List of Journal Publications
2020
Aragon, A. M., Simone, A.
Discussion on “A linear complete extended finite element method for dynamic fracture simulation with non-nodal enrichments” [Finite Elem. Anal. Des. 152 (2018)] by I. Asareh, T.-Y. Kim, and J.-H. Song Journal Article
In: FINITE ELEMENTS IN ANALYSIS AND DESIGN, vol. 168, 2020.
Abstract | BibTeX | Tags: DE-FEM, IGFEM, NXFEM, strong discontinuities, Weak discontinuities, XFEM | Links:
@article{Aragon2020,
title = {Discussion on “A linear complete extended finite element method for dynamic fracture simulation with non-nodal enrichments” [Finite Elem. Anal. Des. 152 (2018)] by I. Asareh, T.-Y. Kim, and J.-H. Song},
author = {A. M. Aragon and A. Simone},
doi = {10.1016/j.finel.2019.103340},
year = {2020},
date = {2020-01-01},
journal = {FINITE ELEMENTS IN ANALYSIS AND DESIGN},
volume = {168},
publisher = {Elsevier B.V.},
abstract = {The subject paper purportedly proposes a novel enriched finite element method for modeling problems with strong discontinuities such as those encountered in fracture mechanics. The purpose of this document is to demonstrate that the method in the subject paper (Non-nodal eXtended Finite Element Method, NXFEM) is conceptually identical to the Discontinuity-Enriched Finite Element Method (DE-FEM) [Int. J. Numer. Meth. Eng. 2017; 112:1589–1613] proposed by Aragón and Simone.},
keywords = {DE-FEM, IGFEM, NXFEM, strong discontinuities, Weak discontinuities, XFEM},
pubstate = {published},
tppubtype = {article}
}
2017
Aragón, Alejandro M., Simone, A.
The Discontinuity-Enriched Finite Element Method Journal Article
In: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, vol. 112, no. 11, pp. 1589–1613, 2017.
Abstract | BibTeX | Tags: cohesive cracks, fracture mechanics, GFEM, IGFEM, strong discontinuities, XFEM | Links:
@article{Aragon2017,
title = {The Discontinuity-Enriched Finite Element Method},
author = {Alejandro M. Aragón and A. Simone},
doi = {10.1002/nme.5570},
year = {2017},
date = {2017-01-01},
journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING},
volume = {112},
number = {11},
pages = {1589–1613},
publisher = {John Wiley and Sons Ltd},
abstract = {We introduce a new methodology for modeling problems with both weak and strong discontinuities independently of the finite element discretization. At variance with the eXtended/Generalized Finite Element Method (X/GFEM), the new method, named the Discontinuity-Enriched Finite Element Method (DE-FEM), adds enriched degrees of freedom only to nodes created at the intersection between a discontinuity and edges of elements in the mesh. Although general, the method is demonstrated in the context of fracture mechanics, and its versatility is illustrated with a set of traction-free and cohesive crack examples. We show that DE-FEM recovers the same rate of convergence as the standard FEM with matching meshes, and we also compare the new approach to X/GFEM.},
keywords = {cohesive cracks, fracture mechanics, GFEM, IGFEM, strong discontinuities, XFEM},
pubstate = {published},
tppubtype = {article}
}
2015
Sillem, A., Simone, A., Sluys, L. J.
The Orthonormalized Generalized Finite Element Method-OGFEM: Efficient and stable reduction of approximation errors through multiple orthonormalized enriched basis functions Journal Article
In: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, vol. 287, pp. 112–149, 2015.
Abstract | BibTeX | Tags: Condition number, GFEM, Improved convergence, Orthonormality, SGFEM, XFEM | Links:
@article{Sillem2015,
title = {The Orthonormalized Generalized Finite Element Method-OGFEM: Efficient and stable reduction of approximation errors through multiple orthonormalized enriched basis functions},
author = {A. Sillem and A. Simone and L. J. Sluys},
doi = {10.1016/j.cma.2014.11.043},
year = {2015},
date = {2015-01-01},
journal = {COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING},
volume = {287},
pages = {112–149},
publisher = {Elsevier},
abstract = {An extension of the Generalized Finite Element Method (GFEM) is proposed with which we efficiently reduce approximation errors. The new method constructs a stiffness matrix with a conditioning that is significantly better than the Stable Generalized Finite Element Method (SGFEM) and the Finite Element Method (FEM). Accordingly, the risk of a severe loss of accuracy in the computed solution, which burdens the GFEM, is prevented. Furthermore, the computational cost of the inversion of the associated stiffness matrix is significantly reduced. The GFEM employs a set of enriched basis functions which is chosen to improve the rate at which the approximation converges to the exact solution. The stiffness matrix constructed from these basis functions is often ill-conditioned and the accuracy of the solution cannot be guaranteed. We prevent this by orthonormalizing the basis functions and refer to the method as the Orthonormalized Generalized Finite Element Method (OGFEM). Because the OGFEM has the flexibility to orthonormalize either a part or all of the basis functions, the method can be considered as a generalization of the GFEM. The method is applicable with single or multiple global and/or local enrichment functions. Problems in blending elements are avoided by a modification of the enrichment functions. The method is demonstrated for the one-dimensional modified Helmholtz and Poisson equations and compared with the FEM, GFEM and SGFEM.},
keywords = {Condition number, GFEM, Improved convergence, Orthonormality, SGFEM, XFEM},
pubstate = {published},
tppubtype = {article}
}