A Complex Mix-Shifted Parallel QR Algorithm for the C-Method

Abstract : The C-method is an exact method for analyzing gratings and rough surfaces. This method leads to large-size dense complex non-Hermitian eigenvalue. In this paper, we introduce a parallel QR algorithm that is specifically designed for the C-method. We define the " early shift " for the matrix according to the observed properties. We propose a combination of the " early shift " , Wilkinson's shift and exceptional shift together to accelerate convergence. First, we use the " early shift " in order to have quick deflation of some eigenvalues. The multi-window bulge chain chasing and parallel aggressive early deflation are used. This approach ensures that most computations are performed in level 3 BLAS operations. The aggressive early deflation approach can detect deflation much quicker and accelerate convergence. Mixed MPI-Open MP techniques are used for performing the codes to hybrid shared and distributed memory platforms. We validate our approach by comparison with experimental data for scattering patterns of two-dimensional rough surfaces.
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Cihui Pan, Richard Dusséaux, Nahid Emad. A Complex Mix-Shifted Parallel QR Algorithm for the C-Method. Progress In Electromagnetics Research B, EMW Publishing, 2016, 68, pp.159-171. ⟨10.2528/PIERB16040806⟩. ⟨insu-01347721⟩

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