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  • 1.
    Effenberger, Cedric
    et al.
    ETH Zurich, Switzerland.
    Kressner, Daniel
    ETH Zurich, Switzerland.
    Engström, Christian
    ETH Zurich, Switzerland.
    Linearization techniques for band structure calculations in absorbing photonic crystals2012In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 89, no 2, p. 180-191Article in journal (Refereed)
    Abstract [en]

    Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modeled by rational functions, such as the Lorentz model, in which case the eigenvalue problems are rational in the eigenvalue parameter. After spatial discretization using an interior penalty discontinuous Galerkin method, we employ a recently developed linearization technique to deal with the resulting rational matrix eigenvalue problems. In particular, the efficient implementation of Krylov subspace methods for solving the linearized eigenvalue problems is investigated in detail. Numerical experiments demonstrate that our new approach is considerably cheaper in terms of memory and computing time requirements compared with the naive approach of turning the rational eigenvalue problem into a polynomial eigenvalue problem and applying standard linearization techniques. Copyright © 2011 John Wiley & Sons, Ltd.

  • 2.
    Engström, Christian
    et al.
    ETH Zurich, Switzerland.
    Wang, Mengyu
    ETH Zurich, Switzerland.
    Complex dispersion relation calculations with the applications to absorptive photonic crystals2010In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 84, p. 849-863Article in journal (Refereed)
    Abstract [en]

    A high-order discontinuous Galerkin method for calculations of complex dispersion relations of two-dimensional photonic crystals is presented. The medium is characterized by a complex-valued permittivityand we relate for this absorptive system the spectral parameter to the time frequency. We transform thenon-linear eigenvalue problem for a Lorentz material in air into a non-Hermitian linear eigenvalue problemand uses a Krylov space method to compute approximate eigenvalues. Moreover, we study the impact ofthe penalty term numerically and illustrate the high convergence rate of the method.

  • 3.
    Nyman, U.
    et al.
    Lund University.
    Gustafsson, P. J.
    Lund University.
    Johannesson, Björn
    Lund University.
    Hägglund, R.
    SCA Packaging Research.
    A numerical method for the evaluation of non-linear transient moisture flow in cellulosic materials2006In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 66, no 12, p. 1859-1883Article in journal (Refereed)
    Abstract [en]

    A numerical method for the transient moisture flow in porous cellulosic materials like paper and wood is presented. The derivation of the model is based on mass conservation for a mixture containing a vapour phase and an adsorbed water phase embedded in a porous solid material. The principle of virtual moisture concentrations in conjunction with a consistent linearization procedure is used to produce the iterative finite element equations. A monolithic solution strategy is chosen in order to solve the coupled non-symmetric equation system. A model for the development of higher order sorption hysteresis is also developed. The model is capable of describing cyclic hardening as well as cyclic softening of the equilibrium water concentration. The model is verified by comparison with the measured response to natural variations in temperature and humidity. A close agreement of the simulated results to measured data is found. Copyright (c) 2005 John Wiley & Sons, Ltd.

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