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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 107
PROCEEDINGS OF THE FOURTH INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED, GRID AND CLOUD COMPUTING FOR ENGINEERING
Edited by:
Paper 6

Microstructure Compression and Reconstruction Techniques based on Schur Complements

J. Kruis, J. Novák and M. Doškár

Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic

Full Bibliographic Reference for this paper
, "Microstructure Compression and Reconstruction Techniques based on Schur Complements", in , (Editors), "Proceedings of the Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 6, 2015. doi:10.4203/ccp.107.6
Keywords: microstructure compression and reconstruction, Wang tiles, Schur complement method, conjugate gradient method.

Summary
Microstructure representation and reconstruction of stochastic realizations of the compressed microstructure without prior periodic assumptions can be done with the help of the Wang tiling proposed in 1961. A set of tiles is generated and the tiles are used in tilings of arbitrary size. The tiles are covered by finite element meshes and they resemble macro-elements or subdomains. The internal degrees of freedom of tiles are eliminated and the Schur complement matrices are used instead of the matrices of the whole tiles. Moreover, the method can be relatively easily and very efficiently implemented in parallel and very good speedup is obtained. Preliminary numerical experiments confirm good performance.

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