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-OpenMP 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.
"A Complex Mix-Shifted Parallel QR Algorithm for the C-Method," Progress In Electromagnetics Research B,
Vol. 68, 159-171, 2016. doi:10.2528/PIERB16040806
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