Which subject should I study for PhD?

[kaveheng]

I have been offered two PhD positions with two different subjects, which one is more useful, applicable and has a better future both in academic and industry?

1- "FEM on Surfaces:surface diffusion, surface tension, elastic shell"

the aim is to develop and study new, structurally simple FEM on surfaces, which will focus on computing the actual surface instead of mapping between the surface and the plane

2-"Multi-objective optimization of machine components" and "Robust optimization"

Additional Details

Well, the Fund is exactly the same! Both are in the same university.

[mathtoscicomp]

It's just my two cents, but both options sound like they could be useful and fulfilling lines of research. That being said, in terms of broader applications, the finite element method project is probably more useful and applicable to other fields. You did not state what department or field this research is in, but it sounds like mechanical or some type of industrial engineering. People who do and work on FEM in engineering are very common, and probably much more so than people who are working on the type of optimization you described. In my view, the optimization route would be more "cutting edge" and probably ultimately more useful, both in academia and industry -- on the condition that you know for sure that you want to stay in your field. If are looking to keep your options open and pursue many different types of applications and potentially change fields, FEM is probably more useful and probably more marketable at the present time.