Iterative solution methods
MPI-The Complete Reference, Volume 1: The MPI Core
MPI-The Complete Reference, Volume 1: The MPI Core
Optimal shape design in biomimetics based on homogenization and adaptivity
Mathematics and Computers in Simulation
Computers & Mathematics with Applications
On Smoothing Surfaces in Voxel Based Finite Element Analysis of Trabecular Bone
Large-Scale Scientific Computing
Parallel DD-MIC(0) Preconditioning of Nonconforming Rotated Trilinear FEM Elasticity Systems
Large-Scale Scientific Computing
Parallel MIC(0) preconditioning for numerical upscaling of anisotropic linear elastic materials
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Performance analysis of parallel alternating directions algorithm for time dependent problems
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
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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.