Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Multiscale coarsening for linear elasticity by energy minimization
 Iliev, O.P.: Numerical Solution of Partial Differential Equations: Theory, Algorithms, and their Applications : In Honor of Professor Raytcho Lazarov's 40 Years of Research in Computational Methods and Applied Mathematics Berlin: Springer, 2013 (Springer Proceedings in Mathematics & Statistics 45) ISBN: 9781461471714 (Print) ISBN: 9781461471721 (Online) pp.2144 

 English 
 Book Article 
 Fraunhofer ITWM () 
Abstract
In this work, we construct energyminimizing coarse spaces for the finite element discretization of mixed boundary value problems for displacements in compressible linear elasticity. Motivated from the multiscale analysis of highly heterogeneous composite materials, basis functions on a triangular coarse mesh are constructed, obeying a minimal energy property subject to global pointwise constraints. These constraints allow that the coarse space exactly contains the rigid body translations, while rigid body rotations are preserved approximately. The application is twofold. Resolving the heterogeneities on the finest scale, we utilize the energyminimizing coarse space for the construction of robust twolevel overlapping domain decomposition preconditioners. Thereby, we do not assume that coefficient jumps are resolved by the coarse grid, nor do we impose assumptions on the alignment of material jumps and the coarse triangulation. Weonly assume that the size of the inclusions is small compared to the coarse mesh diameter. Ournumerical tests show uniform convergence rates independent of the contrast in the Young’s modulus within the heterogeneous material. Furthermore, we numerically observe the properties of the energyminimizing coarse space in an upscaling framework. Therefore, we present numerical results showing the approximation errors of the energyminimizing coarse space w.r.t. the finescale solution.