Resigning

I'm currently in a toxic environment at work and I'm burned out. I have a boss that acts worst than a toddler having a tantrum. If my boss isn't yelling and belittling people, then he's using derogatory and profane language, or he's simply not around and unavailable. So dealing with him is like jumping from one extreme to the next. I have tried to talk to him about it, but that's only results in him talking over me and getting mad. Meetings w/ him are uncomfortable to say the least. To make matters worst, my team calls out every other day leaving the department short staffed, and then complain that they're overwhelmed with work. I've tried meeting w/ them more frequently and being transparent to no avail. I have tried to shift work responsibilities around, but no one wants to give up their duties, and they all withhold information to hold on to some perceived power. I have spoken w/ HR and set up coaching for my team. That hasn't been successful, and HR advised me to get out because it won't get better. The department has had high turn over in the past several years (I have been here a year) and that doesn't seem to be a concern to anyone. I haven't been able to find another position yet, but I'm ready to leave. I don't want to give notice. It's not about sticking it to my employer; I'm simply TIRED! I constantly have a headache and I'd like to just quietly go and recover from all of this. To give notice or not, that is the question. I know there are times and situations when it is okay not to give notice, but I wanted to get the community's thoughts. Thanks in advance!