Figure 1
From: Efficient and accurate numerical quadrature for immersed boundary methods
The core concept of the fictitious domain approach: the physical domain \(\Omega _{phy}\) is extended by the fictitious domain \(\Omega _{fic}\) such that their union forms the embedding domain \(\Omega _{\cup }\). This allows the creation of a structured grid. To extinguish the influence of the fictitious domain, the material parameters of \(\Omega _{fic}\) are penalized by \(\alpha\) [11].