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界长期存在的问题。在这个项目中，PI 和他的合作者将开发新颖的结构保持算法，以准确有效地解决大规模特征值问题。具体来说，他们将重点关注结构化矩阵笔的大规模特征值问题、二次特征值问题和非线性特征值问题。他们将研究用于解决这些特征值问题的结构保持Rayleight-Ritz子空间投影技术，包括Krylov子空间的多级正交化过程、二阶Arnoldi（SOAR）方法和非线性Arnoldi方法。 该项目的目标代表了通过计算数学和模拟的应用在科学努力和工程设计前沿领域的重大进步。目标应用包括电路和 MEMS 器件模拟、结构动力学、声学和电磁学的有限元分析所产生的这些类型的特征值问题。这些应用对于下一代电子产品、汽车效率和安全以及能效监控设备等具有重要的技术重要性。该项目的结果将是对这些问题的有效计算模拟策略的描述以及公开提供的软件。