PML Absorbing Boundary Condition Research Articles

PML absorbing boundary condition for structure-preserving seismic wave modeling

Some efficient structure preserving algorithms have been proposed for high precision seismic exploration and detection in recent years. However, feasible artificial boundary conditions to truncate unbounded medium are never discussed in structure preserving seismic modeling. We pay our emphasis on application of perfectly matched layer absorbing boundary condition (PML ABC) to fit the structure preserving algorithms. In the domain of interest, a typical structure preserving algorithm is presented to discretize the conservative dynamic system, while in the PML region, traditional central difference is applied to solve the dissipative system. In the adjacent region of the interior and exterior domains, the temporary values of wave field between two time steps are approximated by interpolation using the present and the updated value of the wave fields in the PML region. A numerical experiment is adopted to demonstrate compatibility of the algorithms and no visible reflections of outgoing waves occur on the edge of interior domain.

Free and forced wave propagation in a Rayleigh-beam grid: Flat bands, Dirac cones, and vibration localization vs isotropization

In-plane wave propagation in a periodic rectangular frame structure, which includes axial and flexural deformation, the latter enhanced with rotational inertia (so-called ‘Rayleigh beams’), is analyzed both with a Floquet-Bloch exact formulation for free oscillations and with a numerical treatment (developed with PML absorbing boundary conditions) for forced vibrations (including Fourier representation and energy flux evaluations), induced by a concentrated force or moment. A complex interplay is observed between axial and flexural vibrations (not found in the common idealization of out-of-plane motion), giving rise to several forms of vibration localization: ‘X-’, ‘cross-’ and ‘star-’ shaped, and channel propagation. These localizations are triggered by several factors, including rotational inertia and slenderness of the beams and the type of forcing source (concentrated force or moment). Although the considered grid of beams introduces an orthotropy in the mechanical response, a surprising ‘isotropization’ of the vibration is observed at special frequencies. Moreover, rotational inertia is shown to ‘sharpen’ degeneracies related to Dirac cones (which become more pronounced when the aspect ratio of the grid is increased), while the slenderness can be tuned to achieve a perfectly flat band in the dispersion diagram. The obtained results can be exploited in the realization of metamaterials designed to filter waves during propagation.

Full-wave simulation of optical waveguides via truncation in the method of moments using PML absorbing boundary conditions.

Full-wave simulations of optical waveguides are often intractable due to their large electrical size. Naively focussing on a smaller part of the waveguide, e.g. to study coupling, offers no solution given the non-negligible interaction with the remaining parts of the structure. Thereto, in this paper, the coordinate stretching formulation of a perfectly matched layer is integrated into a method of moments based boundary integral equation solver in order to damp the interaction between multiple parts, allowing to focus on the part of interest. The new technique is validated using the classical example of scattering by a wedge. By truncation of the simulation domain to merely ten wavelengths from the tip, the advocated method is found to be both efficient and accurate compared to a traditional, analytical solution technique. Next, the method is applied to model a silicon polarization beam splitter excited by a Gaussian beam.

A mixed-grid finite element method with PML absorbing boundary conditions for seismic wave modelling

We have developed a mixed-grid finite element method (MGFEM) to simulate seismic wave propagation in 2D structurally complex media. This method divides the physical domain into two subdomains. One subdomain covering the major part of the physical domain is divided by regular quadrilateral elements, while the other subdomain uses triangular elements to correctly fit a rugged free surface topography. The local stiffness matrix of any quadrilateral element is identical and matrix-vector production is calculated using an element-by-element technique, which avoids assembling a huge global stiffness matrix. As only a few triangular elements exist in the subdomain containing the rugged free surface topography, the memory requirements for storing the assembled subdomain global stiffness matrix are significantly reduced. To eliminate artificial boundary reflections, the MGFEM is also implemented to solve the system equations of PML absorbing boundary conditions (PML ABC). The accuracy and efficiency of the MGFEM is tested in numerical experiments by comparing it with conventional methods, and numerical comparisons also indicate its tremendous ability to describe rugged surfaces.

A GFDM with PML for seismic wave equations in heterogeneous media

The interior of the Earth is heterogeneous with different materials and may have complex geometry. The free surface can also be uneven. Therefore, the use of a meshless method “with the possibility of using an irregular grid-point distribution” can be of interest for modelling this kind of problem.This paper shows the application of GFDM to the problem of seismic wave propagation in 2-D. To use this method in unbounded domains one must truncate the computational grid-point avoiding reflection from the edges. PML absorbing boundary condition has then been included in the numerical model proposed in this work.

On the adjoint problem in duct acoustics and its solution by the time domain wave packet method

The Time Domain Wave Packet (TDWP) method has the advantage of obtaining radiated sound by a given duct mode at all frequencies in one computation. It also makes possible the separation of the acoustic and shear flow instability waves. In this paper, the TDWP method will be applied to the adjoint duct acoustics problem. As a microphone records the sound radiated by all duct modes combined, the adjoint approach has the advantage of obtaining the relative mode strengths of all the propagating modes at all frequencies in one computation. The novelty of the paper is on the formulation of adjoint equations in time domain and the numerical solution using the TDWP method. The theoretical formulation of the duct adjoint problem and derivation of various reciprocal relations are presented. The adjoint equations are then solved numerically in reversed time by the TDWP method, in which a point source in the far field is enforced with a Broadband Acoustic Test Pulse time function. PML absorbing boundary conditions for the adjoint equations are also discussed. By an FFT, the relative strengths of all duct modes at all frequencies to the far field point are computed at once.

Convolutional perfectly matched layer for elastic second-order wave equation

In this work, a method is presented to extend the convolutional perfectly matched layer (C-PML) to simulate acoustic wave propagation in elastic media with a second-order equation formulation. This non-physical layer is used at the computational edge of a finite element method algorithm in frequency domain, and a pseudo-spectral algorithm in time domain, as an absorbing boundary condition (ABC) to truncate unbounded media. Numerical results show that the C-PML ABC attenuates the outgoing surface waves more effectively than classical PML ABC as proposed by Berenger [J. Comput. Phys. 114, 195-200 (1994)] for electromagnetic waves in the case of oblique incidence, where the PML method suffers from large spurious reflections. Moreover, a modification of the proposed C-PML formulation is also discussed in order to stabilize the absorbing layer in anisotropic solids where numerical instabilities can appear.

Aerodynamic noise propagation simulation using immersed boundary method and finite volume optimized prefactored compact scheme

Based on the immersed boundary method (IBM) and the finite volume optimized pre-factored compact (FVOPC) scheme, a numerical simulation of noise propagation inside and outside the casing of a cross flow fan is established. The unsteady linearized Euler equations are solved to directly simulate the aero-acoustic field. In order to validate the FVOPC scheme, a simulation case: one dimensional linear wave propagation problem is carried out using FVOPC scheme, DRP scheme and HOC scheme. The result of FVOPC is in good agreement with the analytic solution and it is better than the results of DRP and HOC schemes. the FVOPC is less dispersion and dissipation than DRP and HOC schemes. Then, numerical simulation of noise propagation problems is performed. The noise field of 36 compact rotating noise sources is obtained with the rotating velocity of 1000r/min. The PML absorbing boundary condition is applied to the sound far field boundary condition for depressing the numerical reflection. Wall boundary condition is applied to the casing. The results show that there are reflections on the casing wall and sound wave interference in the field. The FVOPC with the IBM is suitable for noise propagation problems under the complex geometries for depressing the dispersion and dissipation, and also keeping the high order precision.

On the Huygens absorbing boundary conditions for electromagnetics

A new absorbing boundary condition (ABC) is presented for the solution of Maxwell equations in unbounded spaces. Called the Huygens ABC, this condition is a generalization of two previously published ABCs, namely the multiple absorbing surfaces (MAS) and the re-radiating boundary condition (rRBC). The properties of the Huygens ABC are derived theoretically in continuous spaces and in the finite-difference (FDTD) discretized space. A solution is proposed to render the Huygens ABC effective for the absorption of evanescent waves. Numerical experiments with the FDTD method show that the effectiveness of the Huygens ABC is close to that of the PML ABC in some realistic problems of numerical electromagnetics. It is also shown in the paper that a combination of the Huygens ABC with the PML ABC is very well suited to the solution of some particular problems.

INTEGRAL PML ABSORBING BOUNDARY CONDITIONS FOR THE HIGH-ORDER M24 FDTD ALGORITHM

This work demonstrates an efficient and simple PML absorbing boundary conditions (ABCs) implementation for the highorder extended-stencil M24 FDTD algorithm. To accomplish this objective, the integral forms of the PML split-field formulations were derived and discretized using the same M24 weighted multiple-loop approach, resulting in ABC performances that match the standard FDTD-based PML formulations. This proposed approach eliminates the impedance mismatches caused by switching from M24 to regular FDTD update equations within the PML regions and the necessary cumbersome subgridding implementations needed to minimize the effects of these mismatches. It also eliminates the need to use large separations between the scatterers and the PML regions as a simpler though more costly alternative. This achievement coupled with the recent effective resolution of the PEC modeling issue finally eliminates the last hurdles hindering the wide adoption of the M24 algorithm and its three-dimensional counterpart, the FV24 algorithm, as a viable option for accurate and computationally efficient modeling of electrically large structures.

Full-wave analysis and design of microstrip antenna in-pipe for rectenna using FDTD method

The circular polarized microstrip antenna in the stainless pipe is analyzed by the finite-difference time-domain (FDTD) method with PML absorbing boundary condition. The microstrip antenna is used as a microwave energy supply element for the in-pipe micromachine inspecting. The numerical results agree well with the measured ones.

Application of the PML absorbing boundary conditions to the prism cell time-domain method

Berenger's perfectly matched layer absorbing boundary conditions have been applied to the prism cell time-domain method. The formulations are based on Berenger's split field equations, which are obtained by interpolation and rotation of the field components in the prism cell time-domain algorithm. To verify its accuracy, numerical experiments are conducted for extracting S-parameter of microstrip waveguide with a right-angled bend discontinuity. The present algorithm yields superior accuracy in a large chamfer degrees as compared with FDTD results.

3D-Scalar Fourier Eigenvector Expansion Method (Fourier-EEM) for analyzing optical waveguide discontinuities

In this paper we propose a Fourier Eigenvector Expansion Method (Fourier-EEM) with coordinate-stretching type PML absorbing boundary conditions. This technique has been used to analyze, under the scalar assumption, 3D optical devices with abrupt discontinuities in the longitudinal direction (i.e. Multimode Interference devices (MMI)). The obtained results clearly confirm the accuracy and efficiency of the proposed approach to calculate the transmission and reflection characteristics of photonic devices.

Application of Perfectly Matched Layer Absorbing Boundary Conditions for Propagation of Surface Wave on the Long Plasma Cable

We have developed a computer code for the simulation of large scale SWP plasma excited by a long coaxial antenna with a VHF wave of 300 MHz, this antenna is located along the center axis of a cylindrical chamber. The antenna used in this model structure is so long that the computational region has become very large. Therefore, for the calculation of the electromagnetic field profile in order to design a long and large scale SWP plasma, it is necessary to apply a proper boundary condition to truncate the computational region, and from this viewpoint we have introduced the PML absorbing boundary conditions and have studied the effectiveness of this boundary conditions for our purposes.

Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers

Eigenvalue equations for solving full-vector modes of optical waveguides are formulated using Yee-mesh-based finite difference algorithms and incorporated with perfectly matched layer absorbing boundary conditions. The established method is thus able to calculate the complex propagation constants and the confinement losses of leaky waveguide modes. Proper matching of dielectric interface conditions through the Taylor series expansion of the fields is adopted in the formulation to achieve high numerical accuracy. The method is applied to the study of the holey fiber with triangular lattice, the two-core holey fiber, and the air-guiding photonic crystal fiber.

An unsplit formulation of the Berenger's PML absorbing boundary condition for FDTD meshes

An unsplit formulation of the Berenger's perfectly matched layer absorbing boundary condition (PML ABC) for finite-difference time-domain (FDTD) meshes is presented. This unsplit formulation uses the conventional E-H algorithm, but does not require the E and H fields to be split. The proposed formulation is memory-efficient like that of the previous unsplit PML following the theory of Sacks. This unsplit formulation is easy to be implemented, and many useful modification to the Berenger's PML can also be done to it.

Making use of the pml absorbing boundary condition in coupling and scattering fdtd computer codes

This paper deals with the optimization of the PML absorbing boundary condition in finite-difference time-domain computer codes designed for the solution of scattering and coupling problems encountered in the field of electromagnetic compatibility. The critical parameters of the perfectly matched layer (PML) are estimated in function of the problem to be solved, and a blackbox PML concept is introduced. The blackbox PML renders use of computer codes easy, reliable, and optimum in terms of PML thickness. This is illustrated by various numerical experiments.

The Improvement of PML Approach for the Calculation of Microwave and Millimeter Waves Circuit

The improved PML absorbing boundary condition have been introduced in this paper. The reflection coefficient of the absorbing boundary condition is less than the reflection coefficient of Berenger's PML algorithm. And in order to validate the theory and its effectiveness, We have applied the absorbing boundary condition to the calculation of microwave and millimeter waves circuit and get its reflection coefficient S11. The numerical result is shown in this paper.

Noncubic cell time-domain method in 3-D coordinates using prism cells applied PML absorbing boundary conditions

We propose an application of the PML absorbing boundary condition to a noncubic cell time-domain method using prism cells for 3-D full-wave analysis. To verify that the noncubic cell time-domain method can accurately simulate pulse propagation on microstrip waveguide terminated by applying the PML absorbing boundary conditions, we extracted S-parameter from a simulation of pulse propagation on a right-angled bend discontinuity. The performance of the noncubic cell time-domain method is shown and it exhibits superior accuracy in a large chamfer degree as compared with FD-TD results.

Unconditionally stable D-H FDTD formulation with anisotropic PML boundary conditions

An unconditionally stable finite difference time domain (FDTD) method based on a D-H formulation and the recently proposed alternating-direction-implicit (ADI) marching scheme is presented. The advantage of the D-H algorithm over the conventional E-H is the possibility to easily implement an unsplit field components formulation of the PML absorbing boundary condition that is independent from the background material used in the FDTD grid. The method allows therefore immersing any dielectric in the PML layers without any special consideration, and is amenable for models truncation often used in biomedical simulations. Furthermore, the proposed scheme can be extended to account for frequency dispersive dielectrics.