Mathematical Sciences: Project in Numerical Solutions of Inverse Problems

数学科学：反问题数值解项目

• 批准号: 8804076
• 负责人: Edward Curtis
• 金额: $ 6.4万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-15 至 1990-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8804076&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Project; Numerical; Solutions

This award establishes an Research Experiences For Undergraduates site for the next two summers at the University of Washington at Seattle for 8 students. The students will work on numerical solutions of inverse problems for partial differential equations. They will focus on certain specific problems, in particular on inverse problems arising from the conductivity equation. The inverse problem is to determine the conductivity throughout a body from measurements of potentials and currents on the boundary. There is no known good way to calculate the conductivity. We intend to explore the recent attempts by Wexler, Isaacson, Kim and others to compute the conductivity numerically. The program will run for eight weeks. For about two weeks there will be lectures by one or the other of the Principal Investigator's describing the problems and various possible numerical approaches. The students can then begin working on projects of their own, using the available computing facilities. The students will be encouraged to work in teams of two, three or more, possibly in collaboration with the faculty members. At the end the students will be expected to give a seminar talk on his/her progress.

该奖项在接下来的两个夏天在西雅图华盛顿大学为 8 名学生建立了一个本科生研究体验网站。 学生将研究偏微分方程反问题的数值解。 他们将重点关注某些特定问题，特别是电导率方程引起的反问题。 反问题是通过测量边界上的电位和电流来确定整个身体的电导率。 目前尚无已知的计算电导率的好方法。 我们打算探索 Wexler、Isaacson、Kim 等人最近在数值计算电导率方面的尝试。 该计划将持续八周。 在大约两周的时间里，首席研究员将进行讲座，描述问题和各种可能的数值方法。 然后，学生可以使用可用的计算设施开始开展自己的项目。 我们将鼓励学生以两人、三人或更多人为一组进行工作，并可能与教师合作。 最后，学生将就他/她的进展进行研讨会演讲。