ETNA - Electronic Transactions on Numerical Analysis最新文献_第7页

Structured shifts for skew-symmetric matrices 斜对称矩阵的结构化移位

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol55s455

C. Greif

引用次数: 2

A stable matrix version of the fast multipole method: stabilization strategies and examples 快速多极方法的稳定矩阵版本:稳定策略和实例

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol54s581

Difeng Cai, J. Xia

{"title":"A stable matrix version of the fast multipole method: stabilization strategies and examples","authors":"Difeng Cai, J. Xia","doi":"10.1553/etna_vol54s581","DOIUrl":"https://doi.org/10.1553/etna_vol54s581","url":null,"abstract":"The fast multipole method (FMM) is an efficient method for evaluating matrix-vector products related to certain discretized kernel functions. The method involves an underlying FMM matrix given by a sequence of smaller matrices (called generators for convenience). Although there has been extensive work in designing and applying FMM techniques, the stability of the FMM and the stable FMM matrix factorization have rarely been studied. In this work, we propose techniques that lead to stable operations with FMM matrices. One key objective is to give stabilization strategies that can be used to provide low-rank approximations and translation relations in the FMM satisfying some stability requirements. The standard Taylor expansions used in FMMs yield basis generators susceptible to instability. Here, we introduce some scaling factors to control the relevant norms of the generators and give a rigorous analysis of the bounds of the entrywise magnitudes. The second objective is to use the one-dimensional case as an example to provide an intuitive construction of FMM matrices satisfying some stability conditions and then convert an FMM matrix into a hierarchically semiseparable (HSS) form that admits stable ULV-type factorizations. This bridges the gap between the FMM and stable FMM matrix factorizations. The HSS construction is done analytically and does not require expensive algebraic compression. Relevant stability studies are given, which show that the resulting matrix forms are suitable for stable operations. Note that the essential stabilization ideas are also applicable to higher dimensions. Extensive numerical tests are given to illustrate the reliability and accuracy.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117016830","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: 7

Construction of the optimal set of quadrature rules in the sense of Borges 博尔赫斯意义下最优正交规则集的构造

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/ETNA_VOL50S164

A. Jovanovic, M. Stanić, Tatjana V. Tomovic

引用次数: 1

An enhancement of the convergence of the IDR method 改进了IDR方法的收敛性

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol58s470

F. Bouyghf, A. Messaoudi, H. Sadok

引用次数: 2

Porting an aggregation-based algebraic multigrid method to GPUs 将基于聚合的代数多网格方法移植到gpu上

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol55s687

Abdeselam El Haman Abdeselam, Artem Napov, Y. Notay

引用次数: 2

Numerical treatment of singularly perturbed fourth-order two-parameter problems 四阶双参数奇摄动问题的数值处理

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/ETNA_VOL51S50

M. Brdar, S. Franz, H. Roos

引用次数: 5

Analysis of stability and convergence for L-type formulas combined with a spatial finite element method for solving subdiffusion problems 结合空间有限元法求解亚扩散问题的l型公式的稳定性和收敛性分析

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol55s568

Mohadese Ramezani, R. Mokhtari, G. Haase

引用次数: 1

Orthogonality on the semicircle: old and new results 半圆上的正交性:新旧结果

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol59s99

G. Milovanović

引用次数: 0

Laminar-turbulent transition in channel flow: wall effects and critical Reynolds number 通道流动中的层流-湍流过渡:壁效应和临界雷诺数

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/ETNA_VOL51S547

H. Kanda

{"title":"Laminar-turbulent transition in channel flow: wall effects and critical Reynolds number","authors":"H. Kanda","doi":"10.1553/ETNA_VOL51S547","DOIUrl":"https://doi.org/10.1553/ETNA_VOL51S547","url":null,"abstract":"This article describes possible causes of natural laminar-turbulent transition in circular pipe flow. Our starting points are the observations that under natural disturbance conditions, transition appears to take place only in the developing entrance region, as observed in Reynolds' color-band experiments, and that the critical Reynolds number Rc has a minimum value of about 2000 when using a sharp-edged uniform radius pipe, as observed in our earlier color-band experiments. The entrance region is defined as the region from the pipe inlet to the point where the inlet flow fully develops into Hagen-Poiseuille flow for a sharp-edged entrance pipe. In the case of a bell-mouth entrance pipe, the entrance region includes the bell-mouth entrance region. We derive for the entrance region a new ratio of the increase in kinetic energy flux (�KE flux) to a wall effect, where the wall effect is the radial wall power (R-Wall-Power) exerted on the wall by the radial component of the viscous term in the Navier-Stokes equations. In dimensionless form, �KE flux is a constant, although R-Wall-Power decreases as the Reynolds number Re increases. Our previous calculations for the case of a sharp-edged entrance pipe indicate thatKE fluxtotal R-Wall-Power (T-R-Wall-Power) at Re � 2000. Accordingly, our hypothesis is that Rc can be derived from the relation betweenKE flux and T-R-Wall-Power. We discuss, moreover, whether or not this criterion can apply to different entrance geometries such as the bell-mouth entrances considered by Reynolds.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122983500","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: 0

Iterative Lavrentiev regularization method under a heuristic rule for nonlinear ill-posed operator equations 非线性不适定算子方程的启发式迭代Lavrentiev正则化方法

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI: 10.1553/etna_vol58s450

P. Mahale, Ankit Singh

引用次数: 0