Time complexity of simulation of biphasic contact problem

[gustav]

Hi,
I am trying to estimate the time complexity of a simulation, that solves the normal contact between a biphasic block and an rigid indenter.
Say the block has a mesh with N x N x M Hex8 elements and the simulation has T time steps. I would then think that the time complexity must at least be O(N^2 M T). But that is certainly far too simplistic: What influence does the implementation of the contact problem (I am using sliding-biphasic), the fact that the material is biphasic, etc. have?
Thanks in advance!

[maas]

Hi gustav,

Estimating time complexity is very difficult, because there are so many factors to consider. The mesh resolution and the time steps are two big ones, of course, but the effect of the nonlinear solver is difficult to predict since it will depend on how many iterations per time step are needed, which in turn depends on how nonlinear the problems is. That depends on how the model is loaded, the boundary conditions, and how well the contact is handling all the non-linearity. In addition, the fact that FEBio uses adaptive time stepping, which adjusts the time step size based on how well the model is running, makes the task of estimating time complexity practically impossible.

Best,

Steve

[gustav]

Thank you for the answer.
I thought it would be very complex. Now I have certainty.