Design and Analysis of Algorithms for Structured Nonlinear Problems
结构化非线性问题的算法设计与分析
基本信息
- 批准号:RGPIN-2015-05481
- 负责人:
- 金额:$ 1.75万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2016
- 资助国家:加拿大
- 起止时间:2016-01-01 至 2017-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Modern science relies very heavily on computer simulation of scenarios that behave according to theoretical models. If the simulations perform as expected in the “testing” phase, then confidence in the theory underlying the model is bolstered. If the simulations manage to predict real-world behavior, especially if it is surprising (or might potentially cost lives or money if unanticipated) then they are of social benefit, not just academic importance. But carrying out such simulations on a computer often involves solving a potentially large number of nonlinear equations. Doing so reliably and efficiently enough that predictions can be made in real time can be (depending on the subject area) extremely challenging. This project aims at producing new algorithms to make such solutions both more reliable and more efficient.
The nonlinear algebraic problems that these algorithms are intended to solve occur in very many branches of engineering and science. Examples include fluid-structure interaction, computer-aided geometric design (CAGD) for manufacture, and what is coming to be known as “Algebraic Biology.” Fluid-structure interaction is important in wind engineering of tall buildings, large bridges, transmission wires, cables and pipes. CAGD is a principal tool for manufacture of automobiles, aircraft, ships and other structures. The economic impact of those industries in total is in the billions in Canada alone. Algebraic Biology might be even more important in the future; already the design of new organisms is worth billions.
Specifically, this project seeks to create numerically stable and efficient algorithms for certain structured mathematical modelling problems. We term this general approach the creation of “Domain Specific Algorithms.” The main tool to be used for these algorithms is the replacement of the problem with a structured eigenvalue problem to be solved by standard or special-purpose iterative numerical methods. The structured matrices to be used come from my earlier work on companion pencils and linearizations from the Lagrange, Hermite and Birkhoff interpolational bases.
现代科学在很大程度上依赖于计算机模拟的情况下,根据理论模型的行为。如果模拟在“测试”阶段的表现符合预期,那么对模型理论的信心就会得到加强。如果这些模拟能够预测真实世界的行为,特别是那些令人惊讶的行为(或者如果没有预料到,可能会导致生命或金钱的损失),那么它们就具有社会效益,而不仅仅是学术上的重要性。要做到足够可靠和有效,以便能够在真实的时间内做出预测,这可能是非常具有挑战性的(取决于主题领域)。该项目旨在产生新的算法,使这些解决方案更可靠,更有效。
这些算法的目的是解决非线性代数问题发生在工程和科学的许多分支。例子包括流体-结构相互作用,用于制造的计算机辅助几何设计(CAGD),以及即将被称为“代数生物学”的东西。流固耦合是高层建筑、大型桥梁、输电线、缆、管道等风工程中的重要问题。CAGD是汽车、飞机、船舶和其他结构制造的主要工具。仅在加拿大,这些行业的经济影响就达数十亿美元。在未来,代数生物学可能会更加重要;新生物体的设计已经价值数十亿美元。
具体而言,该项目旨在为某些结构化数学建模问题创建数值稳定和有效的算法。我们将这种通用方法称为“特定领域算法”的创建。这些算法的主要工具是用标准或专用迭代数值方法解决的结构特征值问题的问题。结构矩阵使用来自我的早期工作同伴铅笔和线性化的拉格朗日,厄米和伯克霍夫插值基地。
项目成果
期刊论文数量(0)
专著数量(0)
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会议论文数量(0)
专利数量(0)
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Corless, Robert其他文献
Corless, Robert的其他文献
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{{ truncateString('Corless, Robert', 18)}}的其他基金
Hybrid Symbolic-Numeric Algorithms for Complex Nonlinear Systems
复杂非线性系统的混合符号数值算法
- 批准号:
RGPIN-2020-06438 - 财政年份:2022
- 资助金额:
$ 1.75万 - 项目类别:
Discovery Grants Program - Individual
Hybrid Symbolic-Numeric Algorithms for Complex Nonlinear Systems
复杂非线性系统的混合符号数值算法
- 批准号:
RGPIN-2020-06438 - 财政年份:2021
- 资助金额:
$ 1.75万 - 项目类别:
Discovery Grants Program - Individual
Hybrid Symbolic-Numeric Algorithms for Complex Nonlinear Systems
复杂非线性系统的混合符号数值算法
- 批准号:
RGPIN-2020-06438 - 财政年份:2020
- 资助金额:
$ 1.75万 - 项目类别:
Discovery Grants Program - Individual
Design and Analysis of Algorithms for Structured Nonlinear Problems
结构化非线性问题的算法设计与分析
- 批准号:
RGPIN-2015-05481 - 财政年份:2019
- 资助金额:
$ 1.75万 - 项目类别:
Discovery Grants Program - Individual
Design and Analysis of Algorithms for Structured Nonlinear Problems
结构化非线性问题的算法设计与分析
- 批准号:
RGPIN-2015-05481 - 财政年份:2018
- 资助金额:
$ 1.75万 - 项目类别:
Discovery Grants Program - Individual
Design and Analysis of Algorithms for Structured Nonlinear Problems
结构化非线性问题的算法设计与分析
- 批准号:
RGPIN-2015-05481 - 财政年份:2017
- 资助金额:
$ 1.75万 - 项目类别:
Discovery Grants Program - Individual
Design and Analysis of Algorithms for Structured Nonlinear Problems
结构化非线性问题的算法设计与分析
- 批准号:
RGPIN-2015-05481 - 财政年份:2015
- 资助金额:
$ 1.75万 - 项目类别:
Discovery Grants Program - Individual
Algorithms for structured nonlinear models
结构化非线性模型的算法
- 批准号:
36393-2010 - 财政年份:2014
- 资助金额:
$ 1.75万 - 项目类别:
Discovery Grants Program - Individual
Algorithms for structured nonlinear models
结构化非线性模型的算法
- 批准号:
36393-2010 - 财政年份:2013
- 资助金额:
$ 1.75万 - 项目类别:
Discovery Grants Program - Individual
Algorithms for structured nonlinear models
结构化非线性模型的算法
- 批准号:
36393-2010 - 财政年份:2012
- 资助金额:
$ 1.75万 - 项目类别:
Discovery Grants Program - Individual
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