Mathematical Sciences: Project in Numerical Solutions of Inverse Problems

该奖项建立了一个研究经验， 大学本科生网站为未来两个夏天在大学 华盛顿到西雅图，8名学生。 学生们将致力于 偏微分反问题的数值解 方程 他们将集中讨论某些具体问题， 特别是由电导率引起的反问题 方程 逆问题是确定电导率 通过测量身体上的电位和电流， 边界 没有已知的好方法来计算 电导率 我们打算探讨最近的尝试， Wexler，Isaacson，Kim等人计算了电导率 数字上的 该计划将持续八周。 约 两周内，将有一个或另一个讲座， 主要研究者描述了问题和各种 可能的数值方法。 学生们可以开始 使用现有的计算技术， 设施 学生将被鼓励在团队中工作， 两个，三个或更多，可能与教师合作 成员 最后，学生们将被要求给出一个 研讨会上谈论他/她的进展。

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.