I used a commercial software LS Dyna in my PhD research. My mechanical engineering PhD research was completely modeling based, no experimental. I have three journal papers, which are in surface engineering journals and not computational modeling journals.
I don't know all details about the software/numerical method I am using. I am not comfortable in teaching or explaining someone how the software actually does the calculations. I always used the software as a tool and thought that a superficial knowledge about the software would be adequate. That's the reason I focused more on research rather than taking courses to fill the knowledge gaps.
Now, I am about to defend and I am feeling that I will fail as the committee might ask me mathematical questions and I will not know how to answer. I am screwed.
I am doing my PhD in top 30 universities in the world. I did not have to take coursework during my PhD. I don't know what will I do if that's the reason I fail my PhD defense. I am freaking out. Sorry for the rant. How should I tackle this problem?