A multiscale stochastic finite element method on elliptic problems involving uncertainties

By X. Frank Xu. 2007

112 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mechanics of Materials, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7fdfa223fbe88b6c373e64081ed28656d0cda28f

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

1. Mathilde Chevreuil
2. Elias Safatly
3. Anthony Nouy
4. Surya R. Kalidindi
5. Anthony R. Ingraffea
6. S. Niezgoda
7. T. Eason
8. Michael Spottswood

In Mechanics of Materials

1. Martin Z. Bazant
2. Jia-Liang Le
3. Mathilde Chevreuil
4. A. Kanjarla
5. S. Niezgoda
6. Surya R. Kalidindi
7. Anthony Nouy
8. Anthony R. Ingraffea

In Statistics and Probability

1. Mathilde Chevreuil
2. Elias Safatly
3. Surya R. Kalidindi
4. Anthony Nouy
5. Anthony R. Ingraffea
6. S. Niezgoda
7. T. Eason
8. Zdenek P. Bazant

Citations in the corpus

• Efficient Analysis of High Dimensional Data in Tensor Formats (2012, unknown): “(14) [1–3, 14, 17, 22, 28, 36, 37, 43, 44, 48, 49].”
• A multiscale method with patch for the solution of stochastic partial differential equations with localized uncertainties (2013, background): “the case of random heterogeneous media allowing a separation of scales, upscaling or homogenenization methods have been introduced, see for instance [5, 6, 7, 8, 9].”
• Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling (2011, background): “The numerical stochastic multiscale approaches proposed so far (e.g. Xu, 2007; Graham-Brady et al., 2006; Williams and Baxer, 2006) do not suffice for handling multiscale transitions of probability distributions and their tails.”
• Novel microstructure quantification framework for databasing, visualization, and analysis of microstructure data (2013, methodology): “Such a method aligns naturally with emerging multi-scale modeling techniques based around stochastic partial differential equations [41-43] and provides an elegant framework for the inclusion of materials uncertainty into material model uncertainty quantification and into component level design vali”
• Reengineering Aircraft Structural Life Prediction Using a Digital Twin (2011, methodology): “Other developments of interest include multiscale SFEM [40] and an extended SFEM (X-SFEM) analogous to XFEM for deterministic FEM [41].”