Comparative Analysis of Mesh Generators and MIC(0) Preconditioning of FEM Elasticity Systems

MIC(0) Preconditioning of Conforming and Non-conforming FEM Problems on Unstructured Grids⋆

In this study, the topics of grid generation and FEM applications are studied together following their natural synergy. We consider the following three grid generators: Triangle, NETGEN and Gmsh. The quantitative analysis is based on the number of elements/nodes needed to obtain a triangulation of a given domain, satisfying a certain minimal angle condition. After that, the performance of the M...

Parallel DD-MIC(0) Preconditioning of Rotated Trilinear FEM Elasticity Systems

A new parallel preconditioning algorithm for 3D nonconforming FEM elasticity systems is presented. The preconditioner is constructed in two steps. First displacement decomposition of the stiffness matrix is used. Than MIC(0) factorization is applied to a proper auxiliary M-matrix to get an approximate factorization of the obtained blockdiagonal matrix. The auxiliary matrix has a special block s...

MIC(0) Preconditioning of Rotated Trilinear FEM Elliptic Systems

Comparative Analysis of High Performance Solvers for 3D Elasticity Problems

We consider the numerical solution of 3D linear elasticity equations. The investigated problem is described by a coupled system of second order elliptic partial differential equations. This system is then discretized by conforming or nonconforming finite elements. After applying the Finite Element Method (FEM) based discretization, a system of linear algebraic equations has to be solved. In thi...

Parallel PCG algorithms for voxel FEM elasticity systems

The presented comparative analysis concerns two parallel iterative solvers for large-scale linear systems related to μFEM simulation of human bones. The benchmark problems represent the strongly heterogeneous structure of real bone specimens. The voxel data are obtained by a high resolution computer tomography. Non-conforming RannacherTurek finite elements are used for discretization of the con...