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 …

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 …

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 …

Abstract Full Waveform Inversion (FWI) is a successful and well-established inverse method
for reconstructing material models from measured wave signals. In the field of seismic …

Ill-conditioning of the system matrix is a well-known complication in immersed finite element
methods and trimmed isogeometric analysis. Elements with small intersections with the …

We present a unified framework for developing and analyzing immersed finite-element (IFE)
spaces for solving typical elliptic interface problems with interface-independent meshes …

This paper proposes a novel Immersed Boundary Method where the embedded domain is
exactly described by using its Computer‐Aided Design (CAD) boundary representation with …

Abstract The Finite Cell Method (FCM) together with Isogeometric analysis (IGA) has been
applied successfully in various problems in solid mechanics, in image-based analysis, fluid …

Embedded or immersed boundary methods (IBM) are powerful mesh-based techniques that
permit to solve partial differential equations (PDEs) in complex geometries circumventing the …

In patient specific biomedical simulation, the numerical model is usually created after
cumbersome, time consuming procedures which often require highly specialized human …