RT Journal Article
T1 Mathematical perspective on XFEM implementation for models involving contribution on interfaces
A1 Cao Rial, María Teresa
A1 Moreno, C.
A1 Quintela Estévez, Peregrina
K1 Extended finite element method
K1 Mathematical tools for numerical implementation
K1 Integration over interfaces
K1 Rayleigh waves
AB Models involving interfaces with discontinuities or even singularities of some fields across them are very frequent in real life problems modelling. In the last decades, the use of the eXtended Finite Element Method (XFEM) instead of the traditional FEM has become more and more popular, mainly because of two advantages: the mesh of the domain can be independent of the interface position, therefore avoiding remeshing, and it allows to enrich an area with specific shape functions fitted to the particular properties (singularities, discontinuities) of the expected solution, obtaining more accurate results with less computational efforts. Nevertheless, a critical point of XFEM is its implementation since it varies from one problem to another, due to the different kind (and number) of degrees of freedom on each node. A diligent organization of nodes, degrees of freedom and enrichment functions is fundamental to achieve an efficient implementation. Our aim in this paper is to provide a common reference framework for the implementation of XFEM from a mathematical point of view, providing the readers with a set of tools that will allow them to apply it to any kind of problem. To this aim, we present a detailed description of XFEM implementation, with special emphasis on the terms that involve integration over interfaces. The proposed tools are presented in a general context, and as an example, we will apply them to a problem of solids mechanics. In particular, we will contextualize the procedure on a Rayleigh waves propagation problem in a cracked structure considering a Signorini contact condition on the crack sides.
PB Elsevier
SN 0378-4754
YR 2024
FD 2024
LK http://hdl.handle.net/10347/33079
UL http://hdl.handle.net/10347/33079
LA eng
NO Mathematics and Computers in Simulation Volume 218, April 2024, Pages 266-291
NO This work has been supported by FEDER, Xunta de Galicia, Spain funds under the ED431C 2017/60 and ED431C 2021/15 grants and by the Ministry of Science and Innovation, Spain through the Agencia Estatal de Investigación (PID2019-105615RB-I00/AEI / 10.13039/501100011033) and European Union Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement No 823731 CONMECH.
DS Minerva
RD 24 abr 2026