An Alternative Coarse Space Method for Overlapping Schwarz Preconditioners for Raviart-Thomas Vector Fields

Conference paper
First Online:
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 91)

Summary

The purpose of this paper is to introduce an overlapping Schwarz method for vector field problems discretized with the lowest order Raviart-Thomas finite elements. The coarse component of the preconditioner is based on energy-minimizing discrete harmonic extensions and the local components consist of traditional solvers on overlapping subdomains. The approach has a couple of benefits compared to the previous methods. The algorithm can be implemented in an algebraic manner. Moreover, the method leads to a condition number independent of the values and jumps of the coefficients across the interface between the substructures. Supporting numerical examples to demonstrate the effectiveness are also presented.

Keywords

Condition Number Iteration Count Domain Decomposition Method Local Component Coarse Space 
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Notes

Acknowledgements

The author would like to thank Prof. Olof Widlund for his suggestions and assistance. The author is also grateful to Dr. Clark Dohrmann for his useful comments. The work of the author has been supported by the NSF under Grant DMS-0914954.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Louisiana State UniversityBaton RougeUSA

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