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 …
Linking ghost penalty and aggregated unfitted methods
In this work, we analyse the links between ghost penalty stabilisation and aggregation-
based discrete extension operators for the numerical approximation of elliptic partial …
based discrete extension operators for the numerical approximation of elliptic partial …
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 …
Robust high-order unfitted finite elements by interpolation-based discrete extension
In this work, we propose a novel formulation for the solution of partial differential equations
using finite element methods on unfitted meshes. The proposed formulation relies on the …
using finite element methods on unfitted meshes. The proposed formulation relies on the …
An accurate, adaptive and scalable parallel finite element framework for the part-scale thermo-mechanical analysis in metal additive manufacturing processes
This work introduces a distributed memory machine and octree-based Finite Element (FE)
framework for modeling metal Additive Manufacturing (AM) processes. In this sense, an …
framework for modeling metal Additive Manufacturing (AM) processes. In this sense, an …
High order unfitted finite element discretizations for explicit boundary representations
PA Martorell, S Badia - Journal of Computational Physics, 2024 - Elsevier
When modeling scientific and industrial problems, geometries are typically modeled by
explicit boundary representations obtained from computer-aided design software. Unfitted …
explicit boundary representations obtained from computer-aided design software. Unfitted …
Robust and scalable h-adaptive aggregated unfitted finite elements for interface elliptic problems
This work introduces a novel, fully robust and highly-scalable, h-adaptive aggregated
unfitted finite element method for large-scale interface elliptic problems. The new method is …
unfitted finite element method for large-scale interface elliptic problems. The new method is …
Space-time unfitted finite element methods for time-dependent problems on moving domains
We propose a space-time scheme that combines an unfitted finite element method in space
with a discontinuous Galerkin time discretisation for the accurate numerical approximation of …
with a discontinuous Galerkin time discretisation for the accurate numerical approximation of …
Geometrical discretisations for unfitted finite elements on explicit boundary representations
Unfitted (also known as embedded or immersed) finite element approximations of partial
differential equations are very attractive because they have much lower geometrical …
differential equations are very attractive because they have much lower geometrical …
Simple, accurate, and efficient embedded finite element methods for fluid–solid interaction
CE Kees, JH Collins, A Zhang - Computer Methods in Applied Mechanics …, 2022 - Elsevier
This work presents a new approach to implementing a recently proposed optimal order Cut
Finite Element Method (CutFEM) for problems with moving embedded solid structures in …
Finite Element Method (CutFEM) for problems with moving embedded solid structures in …