Discrete Electrical Network Approximations for Solving the Dirichlet Problem on the Unit Rectangle

This talk was presented the UGA Math Club by Tyler Johnson, fourth year undergrad at UGA, on research that he had done at an REU the previous summer.

Abstract: The Dirichlet Problem is a classical problem with many applications and of particular interest to physicists: given a region with a specified conductivity function, if a charge distribution is pre-determined on the boundary, what is the induced electrical potential function through the region? Furthermore, is it unique? Generalizations of this problem can be extended to discrete electrical networks; the discrete problem is much easier to solve, requiring no analysis, just relatively simple linear algebra. We'll cover a (partial) proof that the solutions to the discrete problem can be used to approximate the solution to the classical one. Don't worry, there will be pictures.

Видео Discrete Electrical Network Approximations for Solving the Dirichlet Problem on the Unit Rectangle канала E. Santiago Beck