MIC(0) preconditioning of 3D FEM problems on unstructured grids: Conforming and non-conforming elements

Authors:
Svetozar Margenov;Nikola Kosturski
Affiliations:
Acad. G. Bonchev Street, bl. 25A, 1113 Sofia, Bulgaria;Acad. G. Bonchev Street, bl. 25A, 1113 Sofia, Bulgaria
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 2
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Iterative solution methods

Iterative solution methods
Comparative analysis of mesh generators and MIC(0) preconditioning of FEM elasticity systems

NMA'06 Proceedings of the 6th international conference on Numerical methods and applications

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Abstract

In this study, the topics of grid generation and FEM applications are studied together following their natural synergy. We consider the following three tetrahedral grid generators: NETGEN, TetGen, and Gmsh. After that, the performance of the MIC(0) preconditioned conjugate gradient (PCG) solver is analyzed for both conforming and non-conforming linear FEM problems. If positive off-diagonal entries appear in the corresponding matrix, a diagonal compensation is applied to get an auxiliary M-matrix allowing a stable MIC(0) factorization. The presented numerical experiments for elliptic and parabolic problems well illustrate the similar PCG convergence rate of the MIC(0) preconditioner for both, structured and unstructured grids.