Efficient Sructured Direct Solvers and Robust Structured Preconditioners for Large Linear Systems and Their Applications

大型线性系统的高效结构化直接求解器和鲁棒结构化预处理器及其应用

基本信息

  • 批准号:
    1115572
  • 负责人:
  • 金额:
    $ 6.5万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2011
  • 资助国家:
    美国
  • 起止时间:
    2011-08-15 至 2014-07-31
  • 项目状态:
    已结题

项目摘要

In this project, the investigator and his students design new efficient structured matrix techniques for large linear systems, including fast direct solvers and robust effective preconditioners. These techniques take advantage of certain hidden rank structures in linear systems arising from practical applications. Efficient multi-layer structures and flexible rank requirements are considered. The methods have nearly linear complexity for linear systems arising from the discretization of certain partial differential equations. They can also work as effective preconditioners. Robustness of preconditioning for positive definite problems is shown. The methods are useful for problems which have been considered difficult for classical direct or iterative solvers.This project has broader impacts in many complex numerical problems and engineering simulations, such as differential equations, seismic imaging, climate, electromagnetic field simulation, signal processing, and integrated circuit simulation. The major computational work in these applications is often to solve large-scale linear systems, which can benefit from the efficient black-box solvers or preconditioners developed in this project. These methods help break some classical lower complexity bounds. Students are involved in all aspects of the project, and are trained in various mathematical and engineering areas. The investigator's team plan to build a freely available open source package for both practical applications and education. Minisymposia organized by the investigator, as well as conferences talks, seminars, and journal articles, are used to exchange ideas and to disseminate the results.
在这个项目中,研究人员和他的学生为大型线性系统设计了新的高效结构矩阵技术,包括快速直接求解器和稳健有效的预条件。这些技术利用了实际应用中出现的线性系统中的某些隐藏的秩结构。考虑了高效的多层结构和灵活的等级要求。对于某些偏微分方程组的离散化所产生的线性系统,该方法具有近线性的复杂性。它们也可以起到有效的预调节作用。证明了正定问题的预条件的稳健性。该项目在许多复杂的数值问题和工程模拟中具有广泛的影响,如微分方程组、地震成像、气候、电磁场模拟、信号处理和集成电路模拟。这些应用中的主要计算工作通常是求解大规模线性系统,这可以受益于本项目中开发的高效黑盒求解器或预条件器。这些方法有助于打破一些经典的低复杂性界限。学生们参与了项目的各个方面,并接受了各种数学和工程领域的培训。研究人员的团队计划构建一个可免费获得的开放源码包,用于实际应用和教育。由研究人员组织的小型研讨会以及会议、讲座、研讨会和期刊文章被用来交流想法和传播结果。

项目成果

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专利数量(0)

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Jianlin Xia其他文献

Single-shot dark-field imaging
单次暗场成像
  • DOI:
  • 发表时间:
    2018
  • 期刊:
  • 影响因子:
    2.8
  • 作者:
    Zhili Wang;Dalin Liu;Kun Ren;Xiaomin Shi;Jianlin Xia
  • 通讯作者:
    Jianlin Xia
Effective matrix-free preconditioning for the augmented immersed interface method
熔盐在螺旋槽管内的转变和湍流对流换热
  • DOI:
    10.1016/j.expthermflusci.2013.01.014
  • 发表时间:
    2015
  • 期刊:
  • 影响因子:
    4.1
  • 作者:
    Jianlin Xia;Zhilin Li;Xin Ye
  • 通讯作者:
    Xin Ye
A Robust Randomized Indicator Method for Accurate Symmetric Eigenvalue Detection
  • DOI:
    10.1007/s10915-024-02599-x
  • 发表时间:
    2024-06-28
  • 期刊:
  • 影响因子:
    3.300
  • 作者:
    Zhongyuan Chen;Jiguang Sun;Jianlin Xia
  • 通讯作者:
    Jianlin Xia
Low-Rank Update Eigensolver for Supercell Band Structure Calculations
  • DOI:
    10.1023/a:1020724313574
  • 发表时间:
    2002-10-01
  • 期刊:
  • 影响因子:
    2.500
  • 作者:
    Ming Gu;Beresford Parlett;David Z.-Y. Ting;Jianlin Xia
  • 通讯作者:
    Jianlin Xia

Jianlin Xia的其他文献

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{{ truncateString('Jianlin Xia', 18)}}的其他基金

Integration of Randomized Methods and Fast and Reliable Matrix Computations
随机方法与快速可靠的矩阵计算的集成
  • 批准号:
    2111007
  • 财政年份:
    2021
  • 资助金额:
    $ 6.5万
  • 项目类别:
    Standard Grant
Fast and Reliable Hierarchical Structured Methods for More General Matrix Computations
用于更一般矩阵计算的快速可靠的分层结构化方法
  • 批准号:
    1819166
  • 财政年份:
    2018
  • 资助金额:
    $ 6.5万
  • 项目类别:
    Standard Grant
Conference on Fast Direct Solvers
快速直接求解器会议
  • 批准号:
    1901567
  • 财政年份:
    2018
  • 资助金额:
    $ 6.5万
  • 项目类别:
    Standard Grant
CAREER: Structured Matrix Computations: Foundations, Methods, and Applications
职业:结构化矩阵计算:基础、方法和应用
  • 批准号:
    1255416
  • 财政年份:
    2013
  • 资助金额:
    $ 6.5万
  • 项目类别:
    Continuing Grant

相似海外基金

Acquiring and Using Sructured Information in Memory
获取和使用内存中的结构化信息
  • 批准号:
    7682806
  • 财政年份:
    1977
  • 资助金额:
    $ 6.5万
  • 项目类别:
    Standard Grant
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