Locally optimized MIC( 0) preconditioning of Rannacher--Turek FEM systems

Authors:
I. Georgiev;J. Kraus;S. Margenov;J. Schicho
Affiliations:
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Bl. 8, 1113 Sofia, Bulgaria and Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. ...;Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria;Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Bl. 25A, 1113 Sofia, Bulgaria;Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria
Venue:
Applied Numerical Mathematics
Year:
2009

Citing 4
Cited 0

Iterative solution methods

Iterative solution methods
MIC(0) Preconditioning of Rotated Trilinear FEM Elliptic Systems

LSSC '01 Proceedings of the Third International Conference on Large-Scale Scientific Computing-Revised Papers
Convergence analysis for quadrilateral rotated Q1 elements

Scientific computing and applications
Parallel MIC(0) preconditioning of 3D elliptic problems discretized by Rannacher-Turek finite elements

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

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 Au=f. A locally optimized construction for an M-matrix approximation B of the global stiffness matrix A is the first step of the proposed algorithm. Then, the preconditioner is obtained by modified incomplete Cholesky factorization of the auxiliary M-matrix B. A comparative analysis concerning three different approaches for construction of such matrices B is presented. The related spectral condition number estimates are derived. The most important contributions of the paper is the developed original robust preconditioning scheme for strongly anisotropic problems based on properly skewed meshes. A set of numerical tests is presented to illustrate the theoretical investigations.