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 …

We introduce a new method for the numerical integration over curved surfaces and volumes
defined by a level set function. The method is based on the solution of a small linear system …

Digital imaging technologies such as X‐ray scans and ultrasound provide a convenient and
non‐invasive way to capture high‐resolution images. The colour intensity of digital images …

A unified strategy for the higher‐order accurate integration of implicitly defined geometries is
proposed. The geometry is represented by a higher‐order level‐set function. The task is to …

An accurate implicit description of geometries is enabled by the level-set method. Level-set
data is given at the nodes of a higher-order background mesh and the interpolated zero …

We present a higher order discretization scheme for the compressible Euler and Navier–
Stokes equations with immersed boundaries. Our approach makes use of a discontinuous …

The extended finite element method (X‐FEM) has proven to be an accurate, robust method
for solving embedded interface problems. With a few exceptions, the X‐FEM has mostly …

This paper develops a computational framework with unfitted meshes to solve linear
piezoelectricity and flexoelectricity electromechanical boundary value problems including …

We first revisit the mathematical modeling of the flexoelectric effect in the context of
continuum mechanics at infinitesimal deformations. We establish and clarify the relation …

Fictitious domain methods enable to solve physical problems on unfitted grids, thereby
avoiding time-consuming and error prone meshing phases. However, an accurate …