Multiscale enrichment based on partition of unity

By Jacob Fish, Zheng Yuan. 2005

152 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/2dd064cb8e516e9dd5f017e989257437efcc6af4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Bridging the scales in nano engineering and science (2006, methodology): “Examples of complete enrichment spaces can be found in Fish and Markolefas (1992), Fish et al. (1994), Strouboulis et al. (2001) and Fish and Yuan (2005), but such complete enrichment spaces cannot be locally condensed out.”
A 3D interface-enriched generalized finite element method for weakly discontinuous problems with complex internal geometries (2012, methodology): “Application areas of the GFEM/XFEM include fracture mechanics [5–10], multiscale modeling [11], contact problems [12,13], solidification [14], modeling of dislocations [15,16], and phase interfaces [17–19].”
Routes for Efficient Computational Homogenization of Nonlinear Materials Using the Proper Generalized Decompositions (2010, methodology): “The microscopic solution may also enrich the macroscale solu-tion using strategies such as X-FEM and G-FEM, see e.g. [17] and [38] respectively.”
Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method (2016, methodology): “In a general sense, it is possible classify the multiscale models into the concurrent method [9, 19, 28, 31, 32, 47, 62, 67, 84, 117, 127] and the homogenization method, on the latter one will be focused this article.”
Coarse‐graining of multiscale crack propagation (2010, methodology): “An alternative approach is that based on eigenstrains, which has recently been developed by Fish and Yuan [9] and Oskay and Fish [10].”
A computational library for multiscale modeling of material failure (2013, methodology): “While numerous multiscale methods (see e.g. [38,57]) were developed for intact materials, far fewer methods are available for fracture simulations.”