Modeling holes and inclusions by level sets in the extended finite-element method
TLDR
In this paper, a methodology to model arbitrary holes and material interfaces (inclusions) without meshing the internal boundaries is proposed, which couples the level set method with the extended finite element method (X-FEM).About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2001-09-14 and is currently open access. It has received 1112 citations till now. The article focuses on the topics: Extended finite element method & Level set method.read more
Citations
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The extended/generalized finite element method: An overview of the method and its applications
TL;DR: An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented in this article, which enables accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non-smooth features within elements.
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Review: Meshless methods: A review and computer implementation aspects
TL;DR: This manuscript is to give a practical overview of meshless methods (for solid mechanics) based on global weak forms through a simple and well-structured MATLAB code, to illustrate the discourse.
Journal ArticleDOI
Level set methods for fluid interfaces
James A. Sethian,Peter Smereka +1 more
TL;DR: An overview of level set methods, introduced by Osher and Sethian, for computing the solution to fluid-interface problems, which are computational techniques that rely on an implicit formulation of the interface, represented through a time-dependent initial-value partial-differential equation.
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A finite element method for the simulation of strong and weak discontinuities in solid mechanics
Anita Hansbo,Peter Hansbo +1 more
TL;DR: This paper introduces and analyze a finite element method for elasticity problems with interfaces and proposes a general approach that can handle both perfectly and imperfectly bonded interfaces without modifications of the code.
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Modelling crack growth by level sets in the extended finite element method
TL;DR: An algorithm which couples the level set method (LSM) with the extended finite element method (X‐FEM) to model crack growth is described, which requires no remeshing as the crack progresses, making the algorithm very efficient.
References
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Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Stanley Osher,James A. Sethian +1 more
TL;DR: The PSC algorithm as mentioned in this paper approximates the Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws, which can be used also for more general surface motion problems.
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A finite element method for crack growth without remeshing
TL;DR: In this article, a displacement-based approximation is enriched near a crack by incorporating both discontinuous elds and the near tip asymptotic elds through a partition of unity method.
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Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition)
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The partition of unity finite element method: Basic theory and applications
Jens Markus Melenk,Ivo Babuška +1 more
TL;DR: In this article, the basic ideas and the mathematical foundation of the partition of unity finite element method (PUFEM) are presented and a detailed and illustrative analysis is given for a one-dimensional model problem.
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A fast marching level set method for monotonically advancing fronts
TL;DR: A fast marching level set method is presented for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation.
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The partition of unity finite element method: Basic theory and applications
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