ACM Transactions on Mathematical Software (TOMS)最新文献_第2页

Fast Matching Pursuit with Multi-Gabor Dictionaries 基于多gabor词典的快速匹配追踪

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2021-06-25 DOI: 10.1145/3447958

Zdeněk Průša, N. Holighaus, Péter Balázs

引用次数: 3

NEP

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2021-06-25 DOI: 10.1145/3447544

C. Campos, J. Román

引用次数: 9

HyperNOMAD HyperNOMAD

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2021-06-25 DOI: 10.1145/3450975

Dounia Lakhmiri, Sébastien Le Digabel, C. Tribes

引用次数: 23

A Set of Batched Basic Linear Algebra Subprograms and LAPACK Routines 一组批处理基本线性代数子程序和LAPACK例程

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2021-06-25 DOI: 10.1145/3431921

A. Abdelfattah, Timothy B. Costa, J. Dongarra, M. Gates, A. Haidar, S. Hammarling, N. Higham, J. Kurzak, P. Luszczek, S. Tomov, M. Zounon

引用次数: 18

HIFIR: Hybrid Incomplete Factorization with Iterative Refinement for Preconditioning Ill-Conditioned and Singular Systems 预处理病态奇异系统的混合不完全分解与迭代改进

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2021-06-18 DOI: 10.1145/3536165

Qiao Chen, X. Jiao

{"title":"HIFIR: Hybrid Incomplete Factorization with Iterative Refinement for Preconditioning Ill-Conditioned and Singular Systems","authors":"Qiao Chen, X. Jiao","doi":"10.1145/3536165","DOIUrl":"https://doi.org/10.1145/3536165","url":null,"abstract":"We introduce a software package called Hybrid Incomplete Factorization with Iterative Refinement (HIFIR) for preconditioning sparse, unsymmetric, ill-conditioned, and potentially singular systems. HIFIR computes a hybrid incomplete factorization (HIF), which combines multilevel incomplete LU factorization with a truncated, rank-revealing QR (RRQR) factorization on the final Schur complement. This novel hybridization is based on the new theory of ϵ-accurate approximate generalized inverse (AGI). It enables near-optimal preconditioners for consistent systems and enables flexible GMRES to solve inconsistent systems when coupled with iterative refinement. In this article, we focus on some practical algorithmic and software issues of HIFIR. In particular, we introduce a new inverse-based rook pivoting (IBRP) into ILU, which improves the robustness and the overall efficiency for some ill-conditioned systems by significantly reducing the size of the final Schur complement for some systems. We also describe the software design of HIFIR in terms of its efficient data structures for supporting rook pivoting in a multilevel setting, its template-based generic programming interfaces for mixed-precision real and complex values in C++, and its user-friendly high-level interfaces in MATLAB and Python. We demonstrate the effectiveness of HIFIR for ill-conditioned or singular systems arising from several applications, including the Helmholtz equation, linear elasticity, stationary incompressible Navier–Stokes (INS) equations, and time-dependent advection-diffusion equation.","PeriodicalId":7036,"journal":{"name":"ACM Transactions on Mathematical Software (TOMS)","volume":"110 1","pages":"1 - 33"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86234848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Bringing Trimmed Serendipity Methods to Computational Practice in Firedrake 将修剪的意外发现方法引入Firedrake的计算实践

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2021-04-27 DOI: 10.1145/3490485

J. Crum, Cyrus Cheng, D. Ham, L. Mitchell, R. Kirby, J. Levine, A. Gillette

引用次数: 5

Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software 银杏线性代数软件中高性能预处理的自适应精确块-雅可比

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2021-04-26 DOI: 10.1145/3441850

Goran Flegar, H. Anzt, T. Cojean, E. S. Quintana‐Ortí

{"title":"Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software","authors":"Goran Flegar, H. Anzt, T. Cojean, E. S. Quintana‐Ortí","doi":"10.1145/3441850","DOIUrl":"https://doi.org/10.1145/3441850","url":null,"abstract":"The use of mixed precision in numerical algorithms is a promising strategy for accelerating scientific applications. In particular, the adoption of specialized hardware and data formats for low-precision arithmetic in high-end GPUs (graphics processing units) has motivated numerous efforts aiming at carefully reducing the working precision in order to speed up the computations. For algorithms whose performance is bound by the memory bandwidth, the idea of compressing its data before (and after) memory accesses has received considerable attention. One idea is to store an approximate operator–like a preconditioner–in lower than working precision hopefully without impacting the algorithm output. We realize the first high-performance implementation of an adaptive precision block-Jacobi preconditioner which selects the precision format used to store the preconditioner data on-the-fly, taking into account the numerical properties of the individual preconditioner blocks. We implement the adaptive block-Jacobi preconditioner as production-ready functionality in the Ginkgo linear algebra library, considering not only the precision formats that are part of the IEEE standard, but also customized formats which optimize the length of the exponent and significand to the characteristics of the preconditioner blocks. Experiments run on a state-of-the-art GPU accelerator show that our implementation offers attractive runtime savings.","PeriodicalId":7036,"journal":{"name":"ACM Transactions on Mathematical Software (TOMS)","volume":"39 1","pages":"1 - 28"},"PeriodicalIF":0.0,"publicationDate":"2021-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84707846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 10

Algorithm 1016 算法1016

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2021-04-20 DOI: 10.1145/3446979

Jens Hahne, S. Friedhoff, M. Bolten

{"title":"Algorithm 1016","authors":"Jens Hahne, S. Friedhoff, M. Bolten","doi":"10.1145/3446979","DOIUrl":"https://doi.org/10.1145/3446979","url":null,"abstract":"In this article, we introduce the Python framework PyMGRIT, which implements the multigrid-reduction-in-time (MGRIT) algorithm for solving (non-)linear systems arising from the discretization of time-dependent problems. The MGRIT algorithm is a reduction-based iterative method that allows parallel-in-time simulations, i.e., calculating multiple time steps simultaneously in a simulation, using a time-grid hierarchy. The PyMGRIT framework includes many different variants of the MGRIT algorithm, ranging from different multigrid cycle types and relaxation schemes, various coarsening strategies, including time-only and space-time coarsening, and the ability to utilize different time integrators on different levels in the multigrid hierachy. The comprehensive documentation with tutorials and many examples and the fully documented code allow an easy start into the work with the package. The functionality of the code is ensured by automated serial and parallel tests using continuous integration. PyMGRIT supports serial runs suitable for prototyping and testing of new approaches, as well as parallel runs using the Message Passing Interface (MPI). In this manuscript, we describe the implementation of the MGRIT algorithm in PyMGRIT and present the usage from both a user and a developer point of view. Three examples illustrate different aspects of the package itself, especially running tests with pure time parallelism, as well as space-time parallelism through the coupling of PyMGRIT with PETSc or Firedrake.","PeriodicalId":7036,"journal":{"name":"ACM Transactions on Mathematical Software (TOMS)","volume":"26 1","pages":"1 - 22"},"PeriodicalIF":0.0,"publicationDate":"2021-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73177657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Algorithm 1015 算法1015

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2021-04-20 DOI: 10.1145/3442348

S. Guthe, D. Thuerck

引用次数: 1

Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes 多边形和多面体单元网格上任意阶有限元自由度映射的构造

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2021-02-23 DOI: 10.1145/3524456

Matthew W. Scroggs, Jørgen S. Dokken, C. Richardson, G. N. Wells

{"title":"Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes","authors":"Matthew W. Scroggs, Jørgen S. Dokken, C. Richardson, G. N. Wells","doi":"10.1145/3524456","DOIUrl":"https://doi.org/10.1145/3524456","url":null,"abstract":"We develop a method for generating degree-of-freedom maps for arbitrary order Ciarlet-type finite element spaces for any cell shape. The approach is based on the composition of permutations and transformations by cell sub-entity. Current approaches to generating degree-of-freedom maps for arbitrary order problems typically rely on a consistent orientation of cell entities that permits the definition of a common local coordinate system on shared edges and faces. However, while orientation of a mesh is straightforward for simplex cells and is a local operation, it is not a strictly local operation for quadrilateral cells and, in the case of hexahedral cells, not all meshes are orientable. The permutation and transformation approach is developed for a range of element types, including arbitrary degree Lagrange, serendipity, and divergence- and curl-conforming elements, and for a range of cell shapes. The approach is local and can be applied to cells of any shape, including general polytopes and meshes with mixed cell types. A number of examples are presented and the developed approach has been implemented in open-source libraries.","PeriodicalId":7036,"journal":{"name":"ACM Transactions on Mathematical Software (TOMS)","volume":"32 1","pages":"1 - 23"},"PeriodicalIF":0.0,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87908668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 54