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 …
Integrated Finite Element Neural Network (I-FENN) for non-local continuum damage mechanics
We present a new Integrated Finite Element Neural Network framework (I-FENN), with the
objective to accelerate the numerical solution of nonlinear computational mechanics …
objective to accelerate the numerical solution of nonlinear computational mechanics …
Stable GFEM (SGFEM): Improved conditioning and accuracy of GFEM/XFEM for three-dimensional fracture mechanics
In this paper, we present an extension of the Stable Generalized FEM (SGFEM) for 3-D
fracture mechanics problems. Numerical experiments show that the use of available singular …
fracture mechanics problems. Numerical experiments show that the use of available singular …
Improving the conditioning of XFEM/GFEM for fracture mechanics problems through enrichment quasi-orthogonalization
Partition of unity enrichment is known to significantly enhance the accuracy of the finite
element method by allowing the incorporation of known characteristics of the solution in the …
element method by allowing the incorporation of known characteristics of the solution in 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 …
Domain decomposition methods for 3D crack propagation problems using XFEM
S Bakalakos, M Georgioudakis… - Computer Methods in …, 2022 - Elsevier
The extended finite element method (XFEM) has been successfully implemented in solving
crack propagation problems by enriching the polynomial basis functions of standard finite …
crack propagation problems by enriching the polynomial basis functions of standard finite …
Robust and parallel scalable iterative solutions for large-scale finite cell analyses
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 …
Strongly stable generalized finite element method: Application to interface problems
In this paper, we present the theoretical justification for the Stable Generalized Finite
Element Method (SGFEM) when applied to smooth interface problems. We prove that a …
Element Method (SGFEM) when applied to smooth interface problems. We prove that a …
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 …
Stochastic multiscale modeling of crack propagation in random heterogeneous media
A stochastic approach to model crack propagation in random heterogeneous media, using
mesoscopic representations of elastic and fracture properties, is presented. In order to …
mesoscopic representations of elastic and fracture properties, is presented. In order to …