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 …

This review paper discusses the developments in immersed or unfitted finite element
methods over the past decade. The main focus is the analysis and the treatment of the …

Nitsche's method can be used as a coupling tool for non-matching discretizations by weakly
enforcing interface constraints. We explore the use of weak coupling based on Nitsche's …

The advent of isogeometric analysis (IGA) using the same basis functions for design and
analysis constitutes a milestone in the unification of geometric modeling and numerical …

Enforcing essential boundary conditions plays a central role in immersed boundary
methods. Nitsche's idea has proven to be a reliable concept to satisfy weakly boundary and …

Thin shell structures are widely used in the aerospace, automotive and mechanical
engineering industries. They are ideal candidates for the isogeometric analysis paradigm …

This paper reviews the state-of-the-art in numerical wave propagation analysis. The main
focus in that regard is on guided wave-based structural health monitoring (SHM) …

This paper presents an efficient and accurate method for the integration of discontinuous
functions on a background mesh in three dimensions. This task is important in computational …

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 …