Applying the hp–d version of the FEM to locally enhance dimensionally reduced models

By Alexander Düster, A. Niggl, Ernst Rank. 2007

58 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/be0277d2a6ef4a1a7fa254438698a902d41a626e

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

The hp‐d‐adaptive finite cell method for geometrically nonlinear problems of solid mechanics (2012, methodology): “Originally proposed for adaptive domain decomposition (hence the d ) [37], the hp-d method has been successfully adapted for a range of applications, such as multi-scale structural analysis [38, 39, 53] and model adaptivity [40, 54].”
A multiscale method with patch for the solution of stochastic partial differential equations with localized uncertainties (2013, methodology): “Among these deterministic methods, one can distinguish the mono-model methods based on adaptive mesh or enrichment techniques [10, 11, 12, 13] from the multi-model methods based on patches as the global-local iterative methods proposed in [14, 15, 16, 17, 18] or the bridging methods proposed in [19,”
Analysis of three-dimensional fracture mechanics problems: A non-intrusive approach using a generalized finite element method (2012, background): “…standard FEM approx: þ XN a¼1 XDL i¼2 uaiuaðxÞLaiðxÞ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} GFEM enrichment ð8Þ This clearly shows the hierarchical nature of a GFEM approximation.”
The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models (2015, methodology): “Originally proposed in [128, 129] for adaptive domain decomposition (hence the d), thehp-d method has been successfully adapted for the resolution of local features in non-smooth solutions [129], multi-scale structur al analysis [89,132], and model adaptivity [48].”
Analysis of three‐dimensional fracture mechanics problems: A two‐scale approach using coarse‐generalized FEM meshes (2010, methodology): “Among the recent works, we can mention the method of Guidault et al. [36] based on the LATIN method and domain decomposition concepts; the multigrid method proposed in [61]; the method of Cloirec et al. [13] based on Lagrange multipliers; the multiscale projection method of Belytschko et al. [10, 44”
Local enrichment of the finite cell method for problems with material interfaces (2013, methodology): “This approach is very well suited for problems involving singularities in the exact solution of the underlying problem [45,48].”