The finite cell method is an embedded domain method, which combines the fictitious domain
approach with higher-order finite elements, adaptive integration, and weak enforcement of …

In the first part of this chapter the basic algorithmic structure and performance characteristics
of the p-version of the finite element method are surveyed with reference to elliptic problems …

We present a tetrahedral finite cell method for the simulation of incompressible flow around
geometrically complex objects. The method immerses such objects into non-boundary-fitted …

The difficulties in dealing with discontinuities related to a sharp crack are overcome in the
phase-field approach for fracture by modeling the crack as a diffusive object being described …

The implementation of hp hp-adaptivity is challenging as hanging nodes, edges, and faces
have to be constrained to ensure compatibility of the shape functions. For this reason, most …

Fictitious domain methods, such as the finite cell method, simplify the discretization of a
domain significantly. This is because the mesh does not need to conform to the domain of …

Fictitious domain methods, such as the Finite Cell Method (FCM), allow for an efficient and
accurate simulation of complex geometries by utilizing higher-order shape functions and an …

This article presents a detailed study on the potential and limitations of performing higher‐
order multi‐resolution topology optimization with the finite cell method. To circumvent …

In the 1970s during decomposition of hydrocarbons, small diameter carbon fibers were
observed, but because of limitation on characterization and measurement they were not …

In this paper, a combination of the high-order numerical manifold method with material
interpolation is established with the goal of improving the optimization of cracked structures …