How can I find my father’s biological father?

My father was adopted at birth. He recently took the Ancestry DNA test.

Using the information from Ancestry, and what little I knew of his mother, I was able to find her. I did this by matching last names of the listed cousins and created a database.

I have tried this with cousin on his father fathers side (based on geographic communities) with no luck.

Is there any other technique that can be recommended, other than the brute force method I am currently using, that might help?