Omar Ramadan

Auxiliary differential equation formulation: an efficient implementation of the perfectly matched layer

An efficient algorithm for implementing the perfectly matched layer (PML) is presented for truncating finite-difference time-domain domains. The algorithm is based on incorporating the auxiliary differential equation method into the PML formulations. Simple, unsplit-field and material independent PML formulations are obtained. Two dimensional numerical examples are included to validate the proposed formulations.

Z-transform implementation of the perfectly matched layer for truncating FDTD domains

A simple algorithm for implementing the perfectly matched layer (PML) is presented for truncating finite difference time domain (FDTD) computational domains. The algorithm is based on incorporating the Z-transform method into the PML FDTD implementation. The main advantage of the algorithm is its simplicity as it allows direct FDTD implementation of Maxwells equations in the PML region. In addition, the formulations are independent of the material properties of the FDTD computational domain. Numerical examples are included to demonstrate the effectiveness of these formulations.

Unconditionally stable nearly PML algorithm for linear dispersive media

Unconditional stable alternating direction implicit (ADI) formulations of the nearly perfectly matched layer (NPML) are presented for truncating linear dispersive finite difference time domain (FDTD) grids. The digital signal processing (DSP) algorithms developed for digital filters are used to implement the frequency dependent property of the media into the ADI-FDTD algorithm. The formulations have the advantage of simplicity of ADI-FDTD implementation. Numerical examples carried out for linear Debye and Lorentz dispersive domains are included to validate the proposed formulations.

General ADI-FDTD Formulations for Multi-Term Dispersive Electromagnetic Applications

General formulations of the alternating direction implicit finite difference time domain method are presented for modeling multi-term dispersive electromagnetic applications. The proposed formulations, which are based on the exponential evolution operator scheme, allow modeling different types of frequency dependent materials in the same manner and can be easily incorporated with the nearly perfectly matched layer absorbing boundary conditions to model open region problems. 2-D numerical example is included to show the validity of the proposed formulations.

Complex Envelope ADI–PML Algorithm for Truncating Lorentz Dispersive 2-D-FDTD Domains

Unconditionally stable complex envelope perfectly matched layer formulations are presented for truncating dispersive finite difference time domain grids. The method is based on the alternating direction implicit scheme and can be used for modeling electromagnetic applications with band limited sources. Numerical examples carried out in 2-D linear Lorentz dispersive media are included to show the validity of the proposed formulations

Unconditionally stable ADI-FDTD formulations of the APML for frequency-dependent media

Unconditional stable formulations of the anisotropic perfectly matched layer (APML) are presented for truncating frequency-dependent media. The formulations are based on the auxiliary differential equation and the alternating direction implicit finite-difference time-domain (ADI-FDTD) methods. Numerical examples carried out in one and two dimensions show that the proposed formulations remain unconditionally stable with inclusion of material dispersion into ADI-FDTD implementation of APML.

Efficient LOD-SC-PML Formulations for Electromagnetic Fields in Dispersive Media

Efficient locally one dimensional stretched-coordinate perfectly matched layer (LOD-SC-PML) formulations are presented for truncating open region dispersive finite difference time domain (FDTD) applications. The field equations in the PML regions are implemented with the minimal additional auxiliary variables that will be computed only in one of the LOD-FDTD scheme stages. It has been shown that the proposed formulations are computationally efficient more than the alternating direction implicit SC-PML counterpart, while maintaining approximately the same numerical performance.

Three dimensional MPI parallel implementation of the PML algorithm for truncating finite-difference time-domain Grids

Three dimensional parallel implementation of the perfectly matched layer (PML) formulations are presented for truncating finite-difference time-domain (FDTD) Grids. The FDTD computational domain is divided into subdomains using one-dimensional topology and the interprocessor communication operations between the subdomains are carried out by using the message-passing interface (MPI) library. The validity of the proposed algorithm is shown through numerical simulations carried out for a point source radiating in three-dimensional domains of different sizes and performed on a network of PCs interconnected with Ethernet.

Unconditionally stable Crank-Nicolson nearly PML algorithm for truncating linear Lorentz dispersive FDTD domains

In this paper, unconditionally stable formulations of the nearly perfectly matched layer are presented for truncating linear dispersive finite-difference time-domain (FDTD) grids. In the proposed formulations, the Crank-Nicolson and bilinear frequency-approximation techniques are used to obtain the update equations for the field components in linear dispersive media. A numerical example carried out in a one-dimensional Lorentz dispersive FDTD domain is included and it has been observed that the proposed formulations not only give accurate results, but also completely remove the stability limit of the conventional FDTD algorithm

On the accuracy of the nearly PMLfor nonlinear FDTD domains

In this letter, the first implementation of the nearly perfectly matched layer (NPML) for truncating nonlinear dispersive finite-difference time-domain (FDTD) grids is presented. In the proposed method, the Z-transform theory is employed in the FDTD implementations of the NPML formulations. The performance of the NPML was investigated through a numerical example carried out in two-dimensional Kerr-Raman nonlinear and Lorentz-dispersive domain, and it has been observed that the NPML is capable of absorbing nonlinear electromagnetic waves.