Do you think a computational math student should go to student seminars about pure math? I am a first year graduate student with thesis topic on computational math, in particular inverse problem. Based on what I know, this area requires a solid background of functional analysis and numerical PDE. 

Currently I am wondering what kinds of seminars I should attend. My department have weekly student seminars on analysis and theoretical PDE. Basically students presenting their work/research output to their supervisor. As this post and the great mathematician Terence Tao suggested, attending talks and conferences in different areas is beneficial.  Hence I will try to attend other numercial analysis groups' seminars. But I was wondering whether it's helpful for me to attend those pure math seminars about analysis or PDE.

Though I found those seminars are interesting, my main concern is that being lack of suitable background, I may only be able to understand a small part of the seminar (a PHD student working on theoretical PDE once told me he can't understand his group-mates' seminar until his third year). The other concern is I will have less time for my own research . So in your opinion, what kinds of seminars I should attend? Shall I attend seminars in other departments (say physics or engineering) regularly?
You're not going to be able to determine which seminars are useful to you without going to some of them. And yes, some of them will be wastes of time. But I've gone to seminar series that should be extremely topical to me that never benefitted me directly, and some from peripheral departments that turned out to be very useful - as mentioned in one of the comments, even if you don't take away anything from the lecture, it's useful to know people. One day, you might find yourself in need of a graph theorist or some such, and it's helpful to have met them once, or be able to say "I saw your talk..." in an introductory email.

Also, selfishly, from an applied field, having applied participants in more theory heavy fields is helpful for teaching theory students how to present their topics to people outside their narrow subfield.