# Study of efficient homogenization algorithms for nonlinear problems

## Related Articles

- Homogenization with corrector for a periodic elliptic operator near an edge of inner gap. Suslina, T.; Kharin, A. // Journal of Mathematical Sciences;May2009, Vol. 159 Issue 2, p264
For an ellipticoperator with rapidly oscillating coefficients we consider a homogenization procedure near the edge of an interior gap in the spectrum of this operator. At a point close to the edge, we obtain an approximation of the resolvent in the operator L2(â„)-norm. The first order...

- Roughness-Induced Effect at Main order on the Reynolds Approximation. Choquet, Catherine; Chupin, Laurent; Gisclon, Marguerite // AIP Conference Proceedings;9/9/2009, Vol. 1168 Issue 1, p1269
Usually the Stokes equations that govern a flow in a smooth thin domain (with thickness of order [variant_greek_epsilon]) are related to the Reynolds equation for the pressure psmooth. We begin by showing that the flow may be accelerated using adequate rugosity profiles on the bottom. Indeed, we...

- HOMOGENEOUS LANCHESTER EQUATIONS. // Encyclopedia of Operations Research & Management Science;2001, p369
An encyclopedia entry about "homogeneous Lanchester equations" is presented. These equations have one equation for each side and are used when the weapons for each side are homogeneous. It may also be a simplified approximation of a heterogeneous situation.

- Loss of polyconvexity by homogenization: a new example. Barchiesi, Marco // Calculus of Variations & Partial Differential Equations;Oct2007, Vol. 30 Issue 2, p215
This article is devoted to the study of the asymptotic behavior of the zero-energy deformations set of a periodic nonlinear composite material. We approach the problem using two-scale Young measures. We apply our analysis to show that polyconvex energies are not closed with respect to periodic...

- Scale-integration and scale-disintegration in nonlinear homogenization. Visintin, Augusto // Calculus of Variations & Partial Differential Equations;Dec2009, Vol. 36 Issue 4, p565
This work is devoted to scale transformations of stationary nonlinear problems. A class of coarse-scale problems is first derived by integrating a family of two-scale minimization problems ( scale-integration), in presence of appropriate orthogonality conditions. The equivalence between the two...

- Homogenization and Multigrid. Neuss, N.; J�ger, W.; Wittum, G. // Computing;2001, Vol. 66 Issue 1, p1
For elliptic partial differential equations with periodically oscillating coefficients which may have large jumps, we prove robust convergence of a two-grid algorithm using a prolongation motivated by the theory of homogenization. The corresponding Galerkin operator on the coarse grid turns out...

- Computational aspects of tangent moduli tensors in rate-independent crystal elastoplasticity. Terada, K.; Watanabe, I. // Computational Mechanics;Sep2007, Vol. 40 Issue 3, p497
The computational efficiencies of the continuum and consistent (algorithmic) tangent moduli tensors in rate-independent crystal elastoplasticity are examined in conjunction with the available implicit state update algorithms. It is, in this context, shown that the consistent tangent moduli...

- Flux Norm Approach to Finite Dimensional Homogenization Approximations with Non-Separated Scales and High Contrast. Berlyand, Leonid; Owhadi, Houman // Archive for Rational Mechanics & Analysis;Nov2010, Vol. 198 Issue 2, p677
We consider linear divergence-form scalar elliptic equations and vectorial equations for elasticity with rough ( L(Î©), $${\Omega \subset \mathbb R^d}$$) coefficients a( x) that, in particular, model media with non-separated scales and high contrast in material properties. While the...

- Homogenization with corrector for a multidimensional periodic elliptic operator near an edge of an inner gap. Suslina, T.; Kharin, A. // Journal of Mathematical Sciences;Aug2011, Vol. 177 Issue 1, p208
For a second order differential operator $ \mathcal{A} $ = -div g( x/ e)? + ep( x/ e) in L(R) with periodic coefficients and small parameter e > 0 we study an approximation of the resolvent of $ \mathcal{A} $ at a point close to an edge of an inner gap in the spectrum of $ \mathcal{A} $. Under...