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Deflation Techniques for Computational Electromagnetism: Theoretical Considerations

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Title: Deflation Techniques for Computational Electromagnetism: Theoretical Considerations
Authors: Igarashi, Hajime Browse this author →KAKEN DB
Watanabe, Kota Browse this author →KAKEN DB
Keywords: Matrix deflation
Projection matrix
Augmented matrix
Finite element method
AV method
Issue Date: May-2011
Publisher: IEEE : Institute of Electrical and Electronics Engineers
Journal Title: IEEE Transactions on Magnetics
Volume: 47
Issue: 5
Start Page: 1438
End Page: 1441
Publisher DOI: 10.1109/TMAG.2010.2094998
Abstract: This paper describes deflation of finite element (FE) matrices for electromagnetic fields. The condition of the FE matrices is improved by the matrix deflation which replaces small eigenvalues with zeros. It is known that convergence of linear solvers for FE equations can be improved by using the AV method as well as explicit and implicit error correction (EC) methods which have been derived from the multigrid method. These numerical results are theorized on the basis of the matrix deflation. In particular, augmented matrices appeared in the AV and implicit EC methods are shown to have good conditioning after preconditioning. These results suggest that the above methods are based on a common mathematical principle.
Rights: © 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Type: article (author version)
Appears in Collections:情報科学院・情報科学研究院 (Graduate School of Information Science and Technology / Faculty of Information Science and Technology) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 五十嵐 一

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