How long would it take for me to get a divorce in a domestic violence case if my husband refuses to sign papers?

I was looking into filing for a domestic violence divorce, and I just wanted to know how long would a case like mine take if my husband refused to sign papers. I do have two small children but the children are not biologically his. I have full sole custody of both of my children. We don't have any property that we own together, no cars etc. I would like to get divorced as quickly as possible so that I can finally move on with my life. My question is, how long do you think my divorce process will take? Also, he was arrested and was charged with simple assault and I do have court papers for that.