1,593 research outputs found

    On the long-time behavior of unsplit Perfectly Matched Layers

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    Some recent work \cite{jsc} have shown that the «classical» models of Perfectly Matched Layers (PML), typically used as Absorbing Boundary Condition- s in Computational Electromagnetics codes, could lead to long-time linear growth of the solution. We propose here new PML which eliminate this undesirab- le long-time behavior. For these new PML equations, we give energy arguments that show the fields in the layer are bounded by a time-independent constant hence they are long-time stable. Numerical experiments confirm the elimination of the linear growth, and the long-time boundedness of the fields

    Efficient computation of TM- and TE-polarized leaky modes in multilayered circular waveguides

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    In combination with the perfectly matched layer (PML)-paradigm, eigenmode expansion techniques have become increasingly important in the analysis and design of cylindrical and planar waveguides for photonics applications. To achieve high accuracy, these techniques rely on the determination of many modes of the modal spectrum of the waveguide under consideration. In this paper, we focus on the efficient computation of TM- and TE-polarized leaky modes for multilayered cylindrical waveguides. First, quasi-static estimates are derived for the propagation constants of these modes. Second, these estimates are used as a starting point in an advanced Newton iteration scheme after they have been subjected to an adaptive linear error correction. To prove the validity of the computation technique, it is applied to technologically important cases: vertical-cavity surface-emitting lasers and a monomode fiber

    Excessive Memory Usage of the ELLPACK Sparse Matrix Storage Scheme throughout the Finite Element Computations

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    Sparse matrices are occasionally encountered during solution of various problems by means of numerical methods, particularly the finite element method. ELLPACK sparse matrix storage scheme, one of the most widely used methods due to its implementation ease, is investigated in this study. The scheme uses excessive memory due to its definition. For the conventional finite element method, where the node elements are used, the excessive memory caused by redundant entries in the ELLPACK sparse matrix storage scheme becomes negligible for large scale problems. On the other hand, our analyses show that the redundancy is still considerable for the occasions where facet or edge elements have to be used

    Perfectly Matched Layers in a Divergence Preserving ADI Scheme for Electromagnetics

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    For numerical simulations of highly relativistic and transversely accelerated charged particles including radiation fast algorithms are needed. While the radiation in particle accelerators has wavelengths in the order of 100 um the computational domain has dimensions roughly 5 orders of magnitude larger resulting in very large mesh sizes. The particles are confined to a small area of this domain only. To resolve the smallest scales close to the particles subgrids are envisioned. For reasons of stability the alternating direction implicit (ADI) scheme by D. N. Smithe et al. (J. Comput. Phys. 228 (2009) pp.7289-7299) for Maxwell equations has been adopted. At the boundary of the domain absorbing boundary conditions have to be employed to prevent reflection of the radiation. In this paper we show how the divergence preserving ADI scheme has to be formulated in perfectly matched layers (PML) and compare the performance in several scenarios.Comment: 8 pages, 6 figure

    Full Hydrodynamic Model of Nonlinear Electromagnetic Response in Metallic Metamaterials

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    Applications of metallic metamaterials have generated significant interest in recent years. Electromagnetic behavior of metamaterials in the optical range is usually characterized by a local-linear response. In this article, we develop a finite-difference time-domain (FDTD) solution of the hydrodynamic model that describes a free electron gas in metals. Extending beyond the local-linear response, the hydrodynamic model enables numerical investigation of nonlocal and nonlinear interactions between electromagnetic waves and metallic metamaterials. By explicitly imposing the current continuity constraint, the proposed model is solved in a self-consistent manner. Charge, energy and angular momentum conservation laws of high-order harmonic generation have been demonstrated for the first time by the Maxwell-hydrodynamic FDTD model. The model yields nonlinear optical responses for complex metallic metamaterials irradiated by a variety of waveforms. Consequently, the multiphysics model opens up unique opportunities for characterizing and designing nonlinear nanodevices.Comment: 11 pages, 14 figure

    Effective Cell-Centred Time-Domain Maxwell's Equations Numerical Solvers

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    This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed
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