ACM Transactions on Mathematical Software最新文献_第5页

Improvements to SLEPc in Releases 3.14–3.18 版本3.14-3.18对SLEPc的改进

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-06-07 DOI: 10.1145/3603373

J. Román, F. Alvarruiz, C. Campos, Lisandro Dalcin, P. Jolivet, A. L. Daviña

引用次数: 0

Algorithms for Parallel Generic hp-adaptive Finite Element Software 并行通用hp自适应有限元软件算法

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-06-05 DOI: https://dl.acm.org/doi/10.1145/3603372

Marc Fehling, Wolfgang Bangerth

{"title":"Algorithms for Parallel Generic hp-adaptive Finite Element Software","authors":"Marc Fehling, Wolfgang Bangerth","doi":"https://dl.acm.org/doi/10.1145/3603372","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3603372","url":null,"abstract":"The hp-adaptive finite element method (FEM) – where one independently chooses the mesh size (h) and polynomial degree (p) to be used on each cell – has long been known to have better theoretical convergence properties than either h- or p-adaptive methods alone. However, it is not widely used, owing at least in parts to the difficulty of the underlying algorithms and the lack of widely usable implementations. This is particularly true when used with continuous finite elements. Herein, we discuss algorithms that are necessary for a comprehensive and generic implementation of hp-adaptive finite element methods on distributed-memory, parallel machines. In particular, we will present a multi-stage algorithm for the unique enumeration of degrees of freedom (DoFs) suitable for continuous finite element spaces, describe considerations for weighted load balancing, and discuss the transfer of variable size data between processes. We illustrate the performance of our algorithms with numerical examples, and demonstrate that they scale reasonably up to at least 16 384 Message Passing Interface (MPI) processes. We provide a reference implementation of our algorithms as part of the open-source library <monospace>deal.II</monospace>.","PeriodicalId":50935,"journal":{"name":"ACM Transactions on Mathematical Software","volume":"37 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505943","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

Accurate Calculation of Euclidean Norms Using Double-word Arithmetic 用双字算法精确计算欧几里得范数

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-03-21 DOI: https://dl.acm.org/doi/10.1145/3568672

Vincent Lefèvre, Nicolas Louvet, Jean-Michel Muller, Joris Picot, Laurence Rideau

引用次数: 0

Robust Topological Construction of All-hexahedral Boundary Layer Meshes 全六面体边界层网格的鲁棒拓扑构造

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-03-21 DOI: https://dl.acm.org/doi/10.1145/3577196

Maxence Reberol, Kilian Verhetsel, François Henrotte, David Bommes, Jean-François Remacle

{"title":"Robust Topological Construction of All-hexahedral Boundary Layer Meshes","authors":"Maxence Reberol, Kilian Verhetsel, François Henrotte, David Bommes, Jean-François Remacle","doi":"https://dl.acm.org/doi/10.1145/3577196","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3577196","url":null,"abstract":"We present a robust technique to build a topologically optimal all-hexahedral layer on the boundary of a model with arbitrarily complex ridges and corners. The generated boundary layer mesh strictly respects the geometry of the input surface mesh, and it is optimal in the sense that the hexahedral valences of the boundary edges are as close as possible to their ideal values (local dihedral angle divided by 90°). Starting from a valid watertight surface mesh (all-quad in practice), we build a global optimization integer programming problem to minimize the mismatch between the hexahedral valences of the boundary edges and their ideal values. The formulation of the integer programming problem relies on the duality between boundary hexahedral configurations and triangulations of the disk, which we reframe in terms of integer constraints. The global problem is solved efficiently by performing combinatorial branch-and-bound searches on a series of sub-problems defined in the vicinity of complicated ridges/corners, where the local mesh topology is necessarily irregular because of the inherent constraints in hexahedral meshes. From the integer solution, we build the topology of the all-hexahedral layer, and the mesh geometry is computed by untangling/smoothing. Our approach is fully automated, topologically robust, and fast.","PeriodicalId":50935,"journal":{"name":"ACM Transactions on Mathematical Software","volume":"20 8","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505934","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 1031: MQSI—Monotone Quintic Spline Interpolation 算法1031:mqsi -单调五次样条插值

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-03-21 DOI: https://dl.acm.org/doi/10.1145/3570157

Thomas Lux, Layne T. Watson, Tyler Chang, William Thacker

引用次数: 0

Certifying Zeros of Polynomial Systems Using Interval Arithmetic 用区间算法证明多项式系统的零点

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-03-21 DOI: https://dl.acm.org/doi/10.1145/3580277

Paul Breiding, Kemal Rose, Sascha Timme

引用次数: 0

Algorithm 1034: An Accelerated Algorithm to Compute the Qn Robust Statistic, with Corrections to Constants 算法1034:一种计算Qn鲁棒统计量的加速算法，并对常数进行校正

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-03-21 DOI: https://dl.acm.org/doi/10.1145/3576920

Thierry Fahmy

引用次数: 0

Event-Based Automatic Differentiation of OpenMP with OpDiLib 基于OpDiLib的OpenMP事件自动鉴别

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-03-21 DOI: https://dl.acm.org/doi/10.1145/3570159

Johannes Blühdorn, Max Sagebaum, Nicolas Gauger

{"title":"Event-Based Automatic Differentiation of OpenMP with OpDiLib","authors":"Johannes Blühdorn, Max Sagebaum, Nicolas Gauger","doi":"https://dl.acm.org/doi/10.1145/3570159","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3570159","url":null,"abstract":"We present the new software OpDiLib, a universal add-on for classical operator overloading AD tools that enables the automatic differentiation (AD) of OpenMP parallelized code. With it, we establish support for OpenMP features in a reverse mode operator overloading AD tool to an extent that was previously only reported on in source transformation tools. We achieve this with an event-based implementation ansatz that is unprecedented in AD. Combined with modern OpenMP features around OMPT, we demonstrate how it can be used to achieve differentiation without any additional modifications of the source code; neither do we impose a priori restrictions on the data access patterns, which makes OpDiLib highly applicable. For further performance optimizations, restrictions like atomic updates on adjoint variables can be lifted in a fine-grained manner. OpDiLib can also be applied in a semi-automatic fashion via a macro interface, which supports compilers that do not implement OMPT. We demonstrate the applicability of OpDiLib for a pure operator overloading approach in a hybrid parallel environment. We quantify the cost of atomic updates on adjoint variables and showcase the speedup and scaling that can be achieved with the different configurations of OpDiLib in both the forward and the reverse pass.","PeriodicalId":50935,"journal":{"name":"ACM Transactions on Mathematical Software","volume":"49 ","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505960","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

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 : 2023-03-21 DOI: https://dl.acm.org/doi/10.1145/3582493

Patrick Amestoy, Alfredo Buttari, Nicholas J. Higham, Jean-Yves L’Excellent, Theo Mary, Bastien Vieublé

{"title":"Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement","authors":"Patrick Amestoy, Alfredo Buttari, Nicholas J. Higham, Jean-Yves L’Excellent, Theo Mary, Bastien Vieublé","doi":"https://dl.acm.org/doi/10.1145/3582493","DOIUrl":"https://doi.org/https://dl.acm.org/doi/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":"74 ","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505908","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

Newly Released Capabilities in the Distributed-Memory SuperLU Sparse Direct Solver 分布式内存SuperLU稀疏直接求解器新发布的功能

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-03-21 DOI: https://dl.acm.org/doi/10.1145/3577197

Xiaoye S. Li, Paul Lin, Yang Liu, Piyush Sao

{"title":"Newly Released Capabilities in the Distributed-Memory SuperLU Sparse Direct Solver","authors":"Xiaoye S. Li, Paul Lin, Yang Liu, Piyush Sao","doi":"https://dl.acm.org/doi/10.1145/3577197","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3577197","url":null,"abstract":"We present the new features available in the recent release of <monospace>SuperLU_DIST</monospace>, Version 8.1.1. <monospace>SuperLU_DIST</monospace> is a distributed-memory parallel sparse direct solver. The new features include (1) a 3D communication-avoiding algorithm framework that trades off inter-process communication for selective memory duplication, (2) multi-GPU support for both NVIDIA GPUs and AMD GPUs, and (3) mixed-precision routines that perform single-precision LU factorization and double-precision iterative refinement. Apart from the algorithm improvements, we also modernized the software build system to use CMake and Spack package installation tools to simplify the installation procedure. Throughout the article, we describe in detail the pertinent performance-sensitive parameters associated with each new algorithmic feature, show how they are exposed to the users, and give general guidance of how to set these parameters. We illustrate that the solver’s performance both in time and memory can be greatly improved after systematic tuning of the parameters, depending on the input sparse matrix and underlying hardware.","PeriodicalId":50935,"journal":{"name":"ACM Transactions on Mathematical Software","volume":"25 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505961","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