Mathematical Sciences: Parameter Estimation Problems with Discontinuous Coefficients

数学科学：具有不连续系数的参数估计问题

• 批准号: 8702685
• 负责人: Semion Gutman
• 金额: --
• 依托单位: University of Oklahoma Norman Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-08-01 至 1989-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8702685&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Parameter; Estimation; Problems

The subject of this project is parameter estimation problems for flow equations with discontinuous coefficients. These are the problems where parameters of the medium are required to be determined by indirect measurements. Specifically the objective of this project is developing of efficient algorithms for the identification of discontinuous parameters a(x) in 2-D and 3-D problems. The suggested algorithm uses finite elements approximations of the space variable u(x,t) and does not require any discretization of the parameter variable a(x). Special averaging procedure is introduced to eliminate numerical instabilities. The general theory is based on G-convergence of parabolic operators and principle od simultaneous minimization. Preliminary results for 2- d problems show examples of successful identification and significant possibilities for vectorization. We also study the problem of further improvements in the identification by considering additional data sets of observations.

该项目的主题是具有不连续系数的流动方程的参数估计问题。 这些是需要通过间接测量来确定介质参数的问题。 具体来说，该项目的目标是开发有效的算法来识别 2-D 和 3-D 问题中的不连续参数 a(x)。 建议的算法使用空间变量 u(x,t) 的有限元近似，并且不需要参数变量 a(x) 的任何离散化。 引入特殊的平均程序来消除数值不稳定性。 一般理论基于抛物线算子的G收敛和同时最小化原理。 二维问题的初步结果显示了成功识别的示例以及矢量化的重要可能性。 我们还通过考虑额外的观察数据集来研究进一步改进识别的问题。