Perfectly Matched Layer Research Articles

An Efficient Mixed Finite Element Perfectly Matched Layer with Optimal Parameters Selection for Two-Dimensional Time Domain Soil-Structure Interaction Analysis

Perfectly matched layer (PML) is known as one of the best methods to simulate infinite domains in many fields such as soil-structure interaction (SSI). The performance of PML is significantly affected by PML parameters selection. However, the way to select PML parameters still remains unclear. This study proposes a method for PML parameters determination for elastic wave propagation in two-dimensional (2D) media. The scaling and attenuation functions are developed in order to increase the accuracy and effectiveness of the PML. The proposed scheme is applied for a mixed PML in time domain. The finite element method (FEM) formulations of the PML are presented so that it can be easily applied to the existing codes. ABAQUS, a popular FEM code, is used for numerical applications in this study. The proposed PML is imported into ABAQUS by using a user-defined element (UEL) written in Fortran language. Six numerical analyses of SSI are implemented to prove the efficiency of the proposed PML. The numerical analyses cover many realistic problems, including free field, surface structure, and embedded structure problems. The results demonstrate the efficiency of the proposed PML in terms of the accuracy and computational cost.

Multiscale modeling and simulation methods for electromagnetic and multiphysics problems

Multiscale modeling and simulation methods for electromagnetic and multiphysics problems

Performance study of a highly sensitive plasmonic sensor based on microstructure photonics using an outside detecting method

In this article, we design a microstructure based photonic crystal fiber (PCF) with external sensing surface plasmon resonance (SPR) sensor. The performance of the design is numerically evaluated incorporating the finite element method (FEM) with Perfectly Matched Layer (PML) boundary condition of scattering case. Modal analysis is performed using finer mesh analysis. At the optimized thickness (40nm) of chemically stable gold (Au) layer, the ever been maximum reported wavelength sensitivity (WS) and standard amplitude sensitivity (AS) are to 75,000 nm/RIU with wavelength resolution (WR) 1.33×10−6 RIU and 480 per RIU correspondingly. With a large detection range of 1.33 to 1.41 RIU, the sensor also exposed high polynomial fit (R2=0.99) as well as a high figure of merit (FOM) of 300 per RIU. Since very much high sensitivity, high detecting range and FOM, lower the cost of fabrication, the proposed design can be a pleasant competitor in detection of the analyte refractive index (RI). At the last, we can say that the proposed sensor would become a great candidate to detect biological and biochemical samples with fast and smart responses.

A sliced-3D approach to finite-difference time-domain modeling by optimizing perfectly matched layers

Finite-difference time-domain forward modeling is often used to gain a more quantitative understanding of the interactions between electromagnetic fields and targets. To undertake full 3D simulations, the computational demands are challenging, so simulations are often undertaken in two dimensions, in which assumptions in the propagation of electromagnetic fields and source type can result in errors. We have developed the concept of a sliced-3D simulation, wherein a thin slice of a 3D domain with strictly 2D geometry is used to minimize computational demands while obtaining synthetic waveforms that contain full 3D propagation effects. This approach requires optimization of perfectly matched layer (PML) boundary condition parameters so as to minimize the errors associated with the source being located close to the boundary, and as a result of grazing-incident angle wave conversion to evanescent energy. We explore the frequency dependence of PML parameters, and we establish a relationship between complex frequency stretching parameters and effective wavelength. The resultant parameter choice is shown to minimize propagation errors in the context of a simple radioglaciological model, in which 3D domains may be prohibitively large, and for a near-surface cross-borehole survey configuration, a case in which full-waveform inversion may typically be used.

Pseudospectral methods with PML for nonlinear Klein-Gordon equations in classical and non-relativistic regimes

Two different Perfectly Matched Layer (PML) formulations with efficient pseudo-spectral numerical schemes are derived for the standard and non-relativistic nonlinear Klein-Gordon equations (NKGE). A pseudo-spectral explicit exponential integrator scheme for a first-order formulation and a linearly implicit preconditioned finite-difference scheme for a second-order formulation is proposed and analyzed. To obtain a high spatial accuracy, new regularized Bermúdez type absorption profiles are introduced for the PML. It is shown that the two schemes are efficient, but the linearly implicit scheme should be preferred for accuracy purpose when used within the framework of pseudo-spectral methods combined with the regularized Bermúdez type functions. In addition, in the non-relativistic regime, numerical examples lead to the conclusion that the error related to regularized Bermúdez type absorption functions is insensitive to the small parameter ε involved in the NKGE. The paper ends by two extensions of the proposed strategy: one is for the long-term dynamics of NKGE with weak nonlinearity and the other is for a two-dimensional rotating NKGE where the vortex dynamics is very well-reproduced.

Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the L2-norm and L∞-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (Wei et al. [SIAM J. Numer. Anal. 58 (2020) 1918–1940]).

Compact BZT-ME-PML for modeling FDTD subsurface sensing and imaging

Depending on the matrix exponential (ME) method, a compact and highly-accurate implementation of the perfectly matched layer (PML) with the complex-frequency-shifted (CFS) scheme based upon the bilinear Z-transform (BZT) technique is developed for modeling the finite-difference time-domain (FDTD) problems on the very low frequency (VLF) subsurface sensing and the very high frequency (VHF) imaging. By using ME method, the proposal becomes a compact first-order differential matrix form so that it can completely circumvent convolution operations, formula rearrangements, or variable replacements during mathematical derivations. Furthermore, the BZT-ME-PML can not only flexibly terminate arbitrary media because of adding the DB constitutive relation, but efficiently attenuate evanescent waves and decrease late-time reflections due to incorporating the CFS scheme. Besides, the BZT-ME-PML can maintain higher absorption performances when it comes closer to truncate the FDTD domain with targets so that smaller computational regions can be adopted for modeling 3D open-domain subsurface sensing and imaging cases, resulting in palpable improvements in memory requirement and CPU time. The numerical simulations on the subsurface sensing and imaging have been carried out to illustrate the validity and accuracy of the approach.

Dynamic responses of unsaturated ground with or without embankment under moving loads using 2.5D FEM with perfectly match layer

ABSTRACT The dynamic responses of an unsaturated ground with or without an embankment are analysed using 2.5D finite element method (FEM) to investigate the effects of the soil saturation and the embankment. The Galerkin method is utilised to establish the weak form governing equations for an unsaturated poroviscoelastic medium in the framework of 2.5D FEM. To reduce the reflected waves from the truncated boundaries of the 2.5D FE model, the formulations of the perfectly match layer (PML) technique are coupled with the governing equations of the unsaturated medium. The unsaturated ground vibrations with an embankment under moving loads are analysed by the proposed 2.5D FE approach, to investigate the influences of an embankment on unsaturated ground vibrations. The results of this research found that the PML technique can effectively reduce the reflected waves in the 2.5D FE model of unsaturated grounds. The increased soil saturation would increase the ground vibration amplitude, as well as the pore water pressure. Constructing embankment on the unsaturated ground could reduce the vibrations amplitude under the moving load, however increase the ground vibrations at the foot of the embankment.

Time domain analysis and localization of a non-local PML for dispersive wave equations

In this work we design and analyze new perfectly matched layers (PML) for a dispersive waves equation: the Klein Gordon equation. We show that because of the dispersion, classical PMLs do not guarantee the convergence to zero of the error, which hampers the precision in long time simulation. We propose to consider a non-local PML for which we can obtain explicit uniform estimates for the reflected analytical solution in time domain, given by an integral representation formula. This uniform estimates ensure the convergence of the error to zero at fixed time t and guarantee the accuracy of the layer. For the implementation of the new PML, we propose a localization technique that we validate numerically.

Ultra-high negative dispersion compensating modified square shape photonic crystal fiber for optical broadband communication

In this work, a modified square photonic crystal fiber (MS-PCF) architecture is exposed with ultra-high negative dispersion for communication window. The validation of the model is successfully performed by applying an efficient full-vector finite element method (FV-FEM) with anisotropic perfectly matched layers (PMLs) for precise simulation of PCFs. Additionally, waveguide dispersion engineering is accomplished by tuning the structural parameters of the MS-PCF. From the numerical investigation, negative dispersion behavior permits remarkable suppression rather than positive dispersion. It offers the high negative dispersion of −2357.54 ps/nm/km and Kerr nonlinearity (γ) of 74.68 W−1 km−1 simultaneously at the operating wavelength, λ = 1550 nm. Nevertheless, the designed fiber ensures the mono mode operation in the entire band of interest from λ = 1340 nm to λ = 1580 nm. MS-PCF with these outstanding optical performances has distinguished potency to be practiced as a dispersion compensating fiber in optical communication systems.

Parameter Design of Conformal PML Based on 2D Monostatic RCS Optimization

In this study, 2D finite element (FE) solving process with the conformal perfectly matched layer (PML) is elucidated to perform the electromagnetic scattering computation. With the 2D monostatic RCS as the optimization objective, a sensitivity analysis of the basic design parameters of conformal PML (e.g., layer thickness, loss factor, extension order and layer number) is conducted to identify the major parameters of conformal PML that exerts more significant influence on 2D RCS. Lastly, the major design parameters of conformal PML are optimized by the simulated annealing algorithm (SA). As revealed from the numerical examples, the parameter design and optimization method of conformal PML based on SA is capable of enhancing the absorption effect exerted by the conformal PML and decreasing the error of the RCS calculation. It is anticipated that the parameter design method of conformal PML based on RCS optimization can be applied to the cognate absorbing boundary and 3D electromagnetic computation.

An isogeometric formulation of locally-conformal perfectly matched layer for acoustic scattering problems

This paper presents an isogeometric formulation of the locally-conformal perfectly matched layer (PML) for time-harmonic acoustic scattering problems. The new formulation is a generalization of the conventional locally-conformal PML, in which the NURBS patch supporting the PML domain is transformed from real space to complex space. This is achieved by complex coordinate stretching, based on a stretching vector field indicating the directions in which incident sound waves are absorbed. The performance of the isogeometric PML formulation is discussed through several acoustic scattering problems, spanning from one to three dimensions. It is found that the proposed method presents superior computational accuracy, high geometric adaptivity, and good robustness against challenging geometric features. The geometry-preserving ability inherent in the isogeometric framework could bring extra benefits by eliminating geometric errors that are unavoidable in the conventional PML. Meanwhile, these properties are not sensitive to the location of the sound source or the depth of the PML domain.

Condition Investigations of Concrete Cylinders Using Electromagnetic Waves at Microwave Frequencies

Microwave radar non-destructive testing (NDT) technique is used to simulate and measure concrete cylinder containing rebar and void. The interaction of electromagnetic wave and concrete has been observed both by simulation and by measurement. A Finite-Difference Time-Domain (FDTD) method with Perfectly Matched Layer (PML) Absorbing Boundary Condition (ABC) is used to simulate electromagnetic wave propagation in concrete cylinder 2D simulation of a wave generated from a point source at microwave frequencies. Using both TE and TM waves for simulation, which wave is more advantageous is compared. A concrete specimen is prepared in accordance with the simulation setup and measured using a Vivaldi antenna array and vector network analyzer. The reflection and transmission coefficient obtained from the measurement and the reflection and transmission coefficient obtained from the simulation are compared.

Partial RCS Evaluation Method for Low-Observable Aircraft Design using PEC and PMC Boundaries

For the design of low-observable aircrafts, more commonly termed stealth, it is necessary to analyze the influence of each airframe part for radar cross section (RCS) reduction. To achieve this aim, a partial RCS evaluation method is developed via the nonstandard finite-difference time-domain (NS-FDTD) technique. The new scheme handles the scattering waves caused by body parts, such as the intake and cockpit of the aircraft, by masking the perfectly electric conductor (PEC) and perfectly magnetic conductor (PMC) boundaries. Compared to the use of the perfectly matched layer (PML), the proposed algorithm is straightforward to apply to the overall RCS evaluation of various aircraft configurations with electrically large size.

A Perfectly-Matched Layer Formulation Capable of Absorbing Multi-Modal Waves in Cylindrical FDTD

The perfectly-matched-layer (PML) absorbing boundary condition as applied to the finite-difference time-domain method in cylindrical coordinates is investigated. A critical error in implementing coordinate stretching which is present in various published works is identified and shown to diminish wave absorption efficiency for all wave modes except rotationally invariant ones. A correction to the underlying coordinate stretching formulation is proposed and confirmed to improve wave absorption by approximately two orders of magnitude for higher cylindrical wave modes even when the PML absorber is placed within the near-field region to the axis of rotation.

Highly Sensitive Plasmonic PCF Biosensor

Highly efficient dual D-shaped photonic crystal fiber (PCF) biosensor based on surface plasmon resonance (SPR) sensing mechanism is proposed and analyzed. The upper and lower surfaces of the PCF are etched where two gold nanorods are mounted on them. The optimization of the geometrical parameters results in high refractive index (RI) sensitivity of 12800 nm/RIU with resolution of 7. 8×10−6 RIU. The numerical study is performed using full-vectorial finite-element method with perfect matched layer boundary condition.

Anomalous birefringence and nonlinearity enhancement of As2S3 and As2S5 filled D-shape fiber for optical communication

An elliptical core-based D-shape photonic crystal fiber (PCF) has been proposed with achieving extraordinary optical properties in this paper. We deeply observed and evaluated the performance of the designed D-PCF by doping the materials (As2S3 and As2S5) separately into the core region with the variation of the eccentricities (core size). After the whole analysis, this D-PCF prefers the As2S3 core material because it produces a better performance of all the optical features compared to the As2S5 material. The results of the raised PCF shows that the maximum nonlinearity of 9.114 × 104 W−1 km−1, the extreme-high birefringence of 0.254, the better power fraction of 99.51%, the high numerical aperture of 0.78, the large negative dispersion of −2560.12 ps/(nm-km), and the low beat length of 7.09 μm, etc. The finite element method (FEM) has been applied to simulate the optical characteristics and a perfectly matched layer (PML) is used as a boundary condition. So, the above mentioned remarkable outcomes of the designed D-PCF makes it a robust candidate in many helpful applications like biomedical imaging, telecom, super-continuum generation, and polarization-maintaining signal processing.

A 2.5D acoustic finite element method applied to railway acoustics

Railway acoustic problems commonly have a constant cross-section and uniform properties in the longitudinal direction. To solve such 3D acoustic problems with reduced effort, a wavenumber domain acoustic finite element (2.5D acoustic FE) method is introduced in which the cross-section of the domain is meshed and the third dimension is represented by a wavenumber transform. The acoustic wavenumber is thereby decomposed into a combination of wavenumbers in the x direction and in the y-z plane. The method is extended to exterior noise problems by including a perfectly matched layer (PML) with bespoke absorption to prevent reflection of the sound waves at the boundary of the domain. The method as presented can be used with 2D finite element solutions from commercial software. To verify the application of the 2.5D acoustic FE method for interior acoustic problems, sound attenuation in a tunnel is predicted and compared with existing measurements. To verify the implementation for exterior acoustic problems, an example is given of the sound distribution on the side surface of a train due to a compact source below it. The comparison of the solutions obtained from the 2.5D acoustic FE models with measurements shows good agreement in the both validation cases. The method is then used to investigate the effect of the tunnel walls on the sound distribution on the train external surface by comparing the results with the case in the open field. A highly reverberant sound field is found in tunnels, which increases the sound pressure level on the train side-surface above 250 Hz by about 10 dB for a tunnel with a ballasted track and by about a further 6 dB for a slab track.

Hybrid absorbing boundary conditions of PML and CRBC

In this paper we introduce a hybrid absorbing boundary condition (HABC) by combining perfectly matched layer (PML) and complete radiation boundary condition (CRBC) for solving a one-dimensional diffraction grating problem. The new boundary condition is devised in such a way that it can enjoy relative advantages from both methods. The well-posedness of the problem with HABC and the convergence of approximate solutions will be analyzed. Numerical examples to illustrate the efficiency of HABC are also presented.

Design and performance analysis of background material of zeonex based high core power fraction and extremely low effective material loss of photonic crystal fiber in the terahertz (THz) wave pulse for many types of communication areas

In this reported work, an excellent design model of quasi-shape of cladding areas with rotated-Hexa based elliptical shape of core areas in photonic crystal fiber (Q-PCF) has been reported for terahertz (THz) waves of communication signals. Here, we have presented a six-layer circular air hole in the quasi-shape of cladding regions with two layers rotated-Hexa-based ellipse shape of air holes in the core regions of photonic crystal fiber (Q-PCF) for analysis of communication networks in the terahertz (THz) regime. On the other hand, perfectly matched layers (PML) and finite element method (FEM) based on COMSOL software tool are used to design this photonic crystal fiber (Q-PCF). For short and wide-band of communication sectors, our proposed quasi shape-based photonic crystal fiber (Q-PCF) is highly useful because of reducing different types of losses such as ultra-low effective material loss (EML), confinement loss, and scattering loss in the terahertz (THz) regime. After analysis of numerical results, our suggested quasi shape-based photonic crystal fiber (Q-PCF) shows an ultra-low effective material loss (EML) of 0.0163 cm−1, power fraction in the core area and large effective area of 74%, 5.52 × 10−8 m2, confinement loss of 3.25 × 10−12 cm−1 and the scattering loss of 1.23 × 10−10, respectively at 1 terahertz (THz) frequency range. Moreover, our proposed quasi photonic crystal fiber (Q-PCF) discloses a single-mode propagation by the graphical results of V-parameter over 0.80–3 THz frequency range. As a result, we can say clearly that the reported Q-PCF fiber will be highly appropriate for terahertz (THz) wave propagation for many communication networks such as bio-medical signals and various data transfer communications system.