Dear NGSolve community,
I setup a model very similar to the example “intlset.ipynb” from the tutorial. Thereby, I obtained a strange linear approximation for a circle. Did I do something wrong in the setup or is the approximation really like this due to some difficulties in finding intersection points or similar?
intlset_modified.ipynb (18.3 KB)
Thank you for your help.
Best regards,
Michael Loibl
Hi Michael, I think you have done everything right in the sense of approximating the circle geometry with an elementwise P1 candidate discrete geometry in the sense of InterpolateToP1. When it comes to obtaining such an approximation candidate, InterpolateToP1 follows the idea of preserving the nodal values of a lset function to obtain the P1 lset function, and to my best understanding this is exactly what we see here. An alternative would be to use lset_p1.Set(…), which realises a discrete projection containing information from “inside” the elements. In any case, what we mostly care about is the asymptotic behaviour of the approximation (e.g. max diff scales as h^2), and this could be realised in both ways. This also points to the suggestion of decreasing h if a more accurate approximation is needed for e.g. application reasons. Best, Fabian
