Applied Math Seminar- Numerical methods for computing solution structures of  nonlinear PDEs

Date and and Time: Friday, March 4th, at 3:15-4:15 pm

Place: Zoom

Zoom link: https://gwu-edu.zoom.us/s/98013143310

passcode: 349324

Speaker:  Wenrui Hao, Pennsylvania State University , Assistant professor

Title: Numerical methods for computing solution structures of  nonlinear PDEs

Abstract: Many systems of nonlinear PDEs are arising from engineering and biology and have attracted research scientists to study the multiple solution structure such as pattern formation. In this talk, I will present several methods to compute the multiple solutions of nonlinear PDEs. In specific, I will introduce the homotopy continuation technique to compute the multiple steady states of nonlinear differential equations and also to explore the relationship between the number of steady-states and parameters. Then I will also introduce a randomized Newton's method to solve the nonlinear system arising from neural network discretization of the nonlinear PDEs. Several benchmark problems will be used to illustrate these ideas.