LDR's are always tough. I was in one for 6 months with my fiance (now husband). The only thing that made mine bearable was having a defined ending date. If you know when the distance will end, it gives you something to look forward to. If not, plan visits so that you have something positive in your relationship to look forward to, instead of constantly focusing on the negative aspects of distance. A few other things that helped us:
-Schedule a time to talk every day. Use texting to set up a time so you can avoid the frustration of phone tag.
-Talk about what worries you specifically and how you can deal with it, e.g. "I'm worried that the time difference will make it impossible for us to talk every day--how about talking every other day and emailing or texting in between?"
-When you do communicate, remember to include positives and things you are grateful for. It is easy to get mired in the day-to-day crap that bothers everyone, but focusing on the positive makes conversations something to look forward to as opposed to endless rant-fests. This is especially hard to do in LDR's because if you talk at the end of the day when you're frazzled, you give them the leftovers. It is important not to get sucked into that trap.
-This can be a time to work on your friendship. My husband and I sent each other funny videos, care packages, and letters. Without that physical element, we truly became great friends and it has served us well.
Best of luck in your residency program and remember to be kind to each other during this tough time.