PDE eigenvalue iterations with applications in two-dimensional photonic crystals

@article{Altmann2019PDEEI,
  title={PDE eigenvalue iterations with applications in two-dimensional photonic crystals},
  author={R. Altmann and Marine Froidevaux},
  journal={arXiv: Numerical Analysis},
  year={2019}
}
  • R. Altmann, Marine Froidevaux
  • Published 2019
  • Mathematics, Computer Science
  • arXiv: Numerical Analysis
  • The first part of this paper is devoted to the approximative solution of linear and Hermitian eigenvalue problems where the differential operator satisfies a Garding inequality. For this, known iterative schemes for the matrix case such as the inverse power or Arnoldi method are extended to the infinite-dimensional case. This formally allows one to apply different spatial discretizations in each iteration step and thus, justifies the use of adaptive methods. The second part considers eigenvalue… CONTINUE READING
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