Mathematical Sciences: Project in Numerical Solutions of Inverse Problems

该奖项为华盛顿大学西雅图分校未来两个夏季的8名学生建立了本科生研究经验网站。学生们将研究偏微分方程反问题的数值解。他们将专注于某些特定的问题，特别是由电导率方程引起的逆问题。相反的问题是通过测量边界上的电位和电流来确定整个物体的电导率。目前还没有已知的计算电导率的好方法。我们打算探索weexler， Isaacson， Kim等人最近对电导率的数值计算的尝试。该项目将持续八周。在大约两周的时间里，将有一个或另一个首席研究员的讲座，描述问题和各种可能的数值方法。然后，学生们可以利用现有的计算机设备开始自己的项目。学生将被鼓励以两人、三人或更多的团队合作，可能与教师合作。最后，学生将被要求就他/她的进步做一个研讨会。

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.