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I am looking for AMR/re-meshing software (structured grids would suffice) that is NOT based on quad-octrees, i.e., a fixed refinement rate of 2 but (ideally) something user defined, i.e., ratios of 1.2, 1.5, ... of coarse to fine.

Of course, this is a bit more complicated than the standard quad/octree styles, since (for instance in the case of refinement) multiple coarse cells would have to communicate, not every coarse cell on its own.

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    $\begingroup$ The other common AMR technique is nested grids which in theory could do what you want, but I think in practice every implementation also enforces an integer (typically power of 2) refinement ratio. You could look into AMReX and Chombo to see if there might be some way to get them to do what you want. $\endgroup$
    – helloworld922
    Commented Aug 14, 2023 at 15:03
  • $\begingroup$ Can you clarify whether you are interested in things other than equal bisection (as you state in the body) or other than quads/hexes (as you state in the title)? $\endgroup$
    – Wolfgang Bangerth
    Commented Aug 14, 2023 at 16:23
  • $\begingroup$ @WolfgangBangerth The former, i.e., non-integer ratios of coarse to fine. The element type does not matter too much for me. $\endgroup$
    – Dan Doe
    Commented Aug 15, 2023 at 10:11
  • $\begingroup$ @helloworld922 From the overview of Chombo: "Regions requiring additional resolution are identified by computing some local measure of the original error and covered by a disjoint union of rectangles in the domain, which are then refined by some integer factor." For AMReX, all examples seem to have also at least an integer ratio. Seems like your guess seems to be true, but thanks anyway! $\endgroup$
    – Dan Doe
    Commented Aug 15, 2023 at 14:22
  • $\begingroup$ Are you envisioning the outcome from a 1.2 ratio would be something like a coarse grid of 5 elements connected to a "fine" grid of 6 elements, such that only the top and bottom nodes would line up? Because that doesn't sound desirable at all, as it would mean that the only solution compatible with both discretizations along the edge is linear. $\endgroup$
    – Mikael Öhman
    Commented Aug 17, 2023 at 23:28

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deal.II can subdivide cells in ways that are not geometrically 2:1, but "graded" in certain directions. It does this by "mapping" the new mid-points of edges and cells in non-uniform ways. Take a look at section 6.3 and Fig. 13 of this paper to see an example; the mesh shown there starts from a single cell, and when refined the new mid-points are simply placed not at the obvious midpoint of the cell/edge.

Disclaimer: I am one of the principal developers of deal.II.

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  • $\begingroup$ Thanks, interesting approach. Is there an example which is at least somewhat similar to the short discussion in the publication? $\endgroup$
    – Dan Doe
    Commented Aug 15, 2023 at 14:03
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    $\begingroup$ @DanDoe I don't recall, but there are tutorial programs that show the construction of manifolds (e.g., step-53) and it would be relatively straightforward to create a manifold that generates the mesh shown in the paper. In fact, I believe that the FunctionManifold class will do 90% of the work for you already: dealii.org/developer/doxygen/deal.II/classFunctionManifold.html $\endgroup$
    – Wolfgang Bangerth
    Commented Aug 16, 2023 at 17:05

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