Abstract
We describe a GNU-OCTAVE implementation of the Jacobi–Davidson style QR method for the estimation of interior eigenvalues in photonic crystal structures. The photonic eigenproblem is reduced to a matrix eigenproblem using plane-wave expansion. We show that a single-step solution of the Jacobi–Davidson correction equation combined with a simple diagonal Jacobi pre-conditioner are quite time efficient compared to other schemes including the Jacobi–Davidson with bi-orthogonal basis, conjugate gradient minimization of the Rayleigh Ritz quotient and implicitly restarted Lanczos methods. Our implementation is freely available on the web.
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Kamalakis, T. An GNU-OCTAVE implementation of Jacobi–Davidson style QR method for interior eigenvalue calculations using plane-wave expansion in photonic crystal structures. Opt Quant Electron 50, 89 (2018). https://doi.org/10.1007/s11082-018-1352-0
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DOI: https://doi.org/10.1007/s11082-018-1352-0