1,593 research outputs found
On the long-time behavior of unsplit Perfectly Matched Layers
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
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
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
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
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
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
- …