Stability and conditioning of immersed finite element methods: analysis and remedies

F de Prenter, CV Verhoosel, EH van Brummelen… - … Methods in Engineering, 2023 - Springer
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 …

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 …

An immersed boundary hierarchical B-spline method for flexoelectricity

D Codony, O Marco, S Fernández-Méndez… - Computer Methods in …, 2019 - Elsevier
This paper develops a computational framework with unfitted meshes to solve linear
piezoelectricity and flexoelectricity electromechanical boundary value problems including …

Multigrid solvers for immersed finite element methods and immersed isogeometric analysis

F de Prenter, CV Verhoosel, EH van Brummelen… - Computational …, 2020 - Springer
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 …

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 …

A mortar-type finite element approach for embedding 1D beams into 3D solid volumes

I Steinbrecher, M Mayr, MJ Grill, J Kremheller… - Computational …, 2020 - Springer
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 …

Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes

I Steinbrecher, A Popp, C Meier - Computational Mechanics, 2022 - Springer
The present article proposes a mortar-type finite element formulation for consistently
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 …

Anisotropic variational mesh adaptation for embedded finite element methods

S Rahmani, J Baiges, J Principe - Computer Methods in Applied Mechanics …, 2025 - Elsevier
Embedded or immersed boundary methods (IBM) are powerful mesh-based techniques that
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

C Liu, WC Sun - Computer Methods in Applied Mechanics and …, 2020 - Elsevier
Finite element simulations of frictional multi-body contact problems via conformal meshes
can be challenging and computationally demanding. To render geometrical features …