Parallel MIC(0) Preconditioning for Numerical Upscaling of Anisotropic Linear Elastic Materials
نویسندگان
چکیده
Abstract. Numerical homogenization is used for upscaling of the linear elasticity tensor of strongly heterogeneous microstructures. The implemented 3D algorithm is described in terms of six auxiliary elastic problems for the reference volume element (RVE). Rotated trilinear RannacherTurek finite elements are used for discretization of the involved subproblems. A parallel PCG method is implemented for efficient solution of the arising large-scale systems with sparse, symmetric, and positive semidefinite matrices. The implemented preconditioner is based on modified incomplete Cholesky factorization MIC(0). The numerical homogenization scheme is derived on the assumption of periodic microstructure. This implies periodic boundary conditions (PBCs) on the RVE. From algorithmic point of view, an important part of this study concerns the incorporation of PBCs in the parallel MIC(0) solver.
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تاریخ انتشار 2009