Structure-Preserving Algorithms for Solving Large Scale Eigenvalue Problems

用于解决大规模特征值问题的结构保持算法

• 批准号: 0611548
• 负责人: Zhaojun Bai
• 金额: $ 19万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-15 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0611548&HistoricalAwards=false
• 关键词: Structure; Preserving; Algorithms; Solving; Large

Optimization of large scale eigenvalue computations is a long-standingproblem in computational mathematics and scientific computing community. In this project, the PI and his collaborators will develop novel structure-preserving algorithms for accurately and efficiently solvinglarge scale eigenvalue problems. Specifically, they will focus on large scale eigenvalue problems of structured matrix pencils, quadratic eigenvalue problems and nonlinear eigenvalue problems. They will study structure-preserving Rayleight-Ritz subspace projection techniques forsolving these eigenvalue problems, that include the multi-level orthogonalization process of Krylov subspaces, second-order Arnoldi (SOAR) method and the nonlinear Arnoldi method. The goal of the project represents a significant advance in a frontier area of scientific endeavor and engineering design through the application of computational mathematics and simulations. The target applications include these types of eigenvalue problems arising from simulations of electrical circuits and MEMS devices, finite element analysis of structure dynamics, acoustics and electromagnetics. These applications are of great technology importancefor next-generation electronics, automobile efficiency and safety and energy-efficiency monitoring devices and others. The results of this project will be both the description of effective computationalsimulation strategies for these problems and also software made publiclyavailable.

大规模特征值计算的优化是计算数学和科学计算社区中的长期存在问题。在这个项目中，PI及其合作者将开发出新颖的结构性保护算法，以准确有效地求解量表特征值问题。具体而言，他们将着重于结构化基质铅笔，二次特征值问题和非线性特征值问题的大规模特征值问题。他们将研究包含这些特征值问题的延伸结构的Rayleight-Ritz子空间投影技术，其中包括Krylov子空间的多级正交过程，二阶Arnoldi（Soar）方法和非线性Arnoldi方法。 该项目的目标代表了通过应用计算数学和模拟的科学努力和工程设计领域的重大进步。目标应用包括由电路和MEMS设备的模拟引起的这些类型的特征值问题，结构动力学，声学和电磁学的有限元分析。这些应用对于下一代电子产品，汽车效率以及安全性和能源效率监控设备等非常重要。该项目的结果既是这些问题有效的计算模拟策略的描述，也将是公共可用的软件。