Higher order level sets with ngsxfem

NGSolve
1

This is for ngsxfem.

I would like to define my level set fully numerically, i.e. there will be no analytic function for it. For instance, I will start with an analytically defined level set, then perturb it with a FE function that is in the same finite element space as my interpolated level set function.

If I use P1 for the level set function, I can do this no problem. But for higher order, I’m not sure. I looked at the example file “unf_interf_prob.py”, but it isn’t clear.

2

Hi Shawn,

The “reference configuration” is always a P1 level set function, but you can obtain that from a higher order level set function. You can then even take the higher order level set function as input to obtain a mesh deformation for an overall higher order approximation.
There is no explicit assumption on a “closed form”/“exact”/“analytic” level set function in ngsxfem.

Best,
Christoph

3

That’s what I figured. The documentation wasn’t clear on that.