if you got divorce after fullfilling all legal means and valid notice period / notification most of the time HC will not entertain such petition unless she has SOLID proof to prove you wrong.
HC will not take Divorce petition, it can direct Family court to speedup or give any other directions only.
There are certain process in Divorce like Lawyer notice/RCR/Court notice/paper Publication still if she dont respond or drag the case then you have right to appeal in HC to give direction. You have to use you petition wisely by quoting
she left her own
she is not ready to join you
you have right to marital happiness [ you can find these judgments here http://mynation.net/docs/sitemap/
Even after you do all this, some henpecked judges just drag your case for decades, then you have right to complain to CJM of HC