As a lab manager tasked with turning Ph.D's paper concepts into working hardware I noticed a divide between those who were really good with higher math and those who could visualize the workings of a machine or circuit. I can look at a truss and see which elements are in tension or compression but one of my physics teachers couldn't, he had to look for the sign of the force vectors, even for a simple triangular street sign support. OTOH I ran into a brick wall trying to understand Laplace Transforms and the s plane in college, where math was taught as an art form. Fortunately a chemist doesn't need it. Later I took electrical engineering classes in night school, taught by working engineers who used math to solve real-world problems, and their explanations of applying complex number theory to AC and RF circuit problems were MUCH easier to follow. This time instead of nearly flunking I aced Differential Equations and AC Circuit Analysis. Finally I could read the display on a vector network analyzer and know what to change to improve the circuit. In FEA terms that's like finding an unexpected stress riser.
Simulation is easier in electronics because measurements are less intrusive and the failures aren't destructive. It was pretty good at describing something that had already been done before, not so good at predicting into unfamiliar territory. For that we had to build, test, and adjust the sim and hardware models iteratively.
Here's a classic example of a failure caused by a mathematical model that was too difficult to implement: https://en.wikipedia.org/wiki/Hyatt_Regency_walkway_collapse
The original design of the tie rods required the threads to support only one level, the rods' solid cores bore the weight of the walkways below. The redesign left the top level's threads and nuts additionally supporting the lower level.