Stability and conditioning of immersed finite element methods: analysis and remedies
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 …
methods over the past decade. The main focus is the analysis and the treatment of the …
Robust and parallel scalable iterative solutions for large-scale finite cell analyses
JN Jomo, F de Prenter, M Elhaddad, D D'Angella… - Finite Elements in …, 2019 - Elsevier
The finite cell method is a flexible discretization technique for numerical analysis on
domains with complex geometries. By using a non-boundary conforming computational …
domains with complex geometries. By using a non-boundary conforming computational …
An immersed boundary hierarchical B-spline method for flexoelectricity
This paper develops a computational framework with unfitted meshes to solve linear
piezoelectricity and flexoelectricity electromechanical boundary value problems including …
piezoelectricity and flexoelectricity electromechanical boundary value problems including …
Multigrid solvers for immersed finite element methods and immersed isogeometric analysis
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 …
methods and trimmed isogeometric analysis. Elements with small intersections with the …
Mathematical and computational modeling of flexoelectricity
D Codony, A Mocci, J Barceló-Mercader… - Journal of Applied …, 2021 - pubs.aip.org
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 …
continuum mechanics at infinitesimal deformations. We establish and clarify the relation …
A mortar-type finite element approach for embedding 1D beams into 3D solid volumes
In this work we present a novel computational method for embedding arbitrary curved one-
dimensional (1D) fibers into three-dimensional (3D) solid volumes, as eg in fiber-reinforced …
dimensional (1D) fibers into three-dimensional (3D) solid volumes, as eg in fiber-reinforced …
Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes
The present article proposes a mortar-type finite element formulation for consistently
embedding curved, slender beams into 3D solid volumes. Following the fundamental …
embedding curved, slender beams into 3D solid volumes. Following the fundamental …
Preconditioning immersed isogeometric finite element methods with application to flow problems
F de Prenter, CV Verhoosel… - Computer Methods in …, 2019 - Elsevier
Immersed finite element methods generally suffer from conditioning problems when cut
elements intersect the physical domain only on a small fraction of their volume. We present a …
elements intersect the physical domain only on a small fraction of their volume. We present a …
Anisotropic variational mesh adaptation for embedded finite element methods
Embedded or immersed boundary methods (IBM) are powerful mesh-based techniques that
permit to solve partial differential equations (PDEs) in complex geometries circumventing the …
permit to solve partial differential equations (PDEs) in complex geometries circumventing the …
ILS-MPM: An implicit level-set-based material point method for frictional particulate contact mechanics of deformable particles
Finite element simulations of frictional multi-body contact problems via conformal meshes
can be challenging and computationally demanding. To render geometrical features …
can be challenging and computationally demanding. To render geometrical features …