Abstract
Numerical homogenization is used for up-scaling of a linear elasticity tensor of strongly heterogeneous micro-structures. Utilized approach assumes presence of a periodic micro-structure and thus periodic boundary conditions. Rotated trilinear Rannacher-Turek finite elements are used for the discretization, while a parallel PCG method is used to solve arising large-scale systems with sparse, symmetric, positive semidefinite matrices. Applied preconditioner is based on modified incomplete Cholesky factorization MIC(0).
The test problem represents a trabecular bone tissue, and takes into account only the elastic response of the solid phase. The voxel micro-structure of the bone is extracted from a high resolution computer tomography image. Numerical tests performed on parallel computers demonstrate the efficiency of the developed algorithm.
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Lirkov, I., Vutov, Y., Paprzycki, M., Ganzha, M. (2010). Parallel Performance Evaluation of MIC(0) Preconditioning Algorithm for Voxel μFE Simulation. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2009. Lecture Notes in Computer Science, vol 6068. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14403-5_15
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DOI: https://doi.org/10.1007/978-3-642-14403-5_15
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