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.
منابع مشابه
Numerical Homogenization of Heterogeneous Anisotropic Linear Elastic Materials
Abstract. The numerical homogenization of anisotropic linear elastic materials with strongly heterogeneous microstructure is studied. The developed algorithm is applied to the case of trabecular bone tissue. In our previous work [1], the orthotropic case was considered. The homogenized anisotropic tensor is transformed according to the principle directions of anisotropy (PDA). This provides opp...
متن کاملScallability Analysis of Parallel Mic(0) Preconditioning Algorithm for 3d Elliptic Problems
Novel parallel algorithms for the solution of large FEM linear systems arising from second order elliptic partial differential equations in 3D are presented. The problem is discretized by rotated trilinear nonconforming Rannacher–Turek finite elements. The resulting symmetric positive definite system of equations Ax = f is solved by the preconditioned conjugate gradient algorithm. The precondit...
متن کاملOn a Two-Level Parallel MIC(0) Preconditioning of Crouzeix-Raviart Non-conforming FEM Systems
In this paper we analyze a two-level preconditioner for finite element systems arising in approximations of second order elliptic boundary value problems by Crouzeix-Raviart non-conforming triangular linear elements. This study is focused on the efficient implementation of the modified incomplete LU factorization MIC(0) as a preconditioner in the PCG iterative method for the linear algebraic sy...
متن کاملLocally Optimized MIC(0) Preconditioning of Rannacher-Turek FEM Systems
In this paper Rannacher-Turek non-conforming rotated bilinear finite elements are applied for the numerical solution of second order elliptic boundary value problems. The preconditioned conjugate gradient method is used for the iterative solution of the arising linear algebraic system. A locally optimized construction for an M-matrix approximation of the global stiffness matrix is the first ste...
متن کاملThe Complementary Functions Method (CFM) Solution to the Elastic Analysis of Polar Orthotropic Rotating Discs
This study primarily deals with introducing an efficient numerical technique called the Complementary Functions Method (CFM) for the solutions of the initial value problem for the linear elastic analysis of anisotropic rotating uniform discs. To bring the performance of the method to light, first, closed form formulas are derived for such discs. The governing equation of the problem at stake is...
متن کامل