TITLE

Study of efficient homogenization algorithms for nonlinear problems

AUTHOR(S)
Okada, Jun-ichi; Washio, Takumi; Hisada, Toshiaki
PUB. DATE
July 2010
SOURCE
Computational Mechanics;Jul2010, Vol. 46 Issue 2, p247
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
A framework for the homogenization of nonlinear problems is discussed with respect to block LU factorization of the micro�macro coupled equation, and based on the relation between the characteristic deformation and the Schur-Complement as the homogenized tangent stiffness. In addition, a couple of approximation methods are introduced to reduce the computational cost, i.e., a simple scheme to reuse the old characteristic deformation and a sophisticated method based on the mode-superposition method developed by our group. Note that these approximation methods satisfy the equilibrium conditions in both scales. Then, using a simplified FE model, the conventional algorithm, a relative algorithm originating from the block LU factorization, and the above-mentioned algorithms with the approximated Schur-Complement are compared and discussed. Finally, a large-scale heart simulation using parallel computation is presented, based on the proposed method.
ACCESSION #
50498656

 

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(ℝ)-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(Ω), $${\Omega \subset \mathbb R^d}$$) 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...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics