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End date: 2019 × Start date: 2010 × Type: Text × Publisher: Berlin: Weierstraß-Institut für Angewandte Analysis und Stochastik × WGL Institute: WIAS ×

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Now showing 1 - 4 of 4
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    Compact high order finite difference schemes for linear Schrödinger problems on non-uniform meshes
    (Berlin: Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Radziunas, Mindaugas; Čiegis, Raimondas; Mirinavičius, Aleksas
    In the present paper a general technique is developed for construction of compact high-order finite difference schemes to approximate Schrödinger problems on nonuniform meshes. Conservation of the finite difference schemes is investigated. Discrete transparent boundary conditions are constructed for the given high-order finite difference scheme. The same technique is applied to construct compact high-order approximations of the Robin and Szeftel type boundary conditions. Results of computational experiments are presented
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    Scattering of time harmonic electromagnetic plane waves by perfectly conducting diffraction gratings
    (Berlin: Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Hu, Guanghui; Rathsfeld, Andreas
    Consider scattering of time-harmonic lectromagnetic plane waves by a doubly periodic surface in R^3. The medium above the surface is supposed to be homogeneous and isotropic with a constant dielectric coefficient, while below is a perfectly conducting material. This paper is concerned with the existence of quasiperiodic solutions for any frequency of incidence. Based on an equivalent variational formulation established by the mortar technique of Nitsche, we verify the existence of solutions for a broad class of incident waves including plane waves, under the assumption that the grating profile is a Lipschitz biperiodic surface. Our solvability result covers the resonance case where a Rayleigh frequency is allowed. Non-uniqueness examples are also presented in the resonance case and the TE or TM polarization case for classical gratings.
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    The Turing bifurcation in network systems : collective patterns and single differentiated nodes
    (Berlin: Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Wolfrum, Matthias
    We study the emergence of patterns in a diffusively coupled network that undergoes a Turing instability. Our main focus is the emergence of stable solutions with a single differentiated node in systems with large and possibly irregular network topology. Based on a mean-field approach, we study the bifurcations of such solutions for varying system parameters and varying degree of the differentiated node. Such solutions appear typically before the onset of Turing instability and provide the basis for the complex scenario of multistability and hysteresis that can be observed in such systems. Moreover, we discuss the appearance of stable collective patterns and present a codimension-two bifurcation that organizes the interplay between collective patterns and patterns with single differentiated nodes
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    Sensitivity analysis of 2D photonic band gaps of any rod shape and conductivity using a very fast conical integral equation method
    (Berlin: Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Goray, Leonid; Schmidt, Gunther
    The conical boundary integral equation method has been proposed to calculate the sensitive optical response of 2D photonic band gaps (PBGs), including dielectric, absorbing, and highconductive rods of various shapes working in any wavelength range. It is possible to determine the diffracted field by computing the scattering matrices separately for any grating boundary profile. The computation of the matrices is based on the solution of a 2×2 system of singular integral equations at each interface between two different materials. The advantage of our integral formulation is that the discretization of the integral equations system and the factorization of the discrete matrices, which takes the major computing time, are carried out only once for a boundary. It turned out that a small number of collocation points per boundary combined with a high convergence rate can provide adequate description of the dependence on diffracted energy of very different PBGs illuminated at arbitrary incident and polarization angles. The numerical results presented describe the significant impact of rod shape on diffraction in PBGs supporting polariton-plasmon excitation, particularly in the vicinity of resonances and at high filling ratios. The diffracted energy response calculated vs. array cell geometry parameters was found to vary from a few percent up to a few hundred percent. The influence of other types of anomalies (i.e. waveguide anomalies, cavity modes, Fabry-Perot and Bragg resonances, Rayleigh orders, etc), conductivity, and polarization states on the optical response has been demonstrated.