First some perspective: I deal with very large structural (rocket) problems, so for solution time (lots of optimizations) I am highly incented to use single-pass analyses rather than multi-pass. So readers should understand that my question deals with finding an approach that maximizes the prospects of getting reasonable results using single-pass analysis.
Up until now I have "accepted" that if the p-level of my problem was below 9 (the maximum), then I could expect my solutions to be reasonably numerically accurate since "the math hadn't red-lined". The first question is, does anyone know that to be "mostly true" or "a reckless assumption"? To answer that you must know that I deal with concept level designs: I do NOT need absolutely accurate numerical results... I just need results that are accurate enough to yield accurate design insight.
The next question is somewhat related but deals specifically with solution time. Despite the p-level of my model being almost entirely 7 and below, it's taking 3 hours to run a simple 4-parameter optimization. More elements means more equations... but it also means that stress gradients are much easier for the math to deal with. My question is this (kind of hoping a developer will answer). Is there a target "mathematical sweet spot" for geometrically complex problems? If the default, coarse mesh, results in alot of P=8 elements and I want to reduce my solution time, should I refine the mesh just enough to get to most elements being P=7, or should I, if possible, increase the mesh density until most of the model is P=5 or lower?
Thanks.