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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Real-space solution to the electronic structure problem for nearly a million electrons

We report a Kohn–Sham density functional theory calculation of a system with more than 200 000 atoms and 800 000 electrons using a real-space high-order finite-difference method to investigate the electronic structure of large spherical silicon nanoclusters. Our system of choice was a 20 nm large spherical nanocluster with 202 617 silicon atoms and 13 836 hydrogen atoms used to passivate the dangling surface bonds. To speed up the convergence of the eigenspace, we utilized Chebyshev-filtered subspace iteration, and for sparse matrix–vector multiplications, we used blockwise Hilbert space-filling curves, implemented in the PARSEC code. For this calculation, we also replaced our orthonormalization + Rayleigh–Ritz step with a generalized eigenvalue problem step. We utilized all of the 8192 nodes (458 752 processors) on the Frontera machine at the Texas Advanced Computing Center. We achieved two Chebyshev-filtered subspace iterations, yielding a good approximation of the electronic density of states. Our work pushes the limits on the capabilities of the current electronic structure solvers to nearly 106 electrons and demonstrates the potential of the real-space approach to efficiently parallelize large calculations on modern high-performance computing platforms.

Chemistry↗
DOE OSTI2018

High-Performance Sparse Matrix-Matrix Products on Intel KNL and Multicore Architectures

Sparse matrix-matrix multiplication (SpGEMM) is a computational primitive that is vastly used in areas ranging from traditional numerical applications to recent big data analysis and machine learning. While many SpGEMM algorithms have been proposed, hardware specific optimizations for multi- and many-core processors are lacking and a detailed analysis of their performance under various use cases and matrices is not available. We firstly identify and mitigate multiple bottlenecks with memory management and thread scheduling on Intel Xeon Phi (Knights Landing or KNL). Specifically targeting multi- and many-core processors, we develop a hash-table-based algorithm and optimize a heap-based shared-memory SpGEMM algorithm. We investigate their performance together with other publicly available codes. Different from the literature, our evaluation also includes use cases that are representative of real graph algorithms, such as multi-source breadth-first search or triangle counting. Our hash-table and heap-based algorithms are showing significant speedups from libraries in the majority of the cases while different algorithms dominate the other scenarios with different matrix size, sparsity, compression factor and operation type. We wrap up in-depth evaluation results and make a recipe to give the best SpGEMM algorithm for target scenario. In conclusion, a critical finding is that hash-table-based SpGEMM gets a significant performance boost if the nonzeros are not required to be sorted within each row of the output matrix.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Berkeley Efficient Long-Read to Long-Read Aligner and Overlapper (BELLA) v1.0

BELLA is a long-read overlapper and read-to-read aligner that exploits novel approaches for selecting reliable k-mer seeds for filtering and for detecting overlapping read pairs to reconstruct the whole genome. BELLA uses a sparse matrix-matrix multiplication for high-performance overlap detection and then performs pairwise alignment on the overlapping read pairs. BELLA can be built with different pre-existing aligners to use on each read pair, so precision rates are determined by those aligners. Our evaluations include real and synthetic datasets with varying size and complexity and include recall, precision, and running time. BELLA's overlap detection retains nearly all true alignments, with recall rates that exceed other aligners, yet it filters enough read pairs that the running time, including pairwise alignments, is closer to tools that only perform overlapping and is significantly faster than tools that also perform alignment

Guidi, Giulia↗
DOE OSTI2022

Novel Solver Algorithms for Nearly Singular Linear Systems Arising in Combustion Modelling

Direct Numerical Simulations of realistic combustion devices are extremely challenging due to the wide separation of scales in the simulation, for example an internal combustion (IC) engine chamber, and the flame thickness of a high-pressure flame. The PeleLMeX solver uses adaptive mesh refinement (AMR) to evolve multi-species reacting flows in the low Mach number limit at the Exascale and relies on an embedded boundary (EB) approach to represent complex geometries. In that framework, the EB geometries often give rise to very small cut-cells along the boundary, which translate into extreme ill-conditioning of the pressure-projection, with eigenvalues that span 15-16 orders of magnitude. In this talk, we focus on the case of a typical IC piston bowl geometry for which we present on a novel approach towards solving these nearly singular linear systems with ILU-based, C-AMG smoothers on massively parallel architectures. In particular, we use scaling and equilibration algorithms to handle the non-normality of the upper triangular factors. This enables us to approximate the highly sequential triangular solve algorithm, embedded in the AMG smoothing-solve phase, with Jacobi iterations. This approximation can be written as a convergent Neumann series whose terms are composed of highly parallel sparse matrix vector multiplications. The result is an algorithm that substantially decreases setup and solve time, compared to state-of-the-art, for these challenging linear systems.

combustion modelling↗
DOE OSTI2026

A Flexible Forwarding Scheme to Improve Latency-Bound Irregular P2P Communication in MPI

We propose an algorithm to efficiently perform latency-bound communication scenarios that consist of many small messages. In these parallel scenarios, processes typically pass around a lot of small-sized messages of a few KBs of size. Performing communication operations with P2P MPI routines or collective MPI routines (including neighborhood collectives) in such scenarios may not always yield the optimal results and may not resolve the latency bottleneck. To this end, we develop a regular structure called virtual process topology (VPT) on which the messages can be communicated in a structured and controlled manner. Using parameters of this topology, one can tune the rate of aggression in tackling the latency costs. We demonstrate that our communication algorithm is preferable to MPI P2P and collective routines for latency-bound communication and it can easily be adapted only by replacing calls to MPI routines in a parallel application. We show how to adapt existing topology-aware mapping heuristics to address the volume overhead due to communicating messages on the VPT. Moreover, we propose a novel swap-based mapping heuristic to address this overhead by optimizing the maximum volume handled by a process. Experiments on synthetic communication graphs as well as real-world applications such as parallel Canonical Polyadic sparse tensor decomposition and parallel sparse matrix-dense matrix multiplication show that our approach is a powerful way of overcoming the bottlenecks posed by sparse and latency-bound irregular communication.

communication algorithm↗
DOE OSTI2020

Sparse Matrix-Based HPC Tomography

Tomographic imaging has benefited from advances in X-ray sources, detectors and optics to enable novel observations in science, engineering and medicine. These advances have come with a dramatic increase of input data in the form of faster frame rates, larger fields of view or higher resolution, so high performance solutions are currently widely used for analysis. Tomographic instruments can vary significantly from one to another, including the hardware employed for reconstruction: from single CPU workstations to large scale hybrid CPU/GPU supercomputers. Furthermore, flexibility on the software interfaces and reconstruction engines are also highly valued to allow for easy development and prototyping. This paper presents a novel software framework for tomographic analysis that tackles all aforementioned requirements. The proposed solution capitalizes on the increased performance of sparse matrix-vector multiplication and exploits multi-CPU and GPU reconstruction over MPI. Furthermore, the solution is implemented in Python and relies on CuPy for fast GPU operators and CUDA kernel integration, and on SciPy for CPU sparse matrix computation. As opposed to previous tomography solutions that are tailor-made for specific use cases or hardware, the proposed software is designed to provide flexible, portable and high-performance operators that can be used for continuous integration at different production environments, but also for prototyping new experimental settings or for algorithmic development. The experimental results demonstrate how our implementation can even outperform state-of-the-art software packages used at advanced X-ray sources worldwide.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Spray: Sparse Reductions of Arrays in OPEN MP

We present SPRAY, an open-source header-only C++ library for sparse reductions of arrays. SPRAY is meant for applications in which a large array is collaboratively updated by multiple threads using an associative and commutative operation such as +=. Especially when each thread accesses only parts of the array, SPRAY can perform significantly better than OPENMP's built-in reduction clause or atomic updates, while also using less memory than the former. SPRAY provides both an easy-to-use interface that can serve as a drop-in replacement for OPENMP reductions and a selection of reducer objects that accumulate the final result in different thread-safe ways. We demonstrate SPRAY through multiple test cases including the LULESH shock hydrodynamics code and a transpose-matrix-vector multiplication for sparse matrices stored in CSR format. SPRAY reductions outperform built-in OPENMP reductions consistently, in some cases improving run time and memory overhead by 20X, and even beating domain-specific approaches such as Intel MKI, by over 2X in some cases. Furthermore, SPRAY reductions have a minimal impact on the code base, requiring only a few lines of source code changes. Once in place, SPRAY reduction schemes can be switched easily, allowing performance portability and tuning opportunities by separating performance-critical implementation details from application code.

OpenMP↗
DOE OSTI2019

A microbenchmark characterization of the Emu chick

The Emu Chick is a prototype system designed around the concept of migratory memory-side processing. Rather than transferring large amounts of data across power-hungry, high-latency interconnects, the Emu Chick moves lightweight thread contexts to near-memory cores before the beginning of each memory read. The current prototype hardware uses FPGAs to implement cache-less “Gossamer” cores for computational work and rely on a typical stationary core (PowerPC) to run basic operating system functions and migrate threads between nodes. In this multi-node characterization of the Emu Chick, we extend an earlier single-node investigation of the the memory bandwidth characteristics of the system through benchmarks like STREAM, pointer chasing, and sparse matrix-vector multiplication. Here, we compare the Emu Chick hardware to architectural simulation and an Intel Xeon-based platform. Our results demonstrate that for many basic operations the Emu Chick can use available memory bandwidth more efficiently than a more traditional, cache-based architecture although bandwidth usage suffers for computationally intensive workloads like SpMV. Moreover, the Emu Chick provides stable, predictable performance with up to 65% of the peak bandwidth utilization on a random-access pointer chasing benchmark with weak locality.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Optimization of Condensed Matter Physics Application with OpenMP Tasking Model

The Density Matrix Renormalization Group (DMRG++) is a condensed matter physics application used to study superconductivity properties of materials. It’s main computations consist of calculating hamiltonian matrix which requires sparse matrix-vector multiplications. This paper presents task-based parallelization and optimization strategies of the Hamiltonian algorithm. The algorithm is implemented as a mini-application in C++ and parallelized with OpenMP. The optimization leverages tasking features, such as dependencies or priorities included in the OpenMP standard 4.5. The code refactoring targets performance as much as programmability. The optimized version achieves a speedup of 8.0× with 8 threads and 20.5× with 40 threads on a Power9 computing node while reducing the memory consumption to 90 MB with respect to the original code, by adding less than ten OpenMP directives.

Criado, Joel↗
DOE OSTI2023

Solving the electronic structure problem for over 100000 atoms in real space

Using a real-space high-order finite-difference approach, we investigate the electronic structure of large spherical silicon nanoclusters. Within Kohn-Sham density functional theory and using pseudopotentials, we report the self-consistent field convergence of a system with over 100000 atoms: a Si 107,641 ⁢H 9,084 nanocluster with a diameter of 16 nm. Our approach uses Chebyshev-filtered subspace iteration to speed up the convergence of the eigenspace, and blockwise Hilbert space-filling curves to speed up sparse matrix-vector multiplications, all of which are implemented in the parsec code. For the largest system, we utilized 2048 nodes (114 688 cores) on the Frontera machine in the Texas Advanced Computing Center. Our quantitative analysis of the electronic structure shows how it gradually approaches its bulk counterpart as a function of nanocluster size. The band gap is enlarged due to quantum confinement in nanoclusters, but decreases as the system size increases, as expected. In conclusion, our work serves as a proof of concept for the capacity of the real-space approach in efficiently parallelizing very large calculations using high-performance computer platforms, which can straightforwardly be replicated in other systems with more than 10 5 atoms.

0-dimensional systems↗
DOE OSTI2014

On the Suitability of MPI as a PGAS Runtime

Partitioned Global Address Space (PGAS) models are emerging as a popular alternative to MPI models for designing scalable applications. At the same time, MPI remains a ubiquitous communication subsystem due to its standardization, high performance, and availability on leading platforms. In this paper, we explore the suitability of using MPI as a scalable PGAS communication subsystem. We focus on the Remote Memory Access (RMA) communication in PGAS models which typically includes {\em get, put,} and {\em atomic memory operations}. We perform an in-depth exploration of design alternatives based on MPI. These alternatives include using a semantically-matching interface such as MPI-RMA, as well as not-so-intuitive interfaces such as MPI two-sided with a combination of multi-threading and dynamic process management. With an in-depth exploration of these alternatives and their shortcomings, we propose a novel design which is facilitated by the data-centric view in PGAS models. This design leverages a combination of highly tuned MPI two-sided semantics and an automatic, user-transparent split of MPI communicators to provide asynchronous progress. We implement the asynchronous progress ranks approach and other approaches within the Communication Runtime for Exascale which is a communication subsystem for Global Arrays. Our performance evaluation spans pure communication benchmarks, graph community detection and sparse matrix-vector multiplication kernels, and a computational chemistry application. The utility of our proposed PR-based approach is demonstrated by a 2.17x speed-up on 1008 processors over the other MPI-based designs.

Computational modeling↗
DOE OSTI2016

Reducing Parallel Communication in Algebraic Multigrid through Sparsification

Algebraic multigrid (AMG) is an $\mathcal{O}(n)$ solution process for many large sparse linear systems. A hierarchy of progressively coarser grids which utilize complementary relaxation and interpolation operators is constructed. High-energy error is reduced by relaxation, while low-energy error is mapped to coarse-grid matrices and reduced there. However, large parallel communication costs often limit parallel scalability. Furthermore, as the multigrid hierarchy is formed, each coarse matrix is formed through a triple matrix product. The resulting coarse grids often have significantly more nonzeros per row than the original fine-grid operator, thereby generating high parallel communication costs associated with sparse matrix-vector multiplication (SpMV) on coarse levels. In this paper, we introduce a method that systematically removes entries in coarse-grid matrices after the hierarchy is formed, leading to improved communication costs. We sparsify by removing weakly connected or unimportant entries in the matrix, leading to improved solve time. The main trade-off is that if the heuristic identifying unimportant entries is used too aggressively, then AMG convergence can suffer. To counteract this, the original hierarchy is retained, allowing entries to be reintroduced into the solver hierarchy if convergence is too slow. This enables a balance between communication cost and convergence, as necessary. In this paper we present new algorithms for reducing communication and present a number of computational experiments in support.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Optimizing Irregular Communication with Neighborhood Collectives and Locality-Aware Parallelism

Irregular communication often limits both the performance and scalability of parallel applications. Typically, applications individually implement irregular communication as point-to-point, and any optimizations are integrated directly into the application. As a result, these optimizations lack portability. It is difficult to optimize point-to-point messages within MPI, as the interface for single messages provides no information on the collection of all communication to be performed. However, the persistent neighbor collective API, released in the MPI 4 standard, provides an interface for portable optimizations of irregular communication within MPI libraries. This paper presents methods for implementing existing optimizations for irregular communication within neighborhood collectives, analyzes the impact of replacing point-to-point communication in existing codebases such as Hypre BoomerAMG with neighborhood collectives, and finally shows up to a 1.38x speedup on sparse matrix-vector multiplication communication within a BoomerAMG solve through the use of our optimized neighbor collectives. Here, the authors analyze three implementations of persistent neighborhood collectives for Alltoallv: an unoptimized wrapper of standard point-to-point communication, and two locality-aware aggregating methods. The second locality-aware implementation exposes an non-standard interface to perform additional optimization, and the authors present the additional 0.07x speedup from the extended interface. All optimizations are available in an open-source codebase, MPI Advance, which sits on top of MPI, allowing for optimizations to be added into existing codebases regardless of the system MPI install.

AMG↗
DOE OSTI2021

Understanding HPC Benchmark Performance on Intel Broadwell and Cascade Lake Processors

Hardware platforms in high performance computing are constantly getting more complex to handle even when considering multicore CPUs alone. Numerous features and configuration options in the hardware and the software environment that are relevant for performance are not even known to most application users or developers. Microbenchmarks, i.e., simple codes that fathom a particular aspect of the hardware, can help to shed light on such issues, but only if they are well understood and if the results can be reconciled with known facts or performance models. The insight gained from microbenchmarks may then be applied to real applications for performance analysis or optimization. In this paper we investigate two modern Intel x86 server CPU architectures in depth: Broadwell EP and Cascade Lake SP. We highlight relevant hardware configuration settings that can have a decisive impact on code performance and show how to properly measure on-chip and off-chip data transfer bandwidths. The new victim L3 cache of Cascade Lake and its advanced replacement policy receive due attention. Finally we use DGEMM, sparse matrix-vector multiplication, and the HPCG benchmark to make a connection to relevant application scenarios.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Performance Analysis and Optimal Node-aware Communication for Enlarged Conjugate Gradient Methods

Krylov methods are a key way of solving large sparse linear systems of equations but suffer from poor strong scalability on distributed memory machines. Furthermore, this is due to high synchronization costs from large numbers of collective communication calls alongside a low computational workload. Enlarged Krylov methods address this issue by decreasing the total iterations to convergence, an artifact of splitting the initial residual and resulting in operations on block vectors. In this article, we present a performance study of an enlarged Krylov method, Enlarged Conjugate Gradients (ECG), noting the impact of block vectors on parallel performance at scale. Most notably, we observe the increased overhead of point-to-point communication as a result of denser messages in the sparse matrix-block vector multiplication kernel. Additionally, we present models to analyze expected performance of ECG, as well as motivate design decisions. Most importantly, we introduce a new point-to-point communication approach based on node-aware communication techniques that increases efficiency of the method at scale.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A Recursive Hypergraph Bipartitioning Framework for Reducing Bandwidth and Latency Costs Simultaneously

Intelligent partitioning models are commonly used for efficient parallelization of irregular applications on distributed systems. These models usually aim to minimize a single communication cost metric, which is either related to communication volume or message count. However, both volume- and message-related metrics should be taken into account during partitioning for a more efficient parallelization. There are only a few works that consider both of them and they usually address each in separate phases of a two-phase approach. In this work, we propose a recursive hypergraph bipartitioning framework that reduces the total volume and total message count in a single phase. In this framework, the standard hypergraph models, nets of which already capture the bandwidth cost, are augmented with message nets. The message nets encode the message count so that minimizing conventional cutsize captures the minimization of bandwidth and latency costs together. Our model provides a more accurate representation of the overall communication cost by incorporating both the bandwidth and the latency components into the partitioning objective. The use of the widely-adopted successful recursive bipartitioning framework provides the flexibility of using any existing hypergraph partitioner. In conclusion, the experiments on instances from different domains show that our model on the average achieves up to 52 percent reduction in total message count and hence results in 29 percent reduction in parallel running time compared to the model that considers only the total volume.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Sparse matrix‐vector and matrix‐multivector products for the truncated SVD on graphics processors

Summary Many practical algorithms for numerical rank computations implement an iterative procedure that involves repeated multiplications of a vector, or a collection of vectors, with both a sparse matrix and its transpose. Unfortunately, the realization of these sparse products on current high performance libraries often deliver much lower arithmetic throughput when the matrix involved in the product is transposed. In this work, we propose a hybrid sparse matrix layout, named CSRC, that combines the flexibility of some well‐known sparse formats to offer a number of appealing properties: (1) CSRC can be obtained at low cost from the popular CSR (compressed sparse row) format; (2) CSRC has similar storage requirements as CSR; and especially, (3) the implementation of the sparse product kernels delivers high performance for both the direct product and its transposed variant on modern graphics accelerators thanks to a significant reduction of atomic operations compared to a conventional implementation based on CSR. This solution thus renders considerably higher performance when integrated into an iterative algorithm for the truncated singular value decomposition (SVD), such as the randomized SVD or, as demonstrated in the experimental results, the block Golub–Kahan–Lanczos algorithm.

Aliaga, José I.↗