Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials: Part II: a computational environment for adaptive modeling of heterogeneous elastic solids

By Kumar Vemaganti, J. Tinsley Oden. 2001

120 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/581f76aa59b1e0b618d1214968200b0ba20925ed

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

A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007, methodology): “Some sources of errors arising in computer simulations now can be controlled and reduced by using sophisticated techniques such as a posteriori error estimation [1, 3, 57], mesh adaptivity, and the more recent modeling error analysis [49, 50, 13].”
A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials (2017, unknown): “This work has been applied to multiscale problems also [323,324].”
Heterogeneous Multiscale Methods: A Review (2007, methodology): “Therefore the HMM methodology is closer to that of (adaptive) model refinement [75, 125]: Near defects or singularities, a more refined model is used to supply the data.”
Bridging the scales in nano engineering and science (2006, methodology): “Upper and lower bounds of modelling errors in local quantities of interest for this class of problems were developed in Oden and Vemaganti (2000) and model adaptivity based on the so-called Goals algorithm was first presented in Vemaganti and Oden (2001).”
Navier-Stokes/Darcy Coupling: Modeling, Analysis, and Numerical Approximation (2009, background): “These techniques can be understood as more or less sophisticated averaging procedures where small scale variations in the coefficients are replaced by some kind of effective properties in regions that correspond to a grid block in the numerical model [59, 61, 104, 10, 120].”
Concurrent multi-level model for damage evolution in microstructurally debonding composites (2007, unknown): “…effectively tackled by multi-scale modeling methods e.g. in Smit et al. (1998), Fish and Shek (2000), Fish et al. (1999), Oden and Zohdi (1997), Vemaganti and Oden (2001), Ghosh et al. (2001), Raghavan and Ghosh (2004a,b), Terada and Kikuchi (2000), Zohdi and Wriggers (1999) and Tamma and…”