Has there been any sort of study of AMR versus a uniform grid in ASPECT vis-a-vis the number of iterations for a given tolerance when one uses IMPES? I’m responding to this request from a reviewer with regards to when we only use AMR on an interface, which is being tracked with the Volume-of-Fluid interface tracking algorithm.
A more quantitative analysis should be carried out which analyzes the benefit of
AMR. In other words for a given tolerance, how many iterations are required for
solving~(32) and~(33)? with AMR? without AMR?
A grid refinement study should be carried out with / without AMR acceleration.
Jon Robey has made the computations with AMR and on a uniform grid where the uniform grid size h is the minimum size, say h_{min} allowed for the AMR algorithm and for AMR the entire interface is refined on a grid of (square) cells of size h_{min}.
A comparison between globally refined and an adaptive mesh with the same maximum refinement level? That doesn’t make much sense to me. The globally refined mesh will be 5-20x times bigger and require a lot more computational time.
A comparison between a globally refined and an adaptively refined mesh with the same number of DoFs is a more interesting question. I don’t have published results for ASPECT, but we are looking at this in https://arxiv.org/abs/1904.03317 and you typically pay something like 2-3x for adaptive meshes with geometric multigrid. In my experience this is similar for algebraic multigrid currently used in ASPECT.
If you combine the numbers, I would expect to be about 10x faster by using adaptivity (but this of course depends on the problem considered) for the same minimum resolution.
I’m not sure what you mean by ‘doesn’t make much sense to me’. But Jon did it and the paper has been accepted and we have the Galleys. Shall I send you a copy.
Later I will let you know what we were thinking. I still have to file grades for 256 students.