I am currently working on reproducing CutFEM simulations for multi-material Poisson problems. I have carefully read the paper “CutFEM: Discretizing geometry and partial differential equations” by Prof. Erik Burman and colleagues, as well as the related example files provided in the ngsxfem GitHub repository.

In the paper, the authors provide the penalty parameter formula for the two-material Poisson problem in equation (30). However, I could not find detailed information regarding the specific constants in this formula or the practical steps to compute them. It is possible that I may have overlooked this part. I would appreciate it if someone could help clarify whether this information is provided elsewhere in the paper or in other references.

Additionally, in Section 6.1 of the paper (Stabilized Nitsche fictitious domain method for the Poisson problem), the Ghost Penalty coefficient is defined for the single-material case as 0.1 * h. However, in the GitHub example fictdom.py (located in the demos directory), the Ghost Penalty parameter is set to 0.1 / h². This difference confuses me.

• Why are these two scalings different?
• How should I choose the appropriate Ghost Penalty parameter in CutFEM, especially when dealing with multi-material interface problems?
• Is there a general guideline or best practice for setting this parameter to achieve stable and accurate results?

I would appreciate any insights, explanations, or references on this topic.

Thank you very much for your time and help!