Berenger 's Perfectly Matched Layer Research Articles

Analysis of Side Coupled Microstrip Filters Using Three Dimensional FDTD with Berenger Perfectly Matched Layer (PML).(Dept.E)

Analysis of Side Coupled Microstrip Filters Using Three Dimensional FDTD with Berenger Perfectly Matched Layer (PML).(Dept.E)

Development and analysis of both finite element and fourth-order in space finite difference methods for an equivalent Berenger's PML model

This paper deals with an equivalent Berenger's Perfectly Matched Layer (PML) model. We first develop a finite element scheme using edge elements to solve this model. We prove a discrete stability of this method, which inherits the stability obtained in the continuous case. Then we propose a fourth-order in space finite difference scheme for solving this PML model. Numerical stability similar to the continuous stability and the optimal error estimate are established for the difference scheme. Here only second order time discretizations are considered for both schemes. Finally, numerical results are presented to justify our analysis and demonstrate the effectiveness of this PML model for absorbing impinging waves.

Analysis and application of an equivalent Berenger’s PML model

Abstract The perfectly matched layer (PML) is a technique initially proposed by Berenger for solving unbounded electromagnetic problems with the finite-difference time-domain method. In this work, we first formulate an equivalent PML model from the original Berenger PML model in the corner region, and then establish its stability. We further develop a discontinuous Galerkin method to solve this PML model, and discrete stability similar to the continuous case is proved. To demonstrate the absorbing property of this PML model, we apply it to simulate wave propagation in metamaterials.

Application of Convolution Perfectly Matched Layer in MRTD scattering model for non-spherical aerosol particles and its performance analysis

The performance of absorbing boundary condition (ABC) is an important factor influencing the simulation accuracy of MRTD (Multi-Resolution Time-Domain) scattering model for non-spherical aerosol particles. To this end, the Convolution Perfectly Matched Layer (CPML), an excellent ABC in FDTD scheme, is generalized and applied to the MRTD scattering model developed by our team. In this model, the time domain is discretized by exponential differential scheme, and the discretization of space domain is implemented by Galerkin principle. To evaluate the performance of CPML, its simulation results are compared with those of BPML (Berenger's Perfectly Matched Layer) and ADE-PML (Perfectly Matched Layer with Auxiliary Differential Equation) for spherical and non-spherical particles, and their simulation errors are analyzed as well. The simulation results show that, for scattering phase matrices, the performance of CPML is better than that of BPML; the computational accuracy of CPML is comparable to that of ADE-PML on the whole, but at scattering angles where phase matrix elements fluctuate sharply, the performance of CPML is slightly better than that of ADE-PML. After orientation averaging process, the differences among the results of different ABCs are reduced to some extent. It also can be found that ABCs have a much weaker influence on integral scattering parameters (such as extinction and absorption efficiencies) than scattering phase matrices, this phenomenon can be explained by the error averaging process in the numerical volume integration.

PML Implementation for Efficient 3-D Laguerre-Based FDTD Method Using a New Perturbation Term

In this letter, the three-dimentional Berenger's perfectly matched layer (PML) implementation is proposed for the efficient Laguerre-based finite-difference time-domain method using a new perturbation term. By using this new term and the factorization-splitting scheme, the huge matrix equation of Berenger's PML implementation is split into six tridiagonal matrices and solved efficiently. In the numerical validation, the absorbing performance of the proposed PML implementation is studied as a function of the constitutive parameters and is compared to the existing absorbing boundary conditions (ABCs). Numerical results show that the proposed PML implementation has a better absorbing performance.

Pemodelan Awal Ground Penetrating Radar dengan Metode Discontinuous Galerkin dan PML Berenger

This paper discusses the development of Discontinuous Galerkin method, which has both linear shape function and weight function, for modeling Ground Penetrating Radar (GPR) in heterogeneous media. The triangular meshes are used due to their flexibility to deal with complex geometries. The Berenger Perfectly Matched Layer (PML) is used as absorbing boundary condition at the truncation boundaries. The numerical results of the DG method are compared with the exact solutions and the numerical results of FDTD method and the comparisons show that DG method has better accuracy than FDTD method and more stable for long time simulation. The simulation results of GPR show that the PML works well. Propagating waves at the edge of absorbing boundaries can be suppressed without any significant reflection. The results also show that various waves e.g., transmission waves, reflection waves, and diffraction waves produced by heterogeneous material can be simulated well.

An efficient application of PML in fourth-order precise integration time domain method for the numerical solution of Maxwell's equations

Purpose – The purpose of the paper is to introduce a perfectly matched layer (PML) absorber, based on Berenger's split field PML, to the recently proposed low-dispersion precise integration time domain method using a fourth-order accurate finite difference scheme (PITD(4)). Design/methodology/approach – The validity and effectiveness of the PITD(4) method with the inclusion of the PML is investigated through a two-dimensional (2-D) point source radiating example. Findings – Numerical results indicate that the larger time steps remain unchanged in the procedure of the PITD(4) method with the PML, and meanwhile, the PITD(4) method employing the PML is of the same absorbability as that of the finite-difference time-domain (FDTD) method with the PML. In addition, it is also demonstrated that the later time reflection error of the PITD(4) method employing the PML is much lower than that of the FDTD method with the PML. Originality/value – An efficient application of PML in fourth-order precise integration time domain method for the numerical solution of Maxwell's equations.

A Cylindrical MRTD Algorithm With PML and Quasi-PML

In this paper, we develop an explicit multiresolution time-domain (MRTD) scheme based on Daubechies' scaling functions with a cylindrical grid for time-domain Maxwell's equations. The stability and dispersion property of the scheme is investigated and it is shown that larger cells decrease the numerical phase error, which makes it significantly lower than finite difference time domain (FDTD) for low and medium discretizations, and the MRTD scheme has a slight advantage of high-order FDTD (2, 6). Moreover, two absorbing boundary conditions (ABCs) are derived for the cylindrical MRTD grids. The first one is the perfectly matched layer (PML) based on stretched coordinates, and the other is the straightforward extension of Berenger's PML, which is called the quasi perfectly matched layer (QPML), as it is no longer perfectly matched for cylindrical interfaces. The absorbing effectiveness of the two ABCs are compared and the numerical simulations validate that both PML schemes can provide a satisfactory ABC, while the QPML can save more computation time and computer memory.

Perfectly Matched Layer for the Wave Equation Finite Difference Time Domain Method

The perfectly matched layer (PML) is introduced into the wave equation finite difference time domain (WE-FDTD) method. The WE-FDTD method is a finite difference method in which the wave equation is directly discretized on the basis of the central differences. The required memory of the WE-FDTD method is less than that of the standard FDTD method because no particle velocity is stored in the memory. In this study, the WE-FDTD method is first combined with the standard FDTD method. Then, Berenger's PML is combined with the WE-FDTD method. Some numerical demonstrations are given for the two- and three-dimensional sound fields.

Stability Analysis of Yee Schemes to PML and UPML for Maxwell Equations

We utilize Fourier methods to analyze the stability of the Yee difierence schemes for Berenger PML (perfectly matched layer) as well as the UPML (uniaxial perfectly matched layer) systems of two-dimensional Maxwell equations. Using a practical spectrum stability concept, we flnd that the two schemes are spectrum stable under the same conditions for mesh sizes. Besides, we prove that the UPML schemes with the same damping in both directions are stable. Numerical examples are given to conflrm the stability analysis for the PML method. Mathematics subject classiflcation: 65M12.

FDTD Simulation for Ground Penetrating Radar Wave in Dispersive Medium

AbstractThe earth material probed by Ground Penetrating Radar (GPR) is often dispersive. To investigate the detecting capability of GPR in dispersive medium, we introduced a Finite Difference Time Domain (FDTD) method to solve Maxwell's equations. We give an iterative method for calculation of electrical displacement and magnetic field in Debye medium, and a method to compute electric field from electrical displacement. The physical parameters are used only in calculating electric field. A new absorbing boundary algorithm is introduced by adding fictitious dielectric constant and magnetic permeability, therefore the wave can be attenuated without reflection in absorbing layer. This method overcomes the troubles caused by field split in Berenger's Perfectly Matched Layer (PML), so that the computing efficiency is increased. Examples demonstrate that the electromagnetic wave in dispersive medium attenuates very fast and the measured signals are very weak.

Asymmetric Perfectly Matched Layer for the Absorption of Waves

The perfectly matched layer (PML) has become a standard for comparison in the techniques that have been developed to close the system of Maxwell equations (more generally, wave equations) when simulating an open system. The original Berenger PML formulation relies on a split version of Maxwell equations, with numerical electric and magnetic conductivities. We present here an extension of this formulation, which introduces counterparts of the electric and magnetic conductivities affecting the term which is spatially differentiated in the equations. The phase velocity along each direction is also multiplied by an additional coefficient. We show that under certain constraints on the additional numerical coefficients, this ‘medium’ does not generate any reflection at any angle or any frequency and is thus a perfectly matched layer. Technically it is a superset of Berenger's PML to which it reduces for a specific set of parameters, and like it, it is anisotropic. However, unlike the PML, it introduces some asymmetry in the absorption rate and is therefore labeled an APML, for asymmetric perfectly matched layer. We present here the numerical considerations that have led us to introduce such a medium as well as its theory. Several finite-difference numerical implementations are derived (in one, two, and three dimensions) and the performance of the APML is contrasted with that of the PML in one and two dimensions. Using plane wave analysis, we show that our APML implementations lead to higher absorption rates than the considered PML implementations. Although we have considered in this paper the finite-difference discretization of Maxwell-like equations only, the APML system of equations may be used with other discretization schemes, such as finite elements, and may be applied to other equations, for applications beyond electromagnetics.

Comment on “On the Matching Conditions of Different PML Schemes Applied to Multilayer Isotropic Dielectric Media”

AbstractThe focus of this comment is to correct potential misconceptions regarding the application of perfectly matched layer (PML) absorbing media to terminating inhomogeneous media within the finite‐difference time‐domain (FDTD) method. Initially, it is demonstrated that the PML is material independent by nature. That is, by specifying the constitutive parameters to be independent of the host material medium, both the split‐field form and the anisotropic form (or unsplit form) of the PML are materially independent. It is then demonstrated that the split‐field and nonsplit‐field forms of the “materially independent PML” (MIPML) proposed earlier are identical to Berenger's split‐field PML and the anisotropic PML formulations, respectively, after a simple scaling of the conductivity by a constant. While this validates the MIPML, it also illustrates that the MIPML is a subset of previously proven PML methods. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 30: 289–291, 2001.

Absorbing boundary conditions in the frequency-domain TLM method and their application to planar circuits

The frequency-domain transmission-line-matrix method is extended to include absorbing boundary conditions. Three different approaches are considered: zero-reflection termination (ZRT), Berenger's perfectly matched layer (PML), and anisotropic PML. The ZRT technique is the simplest one of the three. Its main advantage over the PML techniques is that it requires no additional nodes to model the boundary. However, when placed too close to an area with high field intensity, the ZRT boundary takes out substantial parts of the transmitted power, thus giving results on the "lossy side." The numerical losses can be reduced by moving the boundaries further away from the area of interest. The PML techniques are more difficult to implement and require additional nodes for their modeling. However, they offer more flexibility since the numerical reflections from the PML absorbers can be controlled by using several layers with conductivities gradually increasing with depth. The computer simulations show that Berenger's and anisotropic PMLs give virtually the same results. A detailed investigation regarding the optimal number of layers in the PML absorbers and distances between the absorbing boundaries and the structure under analysis is performed.

A finite-difference time-domain approach to waveguide discontinuities using one-dimensional modal perfectly matched layer based on diagonally anisotropic material

In this paper, one-dimensional modal perfectly matched layer (PML) is applied to improve the computational efficiency in waveguide discontinuity problems. The proposed PML formulation is based on an anisotropic medium. A WG-90 rectangular waveguide with a thick asymmetric iris is analyzed via FDTD simulations with Berenger's PML and the proposed one. Numerical results show that the computational efficiency is significantly improved by the new method. © 2000 John Wiley & Sons, Inc. Int J RF and Microwave CAE 10: 264–270, 2000

Fdtd Analysis of Side-Coupled Microstrip Filter

This work presents an application of the FD-TD method in simulating electromagnetic fields and analyzing a planar microstrip filter. The frequency dependent characteristics of the microstrip filter are derived from the full-wave analysis in the time domain. The motivation of this paper is to establish the validity of the FD-TD method in modeling circuit components for MMIC CAD applications. The numerical results are compared to these existing predicted results as well as measurement data. A very good agreement is thus obtained from the comparison. It is, however, realized that with the implementation of the recent Berenger's Perfectly Matched Layer (PML) as an excellent absorbing wall, the computational speed for a given accuracy is much faster than the previous calculation in the filter analysis.

Extension of Berenger's PML for bi-isotropic media

An extension of Berenger's perfectly matched layer (PML) absorbing boundary conditions to adapt bi-isotropic media is formulated. The method is developed under simple algebraic conditions and validated with the finite-difference time-domain method (FDTD).

A novel implementation of Berenger's PML for FDTD applications

In this letter, a new implementation of the three-dimensional (3-D) perfectly matched layer (PML) in finite-difference time-domain (FDTD) applications is introduced. This technique is based on doubling the cell dimensions in PML region where extra averaging of electrical field components are necessary at the edges and faces along the PML-FDTD interfaces. The presented numerical examples are for 3-D structures which exhibit complex wave phenomena. Significant improvement obtained after this implementation, especially at lower frequencies, is demonstrated.

Formulation and validation of Berenger's PML absorbing boundary for the FDTD simulation of acoustic scattering

Berenger's perfectly matched layer (PML) absorbing boundary condition for electromagnetic (EM) waves is derived to absorb 2-D and 3-D acoustic waves in finite difference time domain (FDTD) simulation of acoustic wave propagation and scattering. A PML medium suitable for acoustic waves is constructed. Plane wave propagation in the PML medium is solved for both 2-D and 3-D cases and explicit FDTD boundary conditions are derived. The equations show that a matched PML medium is a perfect simulation of free space in that a plane wave does not change its direction of propagation or its speed when it propagates from free space into a matched PML medium. FDTD simulation of a pulsed point source propagating in two dimensions is carried out to test the performance of the PML boundary for acoustic waves. Results show that an eight layer PML boundary condition reduces the reflected error 40 dB over Mur's second order boundary condition.

A comparison of anisotropic PML to Berenger's PML and its application to the finite-element method for EM scattering

The use of an anisotropic material for the boundary truncation of the finite-element method is considered. The anisotropic material properties can be chosen such that a plane-wave incident from free space into the anisotropic halfspace has no reflection. Because there is no reflection, the material is referred to as a perfectly matched layer (PML). The relationship between the anisotropic PML and the original PML proposed by Berenger (see J. Comp. Phys., vol.114, p.185-200, October 1994) is considered. The anisotropic PML is applied to the finite-element solution of electromagnetic (EM) scattering from three-dimensional (3-D) objects. Numerical results are presented to demonstrate the accuracy of the PML.