NDLI: Parallel QR algorithm for the C-method: application to the diffraction by gratings and rough surfaces

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Parallel QR algorithm for the C-method: application to the diffraction by gratings and rough surfaces

Content Provider	ACM Digital Library
Author	Dusséaux, Richard Emad, Nahid Pan, Cihui
Abstract	The curvilinear coordinate method (C-method) is an exact method for analysing of electromagnetic waves scattering from rough surfaces. It is based on Maxwell's equations under covariant form written in a non-orthogonal coordinate system. This method leads to an eigenvalue system. All the eigenvalues and eigenvectors of the scattering matrix are required. The QR algorithm seems to be a suitable solution for this high dimension, dense, non-symmetric and complex scattering matrix. In this paper, we present the parallel QR algorithm that is specifically designed for the C-method. We define the "early shift" for the scattering matrix according to the property that we have observed. We mixed the "early shift", Wilkinson's shift and exceptional shift together to accelerate the convergence. Especially, we use the "early shift" first in order to have quick deflation of the real eigenvalues of the scattering matrix. The multi-window bulge chain chasing and parallel aggressive early deflation are used. The multi-window bulge chain chasing approach ensures that most computations are performed in 3 BLAS operations. The aggressive early deflation approach can detect deflation much quicker and thus accelerate convergence. Mixed MPI-OpenMP techniques are utilized for performing the codes to distributed memory platforms. Numerical experiments are performed and applications of this parallel QR algorithm are applied to a real physical problem of diffraction.
Starting Page	166
Ending Page	173
Page Count	8
File Format	PDF
ISBN	9781510801011
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2015-04-12
Publisher Place	San Diego
Access Restriction	Subscribed
Subject Keyword	Electromagnetism Shift algorithm Aggressive early deflation Multishift Parallel qr
Content Type	Text
Resource Type	Article

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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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