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Partial differential equations and stochastic methods in molecular dynamics* 分子动力学中的偏微分方程和随机方法*
IF 14.2 1区 数学
Acta Numerica Pub Date : 2016-05-01 DOI: 10.1017/S0962492916000039
T. Lelièvre, G. Stoltz
{"title":"Partial differential equations and stochastic methods in molecular dynamics*","authors":"T. Lelièvre, G. Stoltz","doi":"10.1017/S0962492916000039","DOIUrl":"https://doi.org/10.1017/S0962492916000039","url":null,"abstract":"The objective of molecular dynamics computations is to infer macroscopic properties of matter from atomistic models via averages with respect to probability measures dictated by the principles of statistical physics. Obtaining accurate results requires efficient sampling of atomistic configurations, which are typically generated using very long trajectories of stochastic differential equations in high dimensions, such as Langevin dynamics and its overdamped limit. Depending on the quantities of interest at the macroscopic level, one may also be interested in dynamical properties computed from averages over paths of these dynamics. This review describes how techniques from the analysis of partial differential equations can be used to devise good algorithms and to quantify their efficiency and accuracy. In particular, a crucial role is played by the study of the long-time behaviour of the solution to the Fokker–Planck equation associated with the stochastic dynamics.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"13 1","pages":"681 - 880"},"PeriodicalIF":14.2,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492916000039","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57446940","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: 173
Linear algebra software for large-scale accelerated multicore computing* 线性代数软件大规模加速多核计算*
IF 14.2 1区 数学
Acta Numerica Pub Date : 2016-05-01 DOI: 10.1017/S0962492916000015
A. Abdelfattah, H. Anzt, J. Dongarra, M. Gates, A. Haidar, J. Kurzak, P. Luszczek, S. Tomov, I. Yamazaki, A. YarKhan
{"title":"Linear algebra software for large-scale accelerated multicore computing*","authors":"A. Abdelfattah, H. Anzt, J. Dongarra, M. Gates, A. Haidar, J. Kurzak, P. Luszczek, S. Tomov, I. Yamazaki, A. YarKhan","doi":"10.1017/S0962492916000015","DOIUrl":"https://doi.org/10.1017/S0962492916000015","url":null,"abstract":"Many crucial scientific computing applications, ranging from national security to medical advances, rely on high-performance linear algebra algorithms and technologies, underscoring their importance and broad impact. Here we present the state-of-the-art design and implementation practices for the acceleration of the predominant linear algebra algorithms on large-scale accelerated multicore systems. Examples are given with fundamental dense linear algebra algorithms – from the LU, QR, Cholesky, and LDLT factorizations needed for solving linear systems of equations, to eigenvalue and singular value decomposition (SVD) problems. The implementations presented are readily available via the open-source PLASMA and MAGMA libraries, which represent the next generation modernization of the popular LAPACK library for accelerated multicore systems. To generate the extreme level of parallelism needed for the efficient use of these systems, algorithms of interest are redesigned and then split into well-chosen computational tasks. The task execution is scheduled over the computational components of a hybrid system of multicore CPUs with GPU accelerators and/or Xeon Phi coprocessors, using either static scheduling or light-weight runtime systems. The use of light-weight runtime systems keeps scheduling overheads low, similar to static scheduling, while enabling the expression of parallelism through sequential-like code. This simplifies the development effort and allows exploration of the unique strengths of the various hardware components. Finally, we emphasize the development of innovative linear algebra algorithms using three technologies – mixed precision arithmetic, batched operations, and asynchronous iterations – that are currently of high interest for accelerated multicore systems.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"25 1","pages":"1 - 160"},"PeriodicalIF":14.2,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492916000015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57446084","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: 14
ANU volume 25 Cover and Front matter 澳大利亚国立大学第25卷封面和封面问题
IF 14.2 1区 数学
Acta Numerica Pub Date : 2016-05-01 DOI: 10.1017/s0962492916000052
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引用次数: 0
ANU volume 25 Cover and Back matter 澳大利亚国立大学第25卷封面和封底
IF 14.2 1区 数学
Acta Numerica Pub Date : 2016-05-01 DOI: 10.1017/s0962492916000064
{"title":"ANU volume 25 Cover and Back matter","authors":"","doi":"10.1017/s0962492916000064","DOIUrl":"https://doi.org/10.1017/s0962492916000064","url":null,"abstract":"","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"25 1","pages":"b1 - b2"},"PeriodicalIF":14.2,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/s0962492916000064","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57446617","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
A survey of direct methods for sparse linear systems 稀疏线性系统的直接方法综述
IF 14.2 1区 数学
Acta Numerica Pub Date : 2016-05-01 DOI: 10.1017/S0962492916000076
T. Davis, S. Rajamanickam, Wissam M. Sid-Lakhdar
{"title":"A survey of direct methods for sparse linear systems","authors":"T. Davis, S. Rajamanickam, Wissam M. Sid-Lakhdar","doi":"10.1017/S0962492916000076","DOIUrl":"https://doi.org/10.1017/S0962492916000076","url":null,"abstract":"Wilkinson defined a sparse matrix as one with enough zeros that it pays to take advantage of them.1 This informal yet practical definition captures the essence of the goal of direct methods for solving sparse matrix problems. They exploit the sparsity of a matrix to solve problems economically: much faster and using far less memory than if all the entries of a matrix were stored and took part in explicit computations. These methods form the backbone of a wide range of problems in computational science. A glimpse of the breadth of applications relying on sparse solvers can be seen in the origins of matrices in published matrix benchmark collections (Duff and Reid 1979a, Duff, Grimes and Lewis 1989a, Davis and Hu 2011). The goal of this survey article is to impart a working knowledge of the underlying theory and practice of sparse direct methods for solving linear systems and least-squares problems, and to provide an overview of the algorithms, data structures, and software available to solve these problems, so that the reader can both understand the methods and know how best to use them.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"25 1","pages":"383 - 566"},"PeriodicalIF":14.2,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492916000076","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57446691","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: 160
Bacterial Peptidoglycan Traverses the Placenta to Induce Fetal Neuroproliferation and Aberrant Postnatal Behavior 细菌肽聚糖穿过胎盘诱导胎儿神经增殖和出生后行为异常
IF 30.3 1区 数学
Acta Numerica Pub Date : 2016-03-09 DOI: 10.1016/j.chom.2016.02.009
Jessica Humann, Beth Mann, Geli Gao, Philip Moresco, Joseph Ramahi, Lip Nam Loh, Arden Farr, Yunming Hu, Kelly Durick-Eder, Sophie A Fillon, Richard J Smeyne, Elaine I Tuomanen
{"title":"Bacterial Peptidoglycan Traverses the Placenta to Induce Fetal Neuroproliferation and Aberrant Postnatal Behavior","authors":"Jessica Humann, Beth Mann, Geli Gao, Philip Moresco, Joseph Ramahi, Lip Nam Loh, Arden Farr, Yunming Hu, Kelly Durick-Eder, Sophie A Fillon, Richard J Smeyne, Elaine I Tuomanen","doi":"10.1016/j.chom.2016.02.009","DOIUrl":"10.1016/j.chom.2016.02.009","url":null,"abstract":"<p><p>Maternal infection during pregnancy is associated with adverse outcomes for the fetus, including postnatal cognitive disorders. However, the underlying mechanisms are obscure. We find that bacterial cell wall peptidoglycan (CW), a universal PAMP for TLR2, traverses the murine placenta into the developing fetal brain. In contrast to adults, CW-exposed fetal brains did not show any signs of inflammation or neuronal death. Instead, the neuronal transcription factor FoxG1 was induced, and neuroproliferation leading to a 50% greater density of neurons in the cortical plate was observed. Bacterial infection of pregnant dams, followed by antibiotic treatment, which releases CW, yielded the same result. Neuroproliferation required TLR2 and was recapitulated in vitro with fetal neuronal precursor cells and TLR2/6, but not TLR2/1, ligands. The fetal neuroproliferative response correlated with abnormal cognitive behavior in CW-exposed pups following birth. Thus, the bacterial CW-TLR2 signaling axis affects fetal neurodevelopment and may underlie postnatal cognitive disorders.</p>","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"22 1","pages":"388-99"},"PeriodicalIF":30.3,"publicationDate":"2016-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4787272/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79452461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solving PDEs with radial basis functions * 用径向基函数求解偏微分方程*
IF 14.2 1区 数学
Acta Numerica Pub Date : 2015-04-27 DOI: 10.1017/S0962492914000130
B. Fornberg, N. Flyer
{"title":"Solving PDEs with radial basis functions *","authors":"B. Fornberg, N. Flyer","doi":"10.1017/S0962492914000130","DOIUrl":"https://doi.org/10.1017/S0962492914000130","url":null,"abstract":"Finite differences provided the first numerical approach that permitted large-scale simulations in many applications areas, such as geophysical fluid dynamics. As accuracy and integration time requirements gradually increased, the focus shifted from finite differences to a variety of different spectral methods. During the last few years, radial basis functions, in particular in their ‘local’ RBF-FD form, have taken the major step from being mostly a curiosity approach for small-scale PDE ‘toy problems’ to becoming a major contender also for very large simulations on advanced distributed memory computer systems. Being entirely mesh-free, RBF-FD discretizations are also particularly easy to implement, even when local refinements are needed. This article gives some background to this development, and highlights some recent results.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"24 1","pages":"215 - 258"},"PeriodicalIF":14.2,"publicationDate":"2015-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492914000130","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57445993","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: 229
Preconditioning 预处理
IF 14.2 1区 数学
Acta Numerica Pub Date : 2015-04-27 DOI: 10.1017/S0962492915000021
A. Wathen
{"title":"Preconditioning","authors":"A. Wathen","doi":"10.1017/S0962492915000021","DOIUrl":"https://doi.org/10.1017/S0962492915000021","url":null,"abstract":"The computational solution of problems can be restricted by the availability of solution methods for linear(ized) systems of equations. In conjunction with iterative methods, preconditioning is often the vital component in enabling the solution of such systems when the dimension is large. We attempt a broad review of preconditioning methods.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"24 1","pages":"329 - 376"},"PeriodicalIF":14.2,"publicationDate":"2015-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492915000021","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57446288","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: 162
Generalized barycentric coordinates and applications * 广义质心坐标及其应用*
IF 14.2 1区 数学
Acta Numerica Pub Date : 2015-04-27 DOI: 10.1017/S0962492914000129
M. Floater
{"title":"Generalized barycentric coordinates and applications *","authors":"M. Floater","doi":"10.1017/S0962492914000129","DOIUrl":"https://doi.org/10.1017/S0962492914000129","url":null,"abstract":"This paper surveys the construction, properties, and applications of generalized barycentric coordinates on polygons and polyhedra. Applications include: surface mesh parametrization in geometric modelling; image, curve, and surface deformation in computer graphics; and polygonal and polyhedral finite element methods.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"24 1","pages":"161 - 214"},"PeriodicalIF":14.2,"publicationDate":"2015-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492914000129","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57445940","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: 176
ANU volume 24 Cover and Front matter 澳大利亚国立大学第24卷封面和封面问题
IF 14.2 1区 数学
Acta Numerica Pub Date : 2015-04-27 DOI: 10.1017/s0962492915000045
{"title":"ANU volume 24 Cover and Front matter","authors":"","doi":"10.1017/s0962492915000045","DOIUrl":"https://doi.org/10.1017/s0962492915000045","url":null,"abstract":"","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"24 1","pages":"f1 - f2"},"PeriodicalIF":14.2,"publicationDate":"2015-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/s0962492915000045","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57446330","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
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