I am taking a Thesis-based Master degree now and I am going to choose my supervisor soon. I plan to take a PHD degree after graduation, so if possible, I wish my PHD research area could be an extension of my Master Thesis ( so that the researching experience during my Master wouldn't be wasted).
Currently I am interested in the research areas of two professors. Professor A focuses on Numerical Solution on PDE. Professor B conducted research on Numerical PDE several years ago (He was the supervisor of Professor A's Master Thesis) but it seems that he has changed his research field to Inverse Problems in the last 5 years.
Because I am not quite familiar with Inverse Problem, currently I am more interested in Numerical PDE. But since Professor B has richer researching experience, I think his recommendation may be more helpful for my PHD application.
So may I ask what is the basic knowledge for research on Inverse Problem? Does it share the same research technique with researching on Numerical PDE? Is it possible for me to change from Numerical PDE to Inverse Problem without encountering many difficulties ( in PHD application and researching)?
Thanks for your help. Any comment would be highly appreciated.