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.

这个关于反问题的项目将发展数学 二阶未知系数的恢复方法 多维偏微分方程 的 这些方法的稳定性及其计算成本将 也进行分析。 年龄结构人口的应用 将被调查，出生和死亡等信息 率将从某些泛函的 人口 逆问题出现在描述 系数中含有不确定性的物理系统，或 边界条件 使用附加信息，形式为 边界数据或内部测量，更精确的模型 一个是寻求-其中模型的输出符合 尽可能精确地测量数据。 的重要例子 逆问题是使用CAT扫描的医学成像，声学 超声波图和飞机机翼的无损检测， 寻找损坏或故障的部分。