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

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

Efficient PML for the wave equation

In the last decade, the perfectly matched layer (PML) approach has proved a flexible and accurate method for the simulation of waves in unbounded media. Most PML formulations, however, usually require wave equations stated in their standard second-order form to be reformulated as first-order systems, thereby introducing many additional unknowns. To circumvent this cumbersome and somewhat expensive step, we instead propose a simple PML formulation directly for the wave equation in its second-order form. Inside the absorbing layer, our formulation requires only two auxiliary variables in two space dimensions and four auxiliary variables in three space dimensions; hence it is cheap to implement. Since our formulation requires no higher derivatives, it is also easily coupled with standard finite difference or finite element methods. Strong stability is proved while numerical examples in two and three space dimensions illustrate the accuracy and long time stability of our PML formulation.Comment: 16 pages, 6 figure

Computation of transient electromagnetic fields due to switching in high voltage substations

Switching operations of circuit breakers and disconnect switches radiate transient electromagnetic fields within high-voltage substations. The generated fields may interfere and disrupt normal operations of electronic equipment. Hence, the electromagnetic compatibility (EMC) of this electronic equipment has to be considered as early as the design stage of substation planning and operation. Also, microelectronics are being introduced into the substation environment and are located close to the switching devices in the switchyards more than ever before, often referred to as distributed electronics. Hence, there is the need to re-evaluate the substation environment for EMC assessment, accounting for these issues. This paper deals with the computation of transient electromagnetic fields due to switching within a typical high-voltage air-insulated substation (AIS) using the finite-difference time-domain (FDTD) method

A comparison between PML, infinite elements and an iterative BEM as mesh truncation methods for HP self-adaptive procedures in electromagnetics

Finite element hp-adaptivity is a technology that allows for very accurate numerical solutions. When applied to open region problems such as radar cross section prediction or antenna analysis, a mesh truncation method needs to be used. This paper compares the following mesh truncation methods in the context of hp-adaptive methods: Infinite Elements, Perfectly Matched Layers and an iterative boundary element based methodology. These methods have been selected because they are exact at the continuous level (a desirable feature required by the extreme accuracy delivered by the hp-adaptive strategy) and they are easy to integrate with the logic of hp-adaptivity. The comparison is mainly based on the number of degrees of freedom needed for each method to achieve a given level of accuracy. Computational times are also included. Two-dimensional examples are used, but the conclusions directly extrapolated to the three dimensional case

A Complex Domain Mapping of the SCN for an Effective PML Implementation in TLM

An improved implementation of the perfectly matched layer (PML) is developed for the Transmission Line Modelling (TLM) method based on a mapping of the symmetrical condensed node (SCN) to an analytically extended geometric space. By mapping the TLM node, a medium — circuit equivalence is developed which maps transmission line parameters from real to complex domain. This consequently modifies the TLM scatter-connect process. The PML implementation is demonstrated for canonical cases where it is shown to have a comparable absorption performance and a significantly improved temporal stability relative to previously published TLM-PML formulations

A new construction of perfectly matched layers for the linearized Euler equations

Based on a PML for the advective wave equation, we propose two PML models for the linearized Euler equations. The derivation of the first model can be applied to other physical models. The second model was implemented. Numerical results are shown.Comment: submitted for publication on February 1st 2005 What's new: interface conditions for the first PML model, a 3D section, more numerical result