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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Parallelized domain decomposition for multi-dimensional Lagrangian random walk mass-transfer particle tracking schemes

Lagrangian particle tracking schemes allow a wide range of flow and transport processes to be simulated accurately, but a major challenge is numerically implementing the inter-particle interactions in an efficient manner. This article develops a multi-dimensional, parallelized domain decomposition (DDC) strategy for mass-transfer particle tracking (MTPT) methods in which particles exchange mass dynamically. We show that this can be efficiently parallelized by employing large numbers of CPU cores to accelerate run times. In order to validate the approach and our theoretical predictions we focus our efforts on a well-known benchmark problem with pure diffusion, where analytical solutions in any number of dimensions are well established. In this work, we investigate different procedures for “tiling” the domain in two and three dimensions (2-D and 3-D), as this type of formal DDC construction is currently limited to 1-D. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-D for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work. For an optimally subdivided diffusion problem, the 2-D parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run-up to around 2700 cores, reducing a 5 h simulation to 8 s, while the 3-D algorithm maintains appreciable speedup up to 1700 cores.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

AMReX

AMReX is a software framework for the development and implementation of massively parallel algorithms using block-structured adaptive mesh refinement (AMR). Block-structured AMR provides the basis for the temporal and spatial discretization strategy for a large variety of applications of interest to the DOE. AMReX provides a unified infrastructure with the functionality needed for applications to be able to effectively and efficiently utilize machines from laptops to exascale accelerator-based architectures. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving accurate descriptions of different physical processes in complex multi-physics algorithms. AMReX supports algorithms that solve systems of partial differential equations (PDEs) in simple or complex geometries, and those that use particles and/or particle-mesh operations to represent component physical processes.

Zhang, Weiqun↗
DOE OSTI2016

On-the-fly Doppler Broadening with Probability Table Interpolation for Unresolved Resonance Region in RMC

With the rapid development of computational power and parallel algorithms, Monte Carlo method has been widely investigated and used in neutron transport simulations due to its advantages in geometry modelling and usage of continuous energy point-wise cross sections. Nowadays the road has been paved to couple Monte Carlo codes with thermal-hydraulics codes to make multi-physics calculations. One of the most important aspects of thermal-hydraulics feedback is the detailed temperature distribution, which demands temperature dependent cross sections in neutron transport simulations. The conventional pre-generated cross section libraries at each temperature point are no longer feasible for detailed temperature distributions because of tremendous memory footprint. Hence, different on-the-fly Doppler broadening methods have been proposed for resolved resonance energy region and thermal energy region, such as the interpolation, regress model fitting, multipole representation (MPR), target motion sampling (TMS) and different integration algorithms based on Doppler broadening equation. Compared to resolved resonance energy region and thermal energy region, the representation of cross sections in unresolved resonance region is slightly different. As a result of the limitation of experiment measurements, the overlapped resonances cannot be distinguished from each other and the statistic average resonance parameters are given in the evaluated nuclear data file. In early applications, infinite-dilute pointwise cross sections were obtained from average parameters and were directly used in neutron simulations. However, it was proven that these infinite-dilute pointwise cross sections cannot capture the energy self-shielding effect, thus leading to an overestimate of reaction rates and usually an underestimate of k{sub eff} owing to the increased absorption rates and increased scattering probability to energy below unresolved resonance region where the capture-to-fission ratio is typically higher. This phenomenon is of great importance especially for problems where there is a considerable flux in unresolved resonance region. Then the probability table method was put forward by Levitt to take energy self-shielding effect into account, which provides probability distribution function of cross sections in unresolved resonance region instead of specific cross section values. The probability distribution function is presented in the form of tables and the mean values are equal to the infinite dilution cross sections. To obtain the temperature dependent cross sections in unresolved energy region, there are two different methods. One is to calculate cross sections directly from average resonance parameters and their statistical distributions , which is effective and precise but time-consuming. The other is to interpolate between pre-generated probability table files, which is much more efficient. In this paper, on-the-fly Doppler broadening of cross sections in unresolved resonance regions based on probability tables interpolation was implemented in RMC codes as a supplement to on-the-fly Doppler broadening for resolved resonance energy region and thermal region, which is based on the integration of Doppler broadening equation. The results of criticality calculation and depletion calculation show that on-the-fly Doppler broadening for the whole energy region is accurate and efficient. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

ConnectIt: a framework for static and incremental parallel graph connectivity algorithms

Connected components is a fundamental kernel in graph applications. The fastest existing multicore algorithms for solving graph connectivity are based on some form of edge sampling and/or linking and compressing trees. However, many combinations of these design choices have been left unexplored. In this paper, we design the ConnectIt framework, which provides different sampling strategies as well as various tree linking and compression schemes. ConnectIt enables us to obtain several hundred new variants of connectivity algorithms, most of which extend to computing spanning forest. In addition to static graphs, we also extend ConnectIt to support mixes of insertions and connectivity queries in the concurrent setting. We present an experimental evaluation of ConnectIt on a 72-core machine, which we believe is the most comprehensive evaluation of parallel connectivity algorithms to date. Compared to a collection of state-of-the-art static multicore algorithms, we obtain an average speedup of 12.4x (2.36x average speedup over the fastest existing implementation for each graph). Using ConnectIt, we are able to compute connectivity on the largest publicly-available graph (with over 3.5 billion vertices and 128 billion edges) in under 10 seconds using a 72-core machine, providing a 3.1x speedup over the fastest existing connectivity result for this graph, in any computational setting. For our incremental algorithms, we show that our algorithms can ingest graph updates at up to several billion edges per second. To guide the user in selecting the best variants in ConnectIt for different situations, we provide a detailed analysis of the different strategies. Finally, we show how the techniques in ConnectIt can be used to speed up two important graph applications: approximate minimum spanning forest and SCAN clustering.

Computer Science↗
DOE OSTI2020

Speeding up particle track reconstruction using a parallel Kalman filter algorithm

One of the most computationally difficult problems expected for the High-Luminosity Large Hadron Collider (HL-LHC) is determining the trajectory of charged particles during event reconstruction. Algorithms used at the LHC today rely on Kalman filtering, which builds physical trajectories incrementally while incorporating material effects and error estimation. Recognizing the need for faster computational throughput, we have adapted Kalman-filter-based methods for highly parallel, many-core SIMD architectures that are now prevalent in high-performance hardware. In this paper, we discuss the design and performance of the improved tracking algorithm, referred to as mkFit. A key piece of the algorithm is the Matriplex library, containing dedicated code to optimally vectorize operations on small matrices. The physics performance of the mkFit algorithm is comparable to the nominal CMS tracking algorithm when reconstructing tracks from simulated proton-proton collisions within the CMS detector. We study the scaling of the algorithm as a function of the parallel resources utilized and find large speedups both from vectorization and multi-threading. mkFit achieves a speedup of a factor of 6 compared to the nominal algorithm when run in a single-threaded application within the CMS software framework.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

Multi-jagged: A scalable parallel spatial partitioning algorithm

Geometric partitioning is fast and effective for load-balancing dynamic applications, particularly those requiring geometric locality of data (particle methods, crash simulations). We present, to our knowledge, the first parallel implementation of a multidimensional-jagged geometric partitioner. In contrast to the traditional recursive coordinate bisection algorithm (RCB), which recursively bisects subdomains perpendicular to their longest dimension until the desired number of parts is obtained, our algorithm does recursive multi-section with a given number of parts in each dimension. By computing multiple cut lines concurrently and intelligently deciding when to migrate data while computing the partition, we minimize data movement compared to efficient implementations of recursive bisection. We demonstrate the algorithm's scalability and quality relative to the RCB implementation in Zoltan on both real and synthetic datasets. Our experiments show that the proposed algorithm performs and scales better than RCB in terms of run-time without degrading the load balance. Lastly, our implementation partitions 24 billion points into 65,536 parts within a few seconds and exhibits near perfect weak scaling up to 6K cores.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Parallel Cut-Cell Algorithm for the Free-Boundary Grad--Shafranov Problem

A parallel cut-cell algorithm is described to solve the free-boundary problem of the Grad--Shafranov equation. The algorithm reformulates the free-boundary problem in an irregular bounded domain and its important aspects include a searching algorithm for the magnetic axis and separatrix, a surface integral along the irregular boundary to determine the boundary values, an approach to optimize the coil current based on a targeting plasma shape, Picard iterations with Aitken's acceleration for the resulting nonlinear problem, and a Cartesian grid embedded boundary method to handle the complex geometry. Here the algorithm is implemented in parallel using a standard domain-decomposition approach and a good parallel scaling is observed. Numerical results verify the accuracy and efficiency of the free-boundary Grad--Shafranov solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Hybrid massively parallel fast sweeping method for static Hamilton–Jacobi equations

The fast sweeping method is a popular algorithm for solving a variety of static Hamilton–Jacobi equations. Fast sweeping algorithms for parallel computing have been developed, but are severely limited. In this work, we present a multilevel, hybrid parallel algorithm that combines the desirable traits of two distinct parallel methods. The fine and coarse grained components of the algorithm take advantage of heterogeneous computer architecture common in high performance computing facilities. We present the algorithm and demonstrate its effectiveness on a set of example problems including optimal control, dynamic games, and seismic wave propagation. We give results for convergence, parallel scaling, and show state-of-the-art speedup values for the fast sweeping method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Data communications in a parallel active messaging interface of a parallel computer

Algorithm selection for data communications in a parallel active messaging interface (`PAMI`) of a parallel computer, the PAMI composed of data communications endpoints, each endpoint including specifications of a client, a context, and a task, endpoints coupled for data communications through the PAMI, including associating in the PAMI data communications algorithms and ranges of message sizes so that each algorithm is associated with a separate range of message sizes; receiving in an origin endpoint of the PAMI a data communications instruction, the instruction specifying transmission of a data communications message from the origin endpoint to a target endpoint, the data communications message characterized by a message size; selecting, from among the associated algorithms and ranges, a data communications algorithm in dependence upon the message size; and transmitting, according to the selected data communications algorithm from the origin endpoint to the target endpoint, the data communications message.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Data communications for a collective operation in a parallel active messaging interface of a parallel computer

Algorithm selection for data communications in a parallel active messaging interface (`PAMI`) of a parallel computer, the PAMI composed of data communications endpoints, each endpoint including specifications of a client, a context, and a task, endpoints coupled for data communications through the PAMI, including associating in the PAMI data communications algorithms and bit masks; receiving in an origin endpoint of the PAMI a collective instruction, the instruction specifying transmission of a data communications message from the origin endpoint to a target endpoint; constructing a bit mask for the received collective instruction; selecting, from among the associated algorithms and bit masks, a data communications algorithm in dependence upon the constructed bit mask; and executing the collective instruction, transmitting, according to the selected data communications algorithm from the origin endpoint to the target endpoint, the data communications message.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Reconstruction of Charged Particle Tracks in Realistic Detector Geometry Using a Vectorized and Parallelized Kalman Filter Algorithm

One of the most computationally challenging problems expected for the High-Luminosity Large Hadron Collider (HL-LHC) is finding and fitting particle tracks during event reconstruction. Algorithms used at the LHC today rely on Kalman filtering, which builds physical trajectories incrementally while incorporating material e ects and error estimation. Recognizing the need for faster computational throughput, we have adapted Kalman-filterbased methods for highly parallel, many-core SIMD and SIMT architectures that are now prevalent in high-performance hardware. Previously we observed significant parallel speedups, with physics performance comparable to CMS standard tracking, on Intel Xeon, Intel Xeon Phi, and (to a limited extent) NVIDIA GPUs. While early tests were based on artificial events occurring inside an idealized barrel detector, we showed subsequently that our mkFit software builds tracks successfully from complex simulated events (including detector pileup) occurring inside a geometrically accurate representation of the CMS-2017 tracker. Here, we report on advances in both the computational and physics performance of mkFit, as well as progress toward integration with CMS production software. Recently we have improved the overall eciency of the algorithm by preserving short track candidates at a relatively early stage rather than attempting to extend them over many layers. Moreover, mkFit formerly produced an excess of duplicate tracks; these are now explicitly removed in an additional processing step. We demonstrate that with these enhancements, mkFit becomes a suitable choice for the first iteration of CMS tracking, and eventually for later iterations as well. We plan to test this capability in the CMS High Level Trigger during Run 3 of the LHC, with an ultimate goal of using it in both the CMS HLT and oine reconstruction for the HL-LHC CMS tracker.

Cerati, Giuseppe↗
DOE OSTI2020

Novel Geometric Operations for Linear Programming

This report summarizes the work performed under the project "Linear Programming in Strongly Polynomial Time." Linear programming (LP) is a classic combinatorial optimization problem heavily used directly and as an enabling subroutine in integer programming (IP). Specifically IP is the same as LP except that some solution variables must take integer values (e.g. to represent yes/no decisions). Together LP and IP have many applications in resource allocation including general logistics, and infrastructure design and vulnerability analysis. The project was motivated by the PI's recent success developing methods to efficiently sample Voronoi vertices (essentially finding nearest neighbors in high-dimensional point sets) in arbitrary dimension. His method seems applicable to exploring the high-dimensional convex feasible space of an LP problem. Although the project did not provably find a strongly-polynomial algorithm, it explored multiple algorithm classes. The new medial simplex algorithms may still lead to solvers with improved provable complexity. We describe medial simplex algorithms and some relevant structural/complexity results. We also designed a novel parallel LP algorithm based on our geometric insights and implemented it in the Spoke-LP code. A major part of the computational step is many independent vector dot products. Our parallel algorithm distributes the problem constraints across processors. Current commercial and high-quality free LP solvers require all problem details to fit onto a single processor or multicore. Our new algorithm might enable the solution of problems too large for any current LP solvers. We describe our new algorithm, give preliminary proof-of-concept experiments, and describe a new generator for arbitrarily large LP instances.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Accelerating population balance-Monte Carlo simulation for coagulation dynamics from the Markov jump model, stochastic algorithm and GPU parallel computing

This paper proposes a comprehensive framework for accelerating population balance-Monte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulation-rule matrix of differentially-weighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule provides a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the two-particle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance–rejection processes by single-looping over all particles, and meanwhile the mean time-step of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentially-weighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number of simulation particles in a zero-dimensional system (single cell). Finally, for a spatially inhomogeneous multi-dimensional (multi-cell) simulation, the proposed fast PBMC is performed in each cell, and multiple cells are parallel processed by multi-cores on a GPU that can implement the massively threaded data-parallel tasks to obtain remarkable speedup ratio (comparing with CPU computation, the speedup ratio of GPU parallel computing is as high as 200 in a case of 100 cells with 10 000 simulation particles per cell). These accelerating approaches of PBMC are demonstrated in a physically realistic Brownian coagulation case. The computational accuracy is validated with benchmark solution of discrete-sectional method. The simulation results show that the comprehensive approach can attain very favorable improvement in cost without sacrificing computational accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

PASTA: A Parallel Sparse Tensor Algorithm Benchmark Suite

Tensor methods have gained increasingly attention from various applications, including machine learning, quantum chemistry, healthcare analytics, social network analysis, data mining, and signal processing, to name a few. Sparse tensors and their algorithms become critical to further improve the performance of these methods and enhance the interpretability of their output. This work presents a sparse tensor algorithm benchmark suite (PASTA) for single- and multi-core CPUs. To the best of our knowledge, this is the first benchmark suite for sparse tensor world. PASTA targets on: 1) helping application users to evaluate different computer systems using its representative computational workloads; 2) providing insights to better utilize existed computer architecture and systems and inspiration for the future design. This benchmark suite will be publicly released.

HPC, sparse tensor, benchmark↗
DOE OSTI2019

Speeding up Particle Track Reconstruction in the CMS Detector using a Vectorized and Parallelized Kalman Filter Algorithm

Building particle tracks is the most computationally intense step of event reconstruction at the LHC. With the increased instantaneous luminosity and associated increase in pileup expected from the High-Luminosity LHC, the computational challenge of track finding and fitting requires novel solutions. The current track reconstruction algorithms used at the LHC are based on Kalman filter methods that achieve good physics performance. By adapting the Kalman filter techniques for use on many-core SIMD architectures such as the Intel Xeon and Intel Xeon Phi and (to a limited degree) NVIDIA GPUs, we are able to obtain significant speedups and comparable physics performance. New optimizations, including a dedicated post-processing step to remove duplicate tracks, have improved the algorithm's performance even further. Here we report on the current structure and performance of the code and future plans for the algorithm.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗