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Article

3 Citations

2,434 Views

19 Pages

A Stable Generalized Finite Element Method Coupled with Deep Neural Network for Interface Problems with Discontinuities

Ying Jiang,
Minghui Nian and
Qinghui Zhang

Axioms2022, 11(8), 384;https://doi.org/10.3390/axioms11080384

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5 August 2022

The stable generalized finite element method (SGFEM) is an improved version of generalized or extended FEM (GFEM/XFEM), which (i) uses simple and unfitted meshes, (ii) reaches optimal convergence orders, and (iii) is stable and robust in the sense th...

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Article

64 Citations

11,523 Views

65 Pages

Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review

Adrian Egger,
Udit Pillai,
Konstantinos Agathos,
Emmanouil Kakouris,
Eleni Chatzi,
Ian A. Aschroft and
Savvas P. Triantafyllou

Appl. Sci.2019, 9(12), 2436;https://doi.org/10.3390/app9122436

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14 June 2019

Three alternative approaches, namely the extended/generalized finite element method (XFEM/GFEM), the scaled boundary finite element method (SBFEM) and phase field methods, are surveyed and compared in the context of linear elastic fracture mechanics...

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908 Views

19 Pages

Multiscale Simulation of 2D Heat Transfer in Composite Media Based on Global–Local Enrichment Functions

Guangzhong Liu,
Jiamin Guo,
Yan Bao and
Huan Ping

Mathematics2025, 13(7), 1027;https://doi.org/10.3390/math13071027

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21 March 2025

In this study, the extended finite element method (XFEM) was integrated into the generalized multiscale finite element method with global–local enrichment (GFEMgl) to simulate 2D heat conduction in highly heterogeneous materials (i.e., matrixes...

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