Varying hausd throughout the volume

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#1

Dear developers,

I was wondering if it is possible in any way to specify a varying hausd throughout the volume to be meshed? The reason I would like to do this is because i am looking at discretizing a level-set where the feature sizes can vary significantly throughout the volume.

Kind regards,
K

#2

Hi Karl,

The hausdorff parameter applies on boundaries only.

For now, you can choose one hausdorff value per boundary condition (Mmg reference) using a local parameter file. Though, it is not possible to have a variable hausdorff field along one given boundary reference.

To simulate a variable Hausdorff value, you can now provide a metric field while discretizing a level-set (since the release 5.5.0). A command line example is provided here. A library example is provided in the libexamples/mmg3d/IsosurfDiscretization_lsAndMetric folder of Mmg.

I hope that it will help you,

Regards,
Algiane

#3

Dear Algiane,

Specifying the Hausdorff parameter per boundary I am afraid is not really a solution for my case as I have continuously varying features.

Regarding the metric you mention, I had indeed noticed that in more recent versions of the develop branch it was possible to specify a metric in addition to the level-set, and actually also tried it out. My understanding was, however, that this metric controlled the size of the mesh, which I can work with, but is not ideal. Given what you said that this metric simulates a variable Hausdorff value I am now in doubt, what do you mean exactly when you say this metric simulates a variable Hausdorff value? Was I correct in thinking that this metric controls the mesh size or does it control something slightly different?

Regards,
K

#4

Dear Karl,

I understand your issue regarding the Hausdorff value per boundary.

For the metric usage, I propose this solution because it is the only one that comes to my mind as Mmg doesn’t allow to have a variable Hausdorff value :

  • you can compute an isotropic or anisotropic metric that depends on the curvature of the implicit boundary (see for example the section 3.2 of the work of A.Claisse, V.Ducrot and P.Frey);
  • By using a variable value for \epsilon I think that you can have almost the same behaviour than using a variable Hausdorff value (i.e. you will impose smaller edges size in high curvature area but the sensitivity to the curvature will be variable).

I am sorry to have nothing simplier to propose,

Regards,
Algiane

#5

Dear Algiane,

Thanks for the suggestion! It looks like it may be useful for my case. I will try it out and see how well it works for my case.

Regards,
K