Mathematical Sciences: Multidimensional Reconstruction Methods for Inverse Problems

数学科学：反问题的多维重构方法

• 批准号: 9202352
• 负责人: William Rundell
• 金额: $ 8.08万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-15 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9202352&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Multidimensional; Reconstruction; Methods

This project on inverse problems will develop mathematical recovery methods for unknown coefficients from second order partial differential equations in multi-dimensions. The stability of these methods and their computational costs will also be analyzed. Applications to age-structured populations will be investigated and information such as birth and death rates will be extracted from certain functionals of the population. Inverse problems arise in mathematical models describing physical systems containing uncertainties in coefficients or boundary conditions. Using additional information, in the form of boundary data or interior measurements, a more accurate model is sought -- one in which the output of the model conforms to the measured data as closely as possible. Important examples of inverse problems are medical imaging using CAT scans, acoustic sonograms, and non-destructive testing of aircraft wings in searching for damaged or failed sections.

该反问题项目将开发多维二阶偏微分方程中未知系数的数学恢复方法。 还将分析这些方法的稳定性及其计算成本。 将研究对年龄结构人口的应用，并从人口的某些功能中提取出生率和死亡率等信息。 逆问题出现在描述包含系数或边界条件不确定性的物理系统的数学模型中。 使用边界数据或内部测量形式的附加信息，寻求一种更准确的模型——模型的输出尽可能接近测量数据。 逆问题的重要例子是使用 CAT 扫描的医学成像、声学超声图以及对飞机机翼进行无损测试以寻找损坏或失效的部分。