ACM Transactions on Mathematical Software最新文献_第7页

Distributed ℋ2-Matrices for Boundary Element Methods 边界元法的分布h - 2矩阵

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-02-01 DOI: 10.1145/3582494

S. Börm

{"title":"Distributed ℋ2-Matrices for Boundary Element Methods","authors":"S. Börm","doi":"10.1145/3582494","DOIUrl":"https://doi.org/10.1145/3582494","url":null,"abstract":"Standard discretization techniques for boundary integral equations, e.g., the Galerkin boundary element method, lead to large densely populated matrices that require fast and efficient compression techniques like the fast multipole method or hierarchical matrices. If the underlying mesh is very large, running the corresponding algorithms on a distributed computer is attractive, e.g., since distributed computers frequently are cost-effective and offer a high accumulated memory bandwidth. Compared to the closely related particle methods, for which distributed algorithms are well-established, the Galerkin discretization poses a challenge, since the supports of the basis functions influence the block structure of the matrix and therefore the flow of data in the corresponding algorithms. This article introduces distributed ℋ2-matrices, a class of hierarchical matrices that is closely related to fast multipole methods and particularly well-suited for distributed computing. While earlier efforts required the global tree structure of the ℋ2-matrix to be stored in every node of the distributed system, the new approach needs only local multilevel information that can be obtained via a simple distributed algorithm, allowing us to scale to significantly larger systems. Experiments show that this approach can handle very large meshes with more than 130 million triangles efficiently.","PeriodicalId":50935,"journal":{"name":"ACM Transactions on Mathematical Software","volume":" ","pages":"1 - 21"},"PeriodicalIF":2.7,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43867034","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 10xx: SuiteSparse:GraphBLAS: parallel graph algorithms in the language of sparse linear algebra 算法10xx: SuiteSparse:GraphBLAS:稀疏线性代数语言中的并行图算法

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-01-25 DOI: https://dl.acm.org/doi/10.1145/3577195

Timothy A. Davis

引用次数: 0

Algorithm 1037: SuiteSparse:GraphBLAS: Parallel Graph Algorithms in the Language of Sparse Linear Algebra 算法1037:SuiteSparse:GraphBLAS:稀疏线性代数语言中的并行图算法

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2023-01-25 DOI: 10.1145/3577195

T. Davis

引用次数: 2

Robust Topological Construction of All-hexahedral Boundary Layer Meshes 所有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 : 2022-12-20 DOI: 10.1145/3577196

M. Reberol, Kilian Verhetsel, F. Henrotte, D. Bommes, J. Remacle

{"title":"Robust Topological Construction of All-hexahedral Boundary Layer Meshes","authors":"M. Reberol, Kilian Verhetsel, F. Henrotte, D. Bommes, J. Remacle","doi":"10.1145/3577196","DOIUrl":"https://doi.org/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":"49 1","pages":"1 - 32"},"PeriodicalIF":2.7,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48482584","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: 3

FastSpline: Automatic Generation of Interpolants for Lattice Samplings FastSpline：网格采样插值的自动生成

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2022-12-20 DOI: 10.1145/3577194

J. Horacsek, U. Alim

{"title":"FastSpline: Automatic Generation of Interpolants for Lattice Samplings","authors":"J. Horacsek, U. Alim","doi":"10.1145/3577194","DOIUrl":"https://doi.org/10.1145/3577194","url":null,"abstract":"Interpolation is a foundational concept in scientific computing and is at the heart of many scientific visualization techniques. There is usually a tradeoff between the approximation capabilities of an interpolation scheme and its evaluation efficiency. For many applications, it is important for a user to navigate their data in real time. In practice, evaluation efficiency outweighs any incremental improvements in reconstruction fidelity. We first analyze, from a general standpoint, the use of compact piece-wise polynomial basis functions to efficiently interpolate data that is sampled on a lattice. We then detail our automatic code-generation framework on both CPU and GPU architectures. Specifically, we propose a general framework that can produce a fast evaluation scheme by analyzing the algebro-geometric structure of the convolution sum for a given lattice and basis function combination. We demonstrate the utility and generality of our framework by providing fast implementations of various box splines on the Body Centered and Face Centered Cubic lattices, as well as some non-separable box splines on the Cartesian lattice. We also provide fast implementations for certain Voronoi-splines that have not yet appeared in the literature. Finally, we demonstrate that this framework may also be used for non-Cartesian lattices in 4D.","PeriodicalId":50935,"journal":{"name":"ACM Transactions on Mathematical Software","volume":"49 1","pages":"1 - 35"},"PeriodicalIF":2.7,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47226907","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

CS-TSSOS: Correlative and Term Sparsity for Large-Scale Polynomial Optimization CS-TSSOS:大规模多项式优化的相关项稀疏性

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2022-12-19 DOI: https://dl.acm.org/doi/10.1145/3569709

Jie Wang, Victor Magron, J. B. Lasserre, Ngoc Hoang Anh Mai

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 : 2022-12-19 DOI: 10.1145/3577197

X. Li, Paul B. S. Lin, Yang Liu, Piyush Sao

引用次数: 2

pylspack: Parallel Algorithms and Data Structures for Sketching, Column Subset Selection, Regression, and Leverage Scores 并行算法和数据结构素描，列子集选择，回归，和杠杆得分

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2022-12-19 DOI: https://dl.acm.org/doi/10.1145/3555370

Aleksandros Sobczyk, Efstratios Gallopoulos

{"title":"pylspack: Parallel Algorithms and Data Structures for Sketching, Column Subset Selection, Regression, and Leverage Scores","authors":"Aleksandros Sobczyk, Efstratios Gallopoulos","doi":"https://dl.acm.org/doi/10.1145/3555370","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3555370","url":null,"abstract":"<p>We present parallel algorithms and data structures for three fundamental operations in Numerical Linear Algebra: (i) Gaussian and CountSketch random projections and their combination, (ii) computation of the Gram matrix, and (iii) computation of the squared row norms of the product of two matrices, with a special focus on “tall-and-skinny” matrices, which arise in many applications. We provide a detailed analysis of the ubiquitous CountSketch transform and its combination with Gaussian random projections, accounting for memory requirements, computational complexity and workload balancing. We also demonstrate how these results can be applied to column subset selection, least squares regression and leverage scores computation. These tools have been implemented in <monospace>pylspack</monospace>, a publicly available Python package<sup>1</sup> whose core is written in C++ and parallelized with OpenMP and that is compatible with standard matrix data structures of SciPy and NumPy. Extensive numerical experiments indicate that the proposed algorithms scale well and significantly outperform existing libraries for tall-and-skinny matrices.</p>","PeriodicalId":50935,"journal":{"name":"ACM Transactions on Mathematical Software","volume":"9 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138537800","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

Exploiting Constant Trace Property in Large-scale Polynomial Optimization 利用大规模多项式优化中的常迹特性

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2022-12-19 DOI: https://dl.acm.org/doi/10.1145/3555309

Ngoc Hoang Anh Mai, J. B. Lasserre, Victor Magron, Jie Wang

引用次数: 0

A Normal Form Algorithm for Tensor Rank Decomposition 张量秩分解的一种范式算法

IF 2.7 1区数学

ACM Transactions on Mathematical Software Pub Date : 2022-12-19 DOI: https://dl.acm.org/doi/10.1145/3555369

Simon Telen, Nick Vannieuwenhoven

引用次数: 0