Acta Numerica最新文献_第10页

Communication lower bounds and optimal algorithms for numerical linear algebra*† 数值线性代数的通信下界和最优算法*†

IF 14.2 1区数学

Acta Numerica Pub Date : 2014-05-01 DOI: 10.1017/S0962492914000038

Grey Ballard, E. Carson, J. Demmel, M. Hoemmen, Nicholas Knight, O. Schwartz

{"title":"Communication lower bounds and optimal algorithms for numerical linear algebra*†","authors":"Grey Ballard, E. Carson, J. Demmel, M. Hoemmen, Nicholas Knight, O. Schwartz","doi":"10.1017/S0962492914000038","DOIUrl":"https://doi.org/10.1017/S0962492914000038","url":null,"abstract":"The traditional metric for the efficiency of a numerical algorithm has been the number of arithmetic operations it performs. Technological trends have long been reducing the time to perform an arithmetic operation, so it is no longer the bottleneck in many algorithms; rather, communication, or moving data, is the bottleneck. This motivates us to seek algorithms that move as little data as possible, either between levels of a memory hierarchy or between parallel processors over a network. In this paper we summarize recent progress in three aspects of this problem. First we describe lower bounds on communication. Some of these generalize known lower bounds for dense classical (O(n3)) matrix multiplication to all direct methods of linear algebra, to sequential and parallel algorithms, and to dense and sparse matrices. We also present lower bounds for Strassen-like algorithms, and for iterative methods, in particular Krylov subspace methods applied to sparse matrices. Second, we compare these lower bounds to widely used versions of these algorithms, and note that these widely used algorithms usually communicate asymptotically more than is necessary. Third, we identify or invent new algorithms for most linear algebra problems that do attain these lower bounds, and demonstrate large speed-ups in theory and practice.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"23 1","pages":"1 - 155"},"PeriodicalIF":14.2,"publicationDate":"2014-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492914000038","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57445585","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: 118

Mathematical analysis of variational isogeometric methods* 变分等几何方法的数学分析*

IF 14.2 1区数学

Acta Numerica Pub Date : 2014-05-01 DOI: 10.1017/S096249291400004X

L. Veiga, A. Buffa, G. Sangalli, Rafael Vázquez Hernández

引用次数: 250

ANU volume 23 Cover and Back matter 澳大利亚国立大学第23卷封面和封底

IF 14.2 1区数学

Acta Numerica Pub Date : 2014-05-01 DOI: 10.1017/s0962492914999986

引用次数: 0

Stochastic finite element methods for partial differential equations with random input data* 具有随机输入数据的偏微分方程的随机有限元方法*

IF 14.2 1区数学

Acta Numerica Pub Date : 2014-05-01 DOI: 10.1017/S0962492914000075

M. Gunzburger, C. Webster, Guannan Zhang

{"title":"Stochastic finite element methods for partial differential equations with random input data*","authors":"M. Gunzburger, C. Webster, Guannan Zhang","doi":"10.1017/S0962492914000075","DOIUrl":"https://doi.org/10.1017/S0962492914000075","url":null,"abstract":"The quantification of probabilistic uncertainties in the outputs of physical, biological, and social systems governed by partial differential equations with random inputs require, in practice, the discretization of those equations. Stochastic finite element methods refer to an extensive class of algorithms for the approximate solution of partial differential equations having random input data, for which spatial discretization is effected by a finite element method. Fully discrete approximations require further discretization with respect to solution dependences on the random variables. For this purpose several approaches have been developed, including intrusive approaches such as stochastic Galerkin methods, for which the physical and probabilistic degrees of freedom are coupled, and non-intrusive approaches such as stochastic sampling and interpolatory-type stochastic collocation methods, for which the physical and probabilistic degrees of freedom are uncoupled. All these method classes are surveyed in this article, including some novel recent developments. Details about the construction of the various algorithms and about theoretical error estimates and complexity analyses of the algorithms are provided. Throughout, numerical examples are used to illustrate the theoretical results and to provide further insights into the methodologies.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"23 1","pages":"521 - 650"},"PeriodicalIF":14.2,"publicationDate":"2014-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492914000075","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57445739","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: 209

ANU volume 23 Cover and Front matter 澳大利亚国立大学第23卷封面和封面问题

IF 14.2 1区数学

Acta Numerica Pub Date : 2014-05-01 DOI: 10.1017/s0962492914999998

引用次数: 0

Numerical methods for kinetic equations* 动力学方程的数值方法*

IF 14.2 1区数学

Acta Numerica Pub Date : 2014-05-01 DOI: 10.1017/S0962492914000063

G. Dimarco, L. Pareschi

引用次数: 266

Topological pattern recognition for point cloud data* 点云数据的拓扑模式识别*

IF 14.2 1区数学

Acta Numerica Pub Date : 2014-05-01 DOI: 10.1017/S0962492914000051

G. Carlsson

引用次数: 224

Numerical methods with controlled dissipation for small-scale dependent shocks* 小尺度相关冲击可控耗散的数值方法*

IF 14.2 1区数学

Acta Numerica Pub Date : 2013-12-04 DOI: 10.1017/S0962492914000099

P. LeFloch, Siddhartha Mishra

{"title":"Numerical methods with controlled dissipation for small-scale dependent shocks*","authors":"P. LeFloch, Siddhartha Mishra","doi":"10.1017/S0962492914000099","DOIUrl":"https://doi.org/10.1017/S0962492914000099","url":null,"abstract":"We provide a ‘user guide’ to the literature of the past twenty years concerning the modelling and approximation of discontinuous solutions to nonlinear hyperbolic systems that admit small-scale dependent shock waves. We cover several classes of problems and solutions: nonclassical undercompressive shocks, hyperbolic systems in nonconservative form, and boundary layer problems. We review the relevant models arising in continuum physics and describe the numerical methods that have been proposed to capture small-scale dependent solutions. In agreement with general well-posedness theory, small-scale dependent solutions are characterized by a kinetic relation, a family of paths, or an admissible boundary set. We provide a review of numerical methods (front-tracking schemes, finite difference schemes, finite volume schemes), which, at the discrete level, reproduce the effect of the physically meaningful dissipation mechanisms of interest in the applications. An essential role is played by the equivalent equation associated with discrete schemes, which is found to be relevant even for solutions containing shock waves.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"23 1","pages":"743 - 816"},"PeriodicalIF":14.2,"publicationDate":"2013-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492914000099","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57445837","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: 28

Multilevel Monte Carlo methods 多层蒙特卡罗方法

IF 14.2 1区数学

Acta Numerica Pub Date : 2013-04-19 DOI: 10.1017/S096249291500001X

M. Giles

引用次数: 224

Finite element methods for surface PDEs* 表面偏微分方程的有限元方法*

IF 14.2 1区数学

Acta Numerica Pub Date : 2013-04-02 DOI: 10.1017/S0962492913000056

G. Dziuk, C. M. Elliott

引用次数: 515