The finite cell method for tetrahedral meshes

• Extension of the finite cell method to unstructured (tetrahedral) discretizations.
• Possibility to reuse existing finite element models.
• Possibility to exploit the advantages of a local mesh refinement.
• Possibility to include both real and virtual defects in the analysis of complex industrial applications.
• Theoretical rates of convergence are retained in the tetrahedral finite cell method.

The recently proposed Finite Cell Method (FCM) is a combination of higher order Finite Element Methods (FEM) and the Fictitious Domain Concept (FDC). So far, the discretization of the structure under investigation has been based on hexahedral cells when applying the FCM. In the current paper, we extend the FCM to tetrahedral cells offering several advantages over the standard approach. If geometrically complex industrial problems have to be solved, often geometry-conforming tetrahedral meshes already exist. Thus, only micro-structural details that are important for the application, such as pores, need to be resolved by the FDC. Another significant advantage of tetrahedral cells over hexahedral ones is the capability for local mesh refinements. This property is of special interest for problems with sharp gradients and highly localized features where a fine mesh is inevitable. By means of the tetrahedral FCM we can easily analyze the influence of the relevant micro-structural details on the mechanical behavior. The geometry of the micro-structures can be obtained using computed tomography (CT) scans. The data from the CT-scans can then be included into the FCM model in a straightforward fashion.In this paper, the performance and accuracy of the tetrahedral FCM is demonstrated using two examples. The first problem is rather academic and examines a cube with a spherical void. Here, we demonstrate that both the FCM and the FEM achieve the same rates of convergence. As a second example we consider a more practical problem where we investigate the influence of a pore on the stress distribution in an exhaust manifold of a diesel particulate filter (DPF). Again, we observe a very good agreement between the results computed using the FEM and the FCM, respectively.