Engineering Transactions, 64, 4, pp. 385–392, 2016
10.24423/engtrans.399.2016

Comparison of Two Methods for Numerical Upscaling

Marek KLIMCZAK
Cracow University of Technology
Poland

Witold CECOT
Cracow University of Technology
Poland

The main objective of this paper is to compare two discretization-based homogenization methods. A local numerical homogenization and a multiscale finite element method (MsFEM) are first briefly presented and next numerically tested. In the case of MsFEM, a new shape function construction is also presented. Extensive comparison of both techniques constitutes the main part of this study. Novelty of this research is to combine forementioned methods with mesh adaptivity at the coarse mesh level and the application of the higher-order approximation.
Keywords: local numerical homogenization; multiscale FEM; multigrid homogenization
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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

Jhurani C., Demkowicz L., Multiscale modeling using goal-oriented adaptivity and numerical homogenization. Part I: Mathematical formulation and numerical results, Computer Methods in Applied Mechanics and Engineering, 213–21: 399–417, 2012.

Klimczak M., Cecot W., Application of local numerical homogenization and hp-adaptive FEM for modeling of heterogeneous viscoelastic materials, Engineering Transactions, 63(3): 317–327, 2015.

Ben-Israel A., Greville T.N.E., Generalized Inverses, Springer-Verlag, 2003.

Neuss N., Jaeger W., Wittum G., Homogenization and multigrid, Computing, 66(1): 1–26, 2001.

Efendiev Y., Hou T., Multiscale finite element methods for porous media flows and their applications, Applied Numerical Mathematics, 57: 577–596, 2007.

Cecot W., Oleksy M., High order FEM for multigrid homogenization, Computers and Mathematics with Applications, 70(7): 1391–1400, 2015.

Demkowicz L., Kurtz J., Pardo D., Paszynski M., Rachowicz W., Zdunek A., Computing with hp-Adaptive Finite Elements. Vol 2. Frontiers: Three-Dimensional Elliptic and Maxwell Problems with Applications, Chapman & Hall/CRC, 2008.




DOI: 10.24423/engtrans.399.2016