesign of the sensor and control electronics to build a novel system small enough to be used within the spacesuit and portable enough to be used by a combat medic. In the new system the filament lamp used in the fiber optic system was replaced with a novel broadband near infrared LED light source. The compact grating spectrometer was replaced with a chip-scale spectrometer. With this new design, the sensor is 4 in 2 in 0.5 in, weighs 60 g, and no fiber optic cables are needed. The sensor, which contains the light source and the spectrometer, is adhered directly to the skin with medical grade adhesive. The sensor can be powered via the USB port of the laptop computer that controls the sensor operation. Alternatively, for studies in the spacesuit, the sensor can be powered by a small battery pack and operated by an ultra-portable hand-held computer. Both the handheld computer and battery pack will easily fit within the PLSS of the test spacesuit. System automation was significantly improved, to add features suggested by our colleagues in the Cardiovascular Laboratory and the NASA JSC Exercise Physiology and Countermeasures Project. The functionality and portability of this system were demonstrated in our UMass laboratory.

Soller, B.↗
NASA NTRS2006

Optics Program Modified for Multithreaded Parallel Computing

A powerful high-performance computer program for simulating and analyzing adaptive and controlled optical systems has been developed by modifying the serial version of the Modeling and Analysis for Controlled Optical Systems (MACOS) program to impart capabilities for multithreaded parallel processing on computing systems ranging from supercomputers down to Symmetric Multiprocessing (SMP) personal computers. The modifications included the incorporation of OpenMP, a portable and widely supported application interface software, that can be used to explicitly add multithreaded parallelism to an application program under a shared-memory programming model. OpenMP was applied to parallelize ray-tracing calculations, one of the major computing components in MACOS. Multithreading is also used in the diffraction propagation of light in MACOS based on pthreads [POSIX Thread, (where "POSIX" signifies a portable operating system for UNIX)]. In tests of the parallelized version of MACOS, the speedup in ray-tracing calculations was found to be linear, or proportional to the number of processors, while the speedup in diffraction calculations ranged from 50 to 60 percent, depending on the type and number of processors. The parallelized version of MACOS is portable, and, to the user, its interface is basically the same as that of the original serial version of MACOS.

Lou, John↗
NASA NTRS2006

SSRL Emergency Response Shore Tool

The SSRL Emergency Response Shore Tool (wherein SSRL signifies Smart Systems Research Laboratory ) is a computer program within a system of communication and mobile-computing software and hardware being developed to increase the situational awareness of first responders at building collapses. This program is intended for use mainly in planning and constructing shores to stabilize partially collapsed structures. The program consists of client and server components, runs in the Windows operating system on commercial off-the-shelf portable computers, and can utilize such additional hardware as digital cameras and Global Positioning System devices. A first responder can enter directly, into a portable computer running this program, the dimensions of a required shore. The shore dimensions, plus an optional digital photograph of the shore site, can then be uploaded via a wireless network to a server. Once on the server, the shore report is time-stamped and made available on similarly equipped portable computers carried by other first responders, including shore wood cutters and an incident commander. The staff in a command center can use the shore reports and photographs to monitor progress and to consult with structural engineers to assess whether a building is in imminent danger of further collapse.

Mah, Robert W.↗
NASA NTRS2004

Micro-Tubular Fuel Cells

Micro-tubular fuel cells that would operate at power levels on the order of hundreds of watts or less are under development as alternatives to batteries in numerous products - portable power tools, cellular telephones, laptop computers, portable television receivers, and small robotic vehicles, to name a few examples. Micro-tubular fuel cells exploit advances in the art of proton-exchange-membrane fuel cells. The main advantage of the micro-tubular fuel cells over the plate-and-frame fuel cells would be higher power densities: Whereas the mass and volume power densities of low-pressure hydrogen-and-oxygen-fuel plate-and-frame fuel cells designed to operate in the targeted power range are typically less than 0.1 W/g and 0.1 kW/L, micro-tubular fuel cells are expected to reach power densities much greater than 1 W/g and 1 kW/L. Because of their higher power densities, micro-tubular fuel cells would be better for powering portable equipment, and would be better suited to applications in which there are requirements for modularity to simplify maintenance or to facilitate scaling to higher power levels. The development of PEMFCs has conventionally focused on producing large stacks of cells that operate at typical power levels >5 kW. The usual approach taken to developing lower-power PEMFCs for applications like those listed above has been to simply shrink the basic plate-and-frame configuration to smaller dimensions. A conventional plate-and-frame fuel cell contains a membrane/electrode assembly in the form of a flat membrane with electrodes of the same active area bonded to both faces. In order to provide reactants to both electrodes, bipolar plates that contain flow passages are placed on both electrodes. The mass and volume overhead of the bipolar plates amounts to about 75 percent of the total mass and volume of a fuel-cell stack. Removing these bipolar plates in the micro-tubular fuel cell significantly increases the power density.

Kimble, Michael C.↗
NASA NTRS2012

Hybrid Rocket Experiment Station for Capstone Design

Portable hybrid rocket motors and test stands can be seen in many papers but none have been reported on the design or instrumentation at such a small magnitude. The design of this hybrid rocket and test stand is to be small and portable (suitcase size). This basic apparatus will be used for demonstrations in rocket propulsion. The design had to include all of the needed hardware to operate the hybrid rocket unit (with the exception of the external Oxygen tank). The design of this project includes making the correlation between the rocket's thrust and its size, the appropriate transducers (physical size, resolution, range, and cost), compatability with a laptop analog card, the ease of setup, and its portability.

Conley, Edgar↗
NASA NTRS2014

Low-Cost, Class D Testing of Spacecraft Photovoltaic Systems Can Reduce Risk

The end-to-end verification of a spacecraft photovoltaic power generation system requires light! A lowcost, portable, and end-to-end photovoltaic-system test appropriate for NASA's new generation of Class D missions is presented. High risk, low-cost, and quick-turn satellites rarely have the resources to execute the traditional approaches from higher-class (A-C) missions. The Class D approach, as demonstrated on the Lunar Atmospheric and Dust Environment Explorer (LADEE), utilizes a portable, metalhalide, theatre lamp for an end-to-end photovoltaic system test. While not as precise and comprehensive as the traditional Large Area Pulsed Solar Simulator (LAPSS) test, the LADEE method leverages minimal resources into an ongoing assessment program that can be applied through numerous stages of the mission. The project takes a true Class D approach in assessing the technical value of a costly, highfidelity performance test versus a simpler approach with less programmatic risk. The resources required are a fraction of that for a LAPSS test, and is easy to repeat due to its portability. Further, the test equipment can be handed down to future projects without building an on-site facility. At the vanguard of Class D missions, the LADEE team frequently wrestled with and challenged the status quo. The philosophy of risk avoidance at all cost, typical to Class A-C missions, simply could not be executed. This innovative and simple testing solution is contextualized to NASA Class D programs and a specific risk encountered during development of the LADEE Electrical Power System (EPS). Selection of the appropriate lamp and safety concerns are discussed, with examples of test results. Combined with the vendor's panellevel data and periodic inspection, the method ensures system integrity from Integration and Test (I&T) through launch. Following launch, mission operations tools are utilized to assess system performance based on a scant amount of available data.

power systems↗
NASA NTRS2014

Low-cost, Risk-Reduction Testing of Class D Spacecraft Photovoltaic Systems

The end-to-end verification of a spacecraft photovoltaic power generation system requires light! A low-cost, portable, and end-to-end photovoltaic-system test appropriate for NASAs new generation of Class D missions is presented. High risk, low-cost, and quick-turn satellites rarely have the resources to execute the traditional approaches from higher-class (A-C) missions. The Class D approach, as demonstrated on the Lunar Atmospheric and Dust Environment Explorer (LADEE), utilizes a portable, metal-halide, theatre lamp for an end-to-end photovoltaic system test. While not as precise and comprehensive as the traditional Large Area Pulsed Solar Simulator (LAPSS) test, the LADEE method leverages minimal resources into an ongoing assessment program that can be applied through numerous stages of the mission. The project takes a true Class D approach in assessing the technical value of a costly, high-fidelity performance test versus a simpler approach with less programmatic risk. The resources required are a fraction of that for a LAPSS test, and is easy to repeat due to its portability. Further, the test equipment can be handed down to future projects without building an on-site facility.At the vanguard of Class D missions, the LADEE team frequently wrestled with and challenged the status quo. The philosophy of risk avoidance at all cost, typical to Class A-C missions, simply could not be executed. This innovative and simple testing solution is contextualized to NASA Class D programs and a specific risk encountered during development of the LADEE Electrical Power System (EPS). Selection of the appropriate lamp and safety concerns are discussed, with examples of test results. Combined with the vendors panel-level data and periodic inspection, the method ensures system integrity from Integration and Test (IT) through launch. Following launch, mission operations tools are utilized to assess system performance based on a scant amount of available data.

photovoltaic↗
DOE OSTI2020

Methodology and Application of Physical Security Effectiveness Based on Dynamic Force-on-Force Modeling

This report describes the research and development being performed at INL towards a dynamic modeling and simulation framework to enable physical security optimization at commercial nuclear power plants. The framework is based on the dynamic modeling tool EMRALD and is demonstrated for applications that can result in physical security optimization. Two main applications are presented: 1. Integrating FLEX portable equipment performance with FOF models of a plant’s physical security posture, and 2. Location optimization of bullet resistant enclosure. The generic framework for modeling FLEX portable equipment is described in detail, followed by a case study modeling an adversarial attack aimed at causing a radiological release by sabotaging the plant’s power supply and its ultimate heat sink capabilities at a hypothetical PWR. Two distinct FLEX deployment strategies, series and parallel, are modeled with distinct timelines. The results of the adversarial attack modeled in a commercial FOF tool, AVERT, are integrated with the FLEX deployment model in EMRALD. Monte Carlo simulation is used to model the distribution of the timeline in FLEX deployment strategies. Thermal-hydraulic analysis of FLEX performance is performed in RELAP5 and integrated with the EMRALD simulations to provide more realistic timelines in the models. The results demonstrate that, even in the extreme case of a successful adversarial attack, deployment of FLEX equipment can result in a significantly high likelihood of preventing radiological release. The modeling and simulation framework of integrating FLEX equipment with FOF models enables the NPPs to credit FLEX portable equipment in the plant security posture, resulting in an efficient and optimized physical security. The objective of location optimization of BRE is to determine the best location in the plant for a new BRE being planned by the plant to enhance their physical security effectiveness. The plant physical security FOF model is integrated with EMRALD that performs Monte Carlo simulation to run different attack scenarios and a discrete set of potential BRE locations. Sensitivity analysis is used to determine the most effective location for the BRE. The optimization approach can be extended to wide applications such as location optimization of remotely operated weapons and other strategic fixed assets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Integrated solid-state rapid thermo-cycling system

Techniques, systems, and devices are disclosed for implementing a portable lab system for PCR testing. The portable lab system comprises a thermal cycling device including a first well and a second well to receive samples to be thermally cycled, a thermoelectric cooling (TEC) element coupled to the first well and the second well, and a controller to control operation of the TEC element. The portable lab system further includes an electronic interface including a power interface to supply power to the TEC element and the controller of the thermal cycling device to allow the TEC element to transfer energy from the first well to the second well when current flows through the TEC element in a first direction, and from the second well to the first well when current flows through the TEC element in a second direction, and a data interface to collect data from the controller.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Software Quality Assurance for High Performance Computing Containers

Software containers are a key channel for delivering portable and reproducible scientific software in high performance computing (HPC) environments. HPC environments are different from other types of computing environments primarily due to usage of the message passing interface (MPI) and drivers for specialized hard- ware to enable distributed computing capabilities. This distinction directly impacts how software containers are built for HPC applications and can complicate software quality assurance efforts including portability and performance. This work introduces a strategy for building containers for HPC applications that adopts layering as a mechanism for software quality assurance. The strategy is demonstrated across three different HPC systems, two of them petaflops scale with entirely different interconnect technologies and/or processor chipsets but running the same container. Performance consequences of the containerization strategy are found to be less than 5-14% while still achieving portable and reproducible containers for HPC systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Porting the Nonlinear Optimization Library HiOp to Accelerator-Based Hardware Architectures

While interior point method has been the centerpiece of nonlinear programming tools used in science and engineering, its reliance on linear solvers that can tackle sparse symmetric indefinite and highly ill-conditioned problems made it difficult to implement it effectively on hardware accelerators. HiOp optimization package attempts to provide an implementation of the interior point method suitable for hardware accelerators by compressing the original sparse problem to produce an underlying linear problem that is dense and of manageable size. Implementations of dense linear solvers are more mature and utilize hardware accelerators better than their sparse counterparts. There is a number of important domain problems, such as optimal power flow analysis for power grids, where the sparse problem can be effectively compressed and deploying dense linear solver within the interior point method can improve performance. Here we describe a portable implementation of HiOp optimization engine, which uses a linear solver from Magma library and runs entirely on hardware accelerators. To compress the problem, HiOp uses customized mixed dense-sparse linear algebra. All HiOp kernels are implemented using Umpire and RAJA portability libraries. We describe details of the implementation and discuss trade-offs between performance, portability and development cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Early experiences on the OLCF Frontier system with AthenaPK and Parthenon–Hydro

The Oak Ridge Leadership Computing Facility (OLCF) has been preparing the nation's first exascale system, Frontier, for production and end users. Frontier is based on HPE Cray's new EX architecture and Slingshot interconnect and features 74 cabinets of optimized 3rd Gen AMD EPYC CPUs for HPC and AI and AMD Instinct 250X accelerators. As a part of this preparation, “real-world” user codes have been selected to help assess the functionality, performance, and usability of the system. This article describes early experiences using the system in collaboration with the Hamburg Observatory for two selected codes, which have since been adopted in the OLCF test harness. Experiences discussed include efforts to resolve performance variability and per-cycle slowdowns. Results are shown for a performance portable astrophysical magnetohydronamics code, AthenaPK, and a mini-application stressing the core functionality of a performance portable block-structured adaptive mesh refinement framework, Parthenon-Hydro. Here, these results show good scaling characteristics to the full system. At the largest scale, the Parthenon-Hydro miniapp reaches a total of $1.7$ $\times$ $10^{13}$ zone-cycles/s on 9216 nodes (73,728 logical GPUs) at ≈92% weak scaling parallel efficiency (starting from a single node using a second-order, finite-volume method).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Vidyut3d: A GPU accelerated fluid solver for non-equilibrium plasmas on adaptive grids

We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures, in this work. Our plasma fluid model solves the coupled conservation equations for species transport, electrostatic Poisson and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive-grid/particle management library, AMReX, and is portable over widely available vendor specific GPU architectures. We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth-order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on capacitive discharges and atmospheric pressure streamer propagation. We demonstrate the use of our solver on two 3D simulation cases: an atmospheric streamer propagation in Ar-H2 mixtures and a low pressure three-electrode radio frequency reactor. Our performance studies on three different CPU+GPU architectures indicate ~ 150-400X speed-up using AMD and NVIDIA GPUs per time step compared to a single CPU core for a 4 million cell simulation with 15 species.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗