Grandmother with dementia doesn't recognize me?

My grandmother has been diagnosed with dementia, and she's been that way for about a year now. Until recently, however, she has always remembered who we all are, but she would sometimes hear voices, and imagine conversations that never happened.

Now, she doesn't recognize me, at all. Worse than that, though, any time she sees me, she thinks I'm my father. Now, he is not the best person, in the world (and that's a huge understatement). He was extremely abusive to my sister and I, as well as our mother. After we left, we haven't seen him in years. Anyway, whenever we go to see her, she starts getting mad, and yelling at me when I walk in, because she thinks I am him. And, she won't ever let me tell her who I am, or that I'm not him. She interrupts me, and screams for me to leave. Honestly, considering how much he put all of us through, I can't blame her for her reaction to seeing someone she believes to be him, but this means that I'm never able to see her anymore, and I'm not sure hours much time she may have left.

I just wish there was something I could do to make her stop thinking I'm him, because I really want to spend time with her, but at the same time, I don't want to cause her to get upset every time I'm there, because of who she thinks I am.

Has anyone else experienced anything like this? Does anyone know of anything I could do to remedy this? Thanks a lot for any kind of advice you may be able to give.