Theory and Applications of Multigrid and Domain Decomposition Methods

多重网格和域分解方法的理论与应用

基本信息

  • 批准号:
    0074246
  • 负责人:
  • 金额:
    $ 9.85万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2000
  • 资助国家:
    美国
  • 起止时间:
    2000-08-01 至 2004-02-29
  • 项目状态:
    已结题

项目摘要

There are three areas of research in the project ``Theory and Applications of Multigrid and Domain Decomposition Methods''. The first area concerns the additive multigrid convergence theory, which is effective in analyzing the asymptotic behavior of the contraction numbers of multigrid algorithms with respect to the number of smoothing steps for boundary value problems with less than full elliptic regularity. The seminal result obtained by the PI for V-cycle algorithm with Richardson relaxation as the smoother will be extended to general smoothers, nonconforming finite elements, the mixed formulation and the F-cycle algorithm. The second area involves multigrid methods for stress intensity factors and singular solutions. These are methods that can take advantage of the form of the solution of the boundary value problem in the regions where it does not have full elliptic regularity. Using this approach, usual quasi-optimal convergence rates have been obtained for simple finite elements on simple grids for boundary value problems on two-dimensional domains with reentrant corners or cracks. The technically more challenging interface problems and three dimensional problems will be investigated in this project. The third area is the analysis of the Finite Element Tearing and Interconnecting (FETI) method, a nonoverlapping domain decomposition method in which the (pseudo) inverse of the Schur complement matrix has to be preconditioned. The goal of this part of the project is to carry out an analysis of the FETI method and some of its variants within the framework of additive Schwarz preconditioners, and to investigate new mechanisms for the global communication among the subdomains. The methods analyzed in this project are efficient algorithms for the numerical solution of partial differential equations. Such equations are extremely important in science and engineering since they are the governing equations for most physical phenomena. Part of the research involves the fast computation of stress intensity factors, which are essential indicators in fracture mechanics. The FETI method to be studied in this project has already been implemented for large scale engineering problems using parallel supercomputers with up to a thousand processors. The advances resulting from this project will therefore have an impact on many areas of science and technology, such as aerospace engineering, fracture prediction and fluid flow problems.
在“多网格和区域分解方法的理论与应用”项目中有三个研究领域。第一个领域涉及加性多网格收敛理论,该理论有效地分析了边值问题的多网格算法的收缩数与光滑步数的渐近性。以Richardson松弛为光滑点的v循环算法的PI所得到的开创性结果将推广到一般光滑点、非协调有限元、混合公式和f循环算法。第二个领域涉及应力强度因子和奇异解的多重网格方法。这些方法可以利用边值问题在不具有完全椭圆正则性的区域的解的形式。利用该方法,对于具有可重入角或裂纹的二维域上的简单有限元边值问题,得到了通常的拟最优收敛速率。技术上更具挑战性的界面问题和三维问题将在本项目中进行研究。第三个领域是有限元撕裂和互连(FETI)方法的分析,这是一种非重叠的区域分解方法,其中舒尔补矩阵的(伪)逆必须是先决条件。该项目的这一部分的目标是在可加性Schwarz预调节器的框架内对FETI方法及其一些变体进行分析,并研究子域之间全局通信的新机制。本课题所分析的方法是求解偏微分方程数值解的有效算法。这些方程在科学和工程中极为重要,因为它们是大多数物理现象的控制方程。部分研究涉及应力强度因子的快速计算,应力强度因子是断裂力学的基本指标。在这个项目中研究的FETI方法已经在使用多达一千个处理器的并行超级计算机的大规模工程问题中实现。因此,该项目取得的进展将对许多科学技术领域产生影响,例如航空航天工程、裂缝预测和流体流动问题。

项目成果

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Susanne Brenner其他文献

Computer-assisted medical history taking prior to patient consultation in the outpatient care setting: a prospective pilot project
  • DOI:
    10.1186/s12913-024-12043-3
  • 发表时间:
    2024-12-18
  • 期刊:
  • 影响因子:
    3.000
  • 作者:
    Roman Hauber;Maximilian Schirm;Mirco Lukas;Clemens Reitelbach;Jonas Brenig;Margret Breunig;Susanne Brenner;Stefan Störk;Frank Puppe
  • 通讯作者:
    Frank Puppe
HEART FAILURE MEDICATION IN THE EXTENDED RANDOMIZED INH STUDY: CLINICAL OUTCOMES ACCORDING TO PRESCRIPTION FREQUENCY AND DOSING OF GUIDELINE-RECOMMENDED DRUGS
  • DOI:
    10.1016/s0735-1097(13)60764-0
  • 发表时间:
    2013-03-12
  • 期刊:
  • 影响因子:
  • 作者:
    Guelmisal Gueder;Stefan Stoerk;Goetz Gelbrich;Susanne Brenner;Caroline Morbach;Dominik Berliner;Ertl Georg;Christiane E. Angermann
  • 通讯作者:
    Christiane E. Angermann
OBSTRUCTIVE VENTILATORY DISORDER IN HEART FAILURE: NOT ALWAYS COPD!
  • DOI:
    10.1016/s0735-1097(10)61263-6
  • 发表时间:
    2010-03-09
  • 期刊:
  • 影响因子:
  • 作者:
    Susanne Brenner;Gülmisal Güder;Kilian Frö;hlich;Gö;tz Gelbrich;Roland Jahns;Berthold Jany;Georg Ertl;Christiane E. Angermann;Stefan Stö;rk
  • 通讯作者:
    Stefan Stö;rk
PREVALENCE AND PROGNOSTIC IMPACT OF ANEMIA AND RENAL INSUFFICIENCY: RELATION TO HEART FAILURE SEVERITY
  • DOI:
    10.1016/s0735-1097(11)60374-4
  • 发表时间:
    2011-04-05
  • 期刊:
  • 影响因子:
  • 作者:
    Gulmisal Guder;Goetz Gelbrich;Susanne Brenner;Burkert Pieske;Rolf Wachter;Frank Edelmann;Bernhard Maisch;Sabine Pankuweit;Georg Ertl;Stefan Störk;Christiane E. Angermann
  • 通讯作者:
    Christiane E. Angermann

Susanne Brenner的其他文献

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{{ truncateString('Susanne Brenner', 18)}}的其他基金

Finite Element Methods for Elliptic Least-Squares Problems with Inequality Constraints
具有不等式约束的椭圆最小二乘问题的有限元方法
  • 批准号:
    2208404
  • 财政年份:
    2022
  • 资助金额:
    $ 9.85万
  • 项目类别:
    Standard Grant
Novel Finite Element Methods for Elliptic Distributed Optimal Control Problems
椭圆分布最优控制问题的新颖有限元方法
  • 批准号:
    1913035
  • 财政年份:
    2019
  • 资助金额:
    $ 9.85万
  • 项目类别:
    Standard Grant
US Participation at the Twenty-fifth International Domain Decomposition Conference
美国参加第二十五届国际域名分解会议
  • 批准号:
    1759877
  • 财政年份:
    2018
  • 资助金额:
    $ 9.85万
  • 项目类别:
    Standard Grant
Higher Order Variational Inequalities: Novel Finite Element Methods and Fast Solvers
高阶变分不等式:新颖的有限元方法和快速求解器
  • 批准号:
    1620273
  • 财政年份:
    2016
  • 资助金额:
    $ 9.85万
  • 项目类别:
    Continuing Grant
Finite Element Methods for Higher Order Variational Inequalities
高阶变分不等式的有限元方法
  • 批准号:
    1319172
  • 财政年份:
    2013
  • 资助金额:
    $ 9.85万
  • 项目类别:
    Standard Grant
Fast Interior Penalty Methods
快速内部惩罚方法
  • 批准号:
    1016332
  • 财政年份:
    2010
  • 资助金额:
    $ 9.85万
  • 项目类别:
    Standard Grant
Novel Nonconforming Finite Element Methods for Maxwell's Equations
麦克斯韦方程组的新颖非协调有限元方法
  • 批准号:
    0713835
  • 财政年份:
    2007
  • 资助金额:
    $ 9.85万
  • 项目类别:
    Standard Grant
Theory and Applications of Multigrid
多重网格理论与应用
  • 批准号:
    0738028
  • 财政年份:
    2007
  • 资助金额:
    $ 9.85万
  • 项目类别:
    Standard Grant
Theory and Applications of Multigrid
多重网格理论与应用
  • 批准号:
    0311790
  • 财政年份:
    2003
  • 资助金额:
    $ 9.85万
  • 项目类别:
    Standard Grant
Theory and Applications of Multigrid and Domain Decomposition Methods in Computational Mechanics
计算力学中多重网格和域分解方法的理论与应用
  • 批准号:
    9600133
  • 财政年份:
    1996
  • 资助金额:
    $ 9.85万
  • 项目类别:
    Standard Grant

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