ACM Transactions on Mathematical Software最新文献_第6页

A Geometric Multigrid Method for Space-Time Finite Element Discretizations of the Navier–Stokes Equations and its Application to 3D Flow Simulation Navier-Stokes方程时空有限元离散的几何多重网格方法及其在三维流动模拟中的应用

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-03-21 DOI: https://dl.acm.org/doi/10.1145/3582492

Mathias Anselmann, Markus Bause

引用次数: 0

Algorithm 1033: Parallel Implementations for Computing the Minimum Distance of a Random Linear Code on Distributed-memory Architectures 算法1033:分布式存储结构下随机线性码最小距离计算的并行实现

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-03-21 DOI: https://dl.acm.org/doi/10.1145/3573383

Gregorio Quintana-Ortí, Fernando Hernando, Francisco D. Igual

引用次数: 0

Algorithm 1032: Bi-cubic Splines for Polyhedral Control Nets 算法1032:多面体控制网的双三次样条

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-03-21 DOI: https://dl.acm.org/doi/10.1145/3570158

Jörg Peters, Kyle Lo, Kȩstutis Karčiauskas

{"title":"Algorithm 1032: Bi-cubic Splines for Polyhedral Control Nets","authors":"Jörg Peters, Kyle Lo, Kȩstutis Karčiauskas","doi":"https://dl.acm.org/doi/10.1145/3570158","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3570158","url":null,"abstract":"For control nets outlining a large class of topological polyhedra, not just tensor-product grids, bi-cubic polyhedral splines form a piecewise polynomial, first-order differentiable space that associates one function with each vertex. Akin to tensor-product splines, the resulting smooth surface approximates the polyhedron. Admissible polyhedral control nets consist of quadrilateral faces in a grid-like layout, star-configuration where n ≠ 4 quadrilateral faces join around an interior vertex, n-gon configurations, where 2n quadrilaterals surround an n-gon, polar configurations where a cone of n triangles meeting at a vertex is surrounded by a ribbon of n quadrilaterals, and three types of T-junctions where two quad-strips merge into one. The bi-cubic pieces of a polyhedral spline have matching derivatives along their break lines, possibly after a known change of variables. The pieces are represented in Bernstein-Bézier form with coefficients depending linearly on the polyhedral control net, so that evaluation, differentiation, integration, moments, and so on, are no more costly than for standard tensor-product splines. Bi-cubic polyhedral splines can be used both to model geometry and for computing functions on the geometry. Although polyhedral splines do not offer nested refinement by refinement of the control net, polyhedral splines support engineering analysis of curved smooth objects. Coarse nets typically suffice since the splines efficiently model curved features. Algorithm 1032 is a C++ library with input-output example pairs and an IGES output choice.","PeriodicalId":50935,"journal":{"name":"ACM Transactions on Mathematical Software","volume":"65 ","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Enabling Research through the SCIP Optimization Suite 8.0 通过SCIP优化套件8.0实现研究

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-03-10 DOI: 10.1145/3585516

Ksenia Bestuzheva, Mathieu Besançon, Weikun Chen, Antonia Chmiela, Tim Donkiewicz, Jasper van Doornmalen, L. Eifler, Oliver Gaul, Gerald Gamrath, A. Gleixner, Leona Gottwald, Christoph Graczyk, Katrin Halbig, A. Hoen, Christopher Hojny, R. V. D. Hulst, T. Koch, M. Lübbecke, Stephen J. Maher, Frederic Matter, Erik Mühmer, Benjamin Müller, M. Pfetsch, D. Rehfeldt, Steffan Schlein, Franziska SchlÃŰsser, Felipe Serrano, Y. Shinano, Boro Sofranac, Mark Turner, Stefan Vigerske, Fabian Wegscheider, Philip A. Wellner, Dieter Weninger, Jakob Witzig

{"title":"Enabling Research through the SCIP Optimization Suite 8.0","authors":"Ksenia Bestuzheva, Mathieu Besançon, Weikun Chen, Antonia Chmiela, Tim Donkiewicz, Jasper van Doornmalen, L. Eifler, Oliver Gaul, Gerald Gamrath, A. Gleixner, Leona Gottwald, Christoph Graczyk, Katrin Halbig, A. Hoen, Christopher Hojny, R. V. D. Hulst, T. Koch, M. Lübbecke, Stephen J. Maher, Frederic Matter, Erik Mühmer, Benjamin Müller, M. Pfetsch, D. Rehfeldt, Steffan Schlein, Franziska SchlÃŰsser, Felipe Serrano, Y. Shinano, Boro Sofranac, Mark Turner, Stefan Vigerske, Fabian Wegscheider, Philip A. Wellner, Dieter Weninger, Jakob Witzig","doi":"10.1145/3585516","DOIUrl":"https://doi.org/10.1145/3585516","url":null,"abstract":"The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this article is on the role of the SCIP Optimization Suite in supporting research. SCIP’s main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP’s application as a research tool and as a platform for further developments. Furthermore, this article gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon SCIP.","PeriodicalId":50935,"journal":{"name":"ACM Transactions on Mathematical Software","volume":"49 1","pages":"1 - 21"},"PeriodicalIF":2.7,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42394524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 15

Algorithm 1036: ATC, An Advanced Tucker Compression Library for Multidimensional Data 算法1036:ATC，一种多维数据的高级Tucker压缩库

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-03-01 DOI: 10.1145/3585514

Wouter Baert, N. Vannieuwenhoven

{"title":"Algorithm 1036: ATC, An Advanced Tucker Compression Library for Multidimensional Data","authors":"Wouter Baert, N. Vannieuwenhoven","doi":"10.1145/3585514","DOIUrl":"https://doi.org/10.1145/3585514","url":null,"abstract":"We present ATC, a C++ library for advanced Tucker-based lossy compression of dense multidimensional numerical data in a shared-memory parallel setting, based on the sequentially truncated higher-order singular value decomposition (ST-HOSVD) and bit plane truncation. Several techniques are proposed to improve speed, memory usage, error control and compression rate. First, a hybrid truncation scheme is described which combines Tucker rank truncation and TTHRESH quantization. We derive a novel expression to approximate the error of truncated Tucker decompositions in the case of core and factor perturbations. We parallelize the quantization and encoding scheme and adjust this phase to improve error control. Implementation aspects are described, such as an ST-HOSVD procedure using only a single transposition. We also discuss several usability features of ATC, including the presence of multiple interfaces, extensive data type support, and integrated downsampling of the decompressed data. Numerical results show that ATC maintains state-of-the-art Tucker compression rates while providing average speed-up factors of 2.2 to 3.5 and halving memory usage. Our compressor provides precise error control, deviating only 1.4% from the requested error on average. Finally, ATC often achieves higher compression than non-Tucker-based compressors in the high-error domain.","PeriodicalId":50935,"journal":{"name":"ACM Transactions on Mathematical Software","volume":"49 1","pages":"1 - 25"},"PeriodicalIF":2.7,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42418864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

CPFloat: A C Library for Simulating Low-precision Arithmetic CPFloat:一个模拟低精度算术的C库

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-02-25 DOI: 10.1145/3585515

M. Fasi, M. Mikaitis

{"title":"CPFloat: A C Library for Simulating Low-precision Arithmetic","authors":"M. Fasi, M. Mikaitis","doi":"10.1145/3585515","DOIUrl":"https://doi.org/10.1145/3585515","url":null,"abstract":"One can simulate low-precision floating-point arithmetic via software by executing each arithmetic operation in hardware and then rounding the result to the desired number of significant bits. For IEEE-compliant formats, rounding requires only standard mathematical library functions, but handling subnormals, underflow, and overflow demands special attention, and numerical errors can cause mathematically correct formulae to behave incorrectly in finite arithmetic. Moreover, the ensuing implementations are not necessarily efficient, as the library functions these techniques build upon are typically designed to handle a broad range of cases and may not be optimized for the specific needs of rounding algorithms. CPFloat is a C library for simulating low-precision arithmetics. It offers efficient routines for rounding, performing mathematical computations, and querying properties of the simulated low-precision format. The software exploits the bit-level floating-point representation of the format in which the numbers are stored and replaces costly library calls with low-level bit manipulations and integer arithmetic. In numerical experiments, the new techniques bring a considerable speedup (typically one order of magnitude or more) over existing alternatives in C, C++, and MATLAB. To our knowledge, CPFloat is currently the most efficient and complete library for experimenting with custom low-precision floating-point arithmetic.","PeriodicalId":50935,"journal":{"name":"ACM Transactions on Mathematical Software","volume":"49 1","pages":"1 - 32"},"PeriodicalIF":2.7,"publicationDate":"2023-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46068558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

Task-based Parallel Programming for Scalable Matrix Product Algorithms 基于任务的可扩展矩阵积算法并行编程

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-02-24 DOI: 10.1145/3583560

E. Agullo, A. Buttari, A. Guermouche, J. Herrmann, Antoine Jego

{"title":"Task-based Parallel Programming for Scalable Matrix Product Algorithms","authors":"E. Agullo, A. Buttari, A. Guermouche, J. Herrmann, Antoine Jego","doi":"10.1145/3583560","DOIUrl":"https://doi.org/10.1145/3583560","url":null,"abstract":"Task-based programming models have succeeded in gaining the interest of the high-performance mathematical software community because they relieve part of the burden of developing and implementing distributed-memory parallel algorithms in an efficient and portable way.In increasingly larger, more heterogeneous clusters of computers, these models appear as a way to maintain and enhance more complex algorithms. However, task-based programming models lack the flexibility and the features that are necessary to express in an elegant and compact way scalable algorithms that rely on advanced communication patterns. We show that the Sequential Task Flow paradigm can be extended to write compact yet efficient and scalable routines for linear algebra computations. Although, this work focuses on dense General Matrix Multiplication, the proposed features enable the implementation of more complex algorithms. We describe the implementation of these features and of the resulting GEMM operation. Finally, we present an experimental analysis on two homogeneous supercomputers showing that our approach is competitive up to 32,768 CPU cores with state-of-the-art libraries and may outperform them for some problem dimensions. Although our code can use GPUs straightforwardly, we do not deal with this case because it implies other issues which are out of the scope of this work.","PeriodicalId":50935,"journal":{"name":"ACM Transactions on Mathematical Software","volume":"49 1","pages":"1 - 23"},"PeriodicalIF":2.7,"publicationDate":"2023-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48323698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Algorithm xxx: Encapsulated error, a direct approach to evaluate floating-point accuracy 算法xxx:封装错误，一种直接计算浮点精度的方法

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-02-17 DOI: 10.1145/3549205

Nestor Demeure, C. Chevalier, C. Denis, P. Dossantos-Uzarralde

引用次数: 0

Algorithm xxx: Encapsulated error, a direct approach to evaluate floating-point accuracy 算法xxx:封装错误，一种直接计算浮点精度的方法

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-02-17 DOI: https://dl.acm.org/doi/10.1145/3549205

Nestor Demeure, Cédric Chevalier, Christophe Denis, Pierre Dossantos-Uzarralde

引用次数: 0

Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement 稀疏近似分解与混合精度迭代细化的结合

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-02-06 DOI: 10.1145/3582493

P. Amestoy, A. Buttari, N. Higham, J. L’Excellent, Théo Mary, Bastien Vieublé

{"title":"Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement","authors":"P. Amestoy, A. Buttari, N. Higham, J. L’Excellent, Théo Mary, Bastien Vieublé","doi":"10.1145/3582493","DOIUrl":"https://doi.org/10.1145/3582493","url":null,"abstract":"The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision iterative refinement to enhance methods for sparse systems based on approximate sparse factorizations. In doing so, we first develop a new error analysis for LU- and GMRES-based iterative refinement under a general model of LU factorization that accounts for the approximation methods typically used by modern sparse solvers, such as low-rank approximations or relaxed pivoting strategies. We then provide a detailed performance analysis of both the execution time and memory consumption of different algorithms, based on a selected set of iterative refinement variants and approximate sparse factorizations. Our performance study uses the multifrontal solver MUMPS, which can exploit block low-rank factorization and static pivoting. We evaluate the performance of the algorithms on large, sparse problems coming from a variety of real-life and industrial applications showing that mixed-precision iterative refinement combined with approximate sparse factorization can lead to considerable reductions of both the time and memory consumption.","PeriodicalId":50935,"journal":{"name":"ACM Transactions on Mathematical Software","volume":"49 1","pages":"1 - 29"},"PeriodicalIF":2.7,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43937560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7