# What kind of runtime behavior should we expect of Finite Element Methods?

For a typical finite element algorithms, what kind of order of growth in solution time (i.e solve stiffness matrix & post-processing) are we expected to see with an increase in number of elements?

Literature I have seen show exponential and power-law like behavior when comparing solve time to number of elements even when viewed on a log-log scale.

I ask this question as I have ran some analysis and plot the solution time vs number of elements, and it is not what I have expected, as it depicts almost linear behavior (loglog scale). Seen below: This was the case for both parallel and serial processing.

Does anyone know why this could be?

• "even when viewed on a log-log scale" -- Do you mean one axis is $\log \log x$ and the other $y$, or that both are $\log x$? Because you are doing the latter, and then linear plot means linear growth. – Raphael Jan 10 '18 at 12:13
• I removed your tech specs as they should be irrelevant. Notes: 1) A plot based on a finite sample need not fit an asymptotic (it may just be that $n_0$ is larger than what you've tried). 2) Literature will probably give worst-case results; what kind of instances are you running here? – Raphael Jan 10 '18 at 12:16
• Thank you Raphael. Both axis are log x, it is a simple bi-linear elastic-plastic analysis with one step done on Abaqus Standard. – craxsh Jan 10 '18 at 12:17
• @Raphael Does anyone use "log-log scale" to mean anything other than "plot the log of one quantity vs the log of the other"? – David Richerby Jan 10 '18 at 12:18
• @DavidRicherby I have no idea, to be honest. I was being confused about what the OP expected to see. – Raphael Jan 10 '18 at 22:15