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.