Perfectly Matched Layer Boundary Condition Research Articles

Mancha3D Code: Multipurpose Advanced Nonideal MHD Code for High-Resolution Simulations in Astrophysics

The Mancha3D code is a versatile tool for numerical simulations of magnetohydrodynamic (MHD) processes in solar/stellar atmospheres. The code includes nonideal physics derived from plasma partial ionization, a realistic equation of state and radiative transfer, which allows performing high-quality realistic simulations of magnetoconvection, as well as idealized simulations of particular processes, such as wave propagation, instabilities or energetic events. The paper summarizes the equations and methods used in the Mancha3D (Multifluid (-purpose -physics -dimensional) Advanced Non-ideal MHD Code for High resolution simulations in Astrophysics 3D) code. It also describes its numerical stability and parallel performance and efficiency. The code is based on a finite difference discretization and a memory-saving Runge–Kutta (RK) scheme. It handles nonideal effects through super-time-stepping and Hall diffusion schemes, and takes into account thermal conduction by solving an additional hyperbolic equation for the heat flux. The code is easily configurable to perform different kinds of simulations. Several examples of the code usage are given. It is demonstrated that splitting variables into equilibrium and perturbation parts is essential for simulations of wave propagation in a static background. A perfectly matched layer (PML) boundary condition built into the code greatly facilitates a nonreflective open boundary implementation. Spatial filtering is an important numerical remedy to eliminate grid-size perturbations enhancing the code stability. Parallel performance analysis reveals that the code is strongly memory bound, which is a natural consequence of the numerical techniques used, such as split variables and PML boundary conditions. Both strong and weak scalings show adequate performance up to several thousands of processors (CPUs).

Scattering and Attenuation in 5G Electromagnetic Propagation (5 GHz and 25 GHz) in the Presence of Rainfall: A Numerical Study

Rainfall has always been a concern for wireless communications systems. As 5G technology relies on high-frequency bands, it is fundamental to model and simulate the interaction of such radio waves with rainfall, as the deployment of large-scale infrastructure for 5G is highly expensive. This research presents a reformulation of the Maxwell equations for a bi-dimensional space in a transverse electric propagation mode, for a linear, inhomogeneous, and isotropic propagation medium with its magnetic and electric properties dependent on time. This reformulation was solved using the Finite Differences in Time Domain (FDTD) method with the Convolutional Perfectly Matched Layer (CPML) boundary condition. Two main frequency propagation scenarios were studied: 5 GHz (corresponding to Wi-Fi in the 802.11n standard as well as to the lowest bands of 5G) and 25 GHz (corresponding to 5G), within a 10m×3m rectangular domain in air and with rain. The rainfall was simulated using a parallel Ziggurat algorithm. According to the findings, while 5 GHz waves experience scattering processes, 25 GHz waves experience substantial dispersion and attenuation throughout the domain in low- to moderate-intensity rain.

Evaluation of the lightning performance of grounding electrodes using FDTD-based computational model: Influence of absorbing boundary conditions and representation of the frequency-dependence of soil parameters

• Lightning response of grounding electrodes is assessed using FDTD. • The effect of absorbing boundary conditions is shown. • Liao's 3rd order and CPML lead to results better than those of Liao's 2nd order. • Modeling the soil as a Debye medium leads to results closer to those of HEM model. • 6 poles are enough to represent the frequency-dependence of soil parameters. This work evaluates the influence of the absorbing boundary conditions (ABC) and the representation of frequency-dependent soil parameters on the assessment of the lightning performance of grounding electrodes using FDTD-based computational model. The results in terms of grounding potential rise (GPR), grounding impulse impedance (Z P ), and low-frequency grounding resistance (R LF ) showed a better agreement with those calculated by the HEM model when Liao's 3rd order and Convolutional perfect matched layer (CPML) boundary conditions were assumed. The increase of the simulation space contributed to improve the results related to Liao's 2nd order but demanding a longer computation time. Despite the observed improvement, they are still far from those provided by the other ABC. Modeling the soil as a Debye medium to consider frequency-dependent soil parameters leaded to lightning response of grounding electrodes very close to that provided by the HEM model. In terms of Z P , the largest percentage difference was about 6%. Also, the work indicated that the adoption of 6 poles identified by the MATLAB function invfreqs was enough to represent the frequency-dependence of soil parameters, contributing to decrease the computation time.

Study on Propagation Characteristics of Ground Penetrating Radar Wave in Dikes and Dams with Polymer Grouting Repair Using Finite-Difference Time-Domain with Perfectly Matched Layer Boundary Condition

Non-aqueous reactive polymer grouting technology has been widely used in the repair engineering of dikes and dams with shallow diseases. By using the finite difference time-domain method and perfectly matched layer boundary conditions, the calculation model of dikes and dams with shallow diseases such as water-filled cave, air-filled cave and incompact area is established. The propagation process of electromagnetic waves of ground-penetrating radar in dikes and dams with shallow diseases using polymer grouting repair is simulated, and the forward simulation profiles and single-channel waveforms are obtained. The propagation characteristics such as waveform amplitude, waveform shape, transmission time, and reflection time are compared and analyzed. The results show that the forward simulation profiles of dikes and dams with water-filled caves before and after polymer grouting repair present two clusters of hyperbolas, but three clusters of hyperbolas with different amplitudes were observed at 50% repair. The amplitude of the hyperbola and the single-channel reflected waves before repair and 50% repair of the cave and incompact area are greater than those of 100% repair. The propagation characteristics of ground-penetrating radar can effectively explain the degree of polymer grouting repair for dikes and dams with shallow diseases, and provide a theoretical basis for using the ground-penetrating radar to evaluate the effect of polymer grouting technology to repair dikes and dams with shallow diseases.

Non-split Perfectly Matched Layer Boundary Conditions for Numerical Solution of 2D Maxwell Equations

Non-split Perfectly Matched Layer Boundary Conditions for Numerical Solution of 2D Maxwell Equations

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.

Dual-core gold coated photonic crystal fiber plasmonic sensor: Design and analysis

A simple circular lattice dual-core photonic crystal fiber (PCF) based plasmonic sensor is numerically investigated in this paper within the visible to near-infrared (450 nm to 1150 nm) region. To examine the sensing performances and the guiding properties of the sensor, Finite Element Method (FEM) based mode solver software is applied in the presence of Perfectly Matched Layer (PML) and Scattering Boundary Conditions (SBC). Chemically inoperative plasmonic material gold is deposited at the outer surface of the raised sensor to create the Surface Plasmon Resonance (SPR) effect. This sensor proffers the maximum wavelength sensitivity of 11,200 nm/RIU and the amplitude sensitivity of 505.037RIU-1 according to the simulation results. It also allows the maximum Figure of Merit (FOM) of 275RIU-1 along with the sensor resolution of 8.92×10-6 RIU for wavelength sensing within the RI range of 1.33 to 1.44. Moreover, the impact of various structural parameters (e.g. air hole, pitch, plasmon layer thickness) on the sensing performance of the structure is also described in detail. All these results indicate that this fabrication friendly, highly sensitive sensor can be a promising applicant in the field of biosensing.

Numerical development of high performance quasi D-shape PCF-SPR biosensor: An external sensing approach employing gold

In this paper, a proper concept of a kind of photonic crystal fiber known as D-shaped PCF sensor based on SPR or Surface Plasmon Resonance phenomenon has been discussed. The analysis has been performed numerically using FEM or Finite Element Method and PML (Perfectly Matched Layer) boundary conditions. Modal analysis has been performed keeping the smallest mesh as possible. The main mechanism of the sensor is the interaction between the core guided light beam and the metal layer surface that generates free electrons. The proposed sensor shows a refractive index detection range of 1.42–1.46 RIU, with a metal thickness variation of 35 nm-45 nm and a pitch variation of 1.8 μm–2.0 μm. The sensor obtained the highest sensitivity of 15000 nm/RIU with a maximum 6.67 × 10-6 RIU resolution, using the wavelength interrogation method. Average spectral sensitivity is 8000 nm/RIU. The amplitude interrogation method found a maximum sensitivity of 230 RIU−1 with a resolution of 4.348 × 10-5 RIU. The sensor also shows high linearity fitting and Figure of Merit (FoM). For ease of design, high detection range, high wavelength and amplitude sensitivity, less fabrication complexity, high linearity and stability, the sensor can be a great competitor of the PCF sensors previously proposed.

Non-Split Perfectly Matched Layer Boundary Conditions for Numerical Solution of 2D Maxwell Equations

Non-Split Perfectly Matched Layer Boundary Conditions for Numerical Solution of 2D Maxwell Equations

Numerical Study of Circularly Slotted Highly Sensitive Plasmonic Biosensor: A Novel Approach

A highly sensitive Photonic Crystal Fiber (PCF) based Surface Plasmon Resonance (SPR) sensor is demonstrated in this paper in the optimized form of circular slotted lattice (CSL) structure. This proposed model performance is numerically scrutinized by using Finite Element Method (FEM) in presence of Perfectly Matched Layer (PML) and Scattering Boundary Condition. Plasmonic material ‘Gold’ which is chemically inert is used in this structure at the outer surface of the slotted area to mitigate fabrication challenge. This model indicates the highest wavelength sensitivity of 16000 nm/RIU using wavelength interrogation, the amplitude sensitivity of 780 RIU−1 by using amplitude interrogation method and the average spectral sensitivity of 6666 nm/RIU, respectively. Besides, this sensor has the potentiality of detecting analytes within Refractive Index (RI) range 1.4 to 1.46 with maximum wavelength resolution of 6.25 × 10−6 RIU and amplitude resolution of 1.28 × 10−6 RIU, respectively and the maximum figure of merits of 400 RIU−1. Moreover, the variation of structural parameters (such as pitch, plasmon layer thickness etc.) and the impact of these changes are also discussed in details. According to the high sensitivity performance, polynomial fit and high Figure of Merit (FOM), this amend structure can be a strong competitor in the field of biosensing.

PML and CFS-PML boundary conditions for a mesh-free finite difference solution of the elastic wave equation

Mesh-free finite difference (FD) methods can improve the geometric flexibility of modeling without the need for lattice mapping or complex meshing process. Radial-basis-function-generated FD is among the most commonly used mesh-free FD methods and can accurately simulate seismic wave propagation in the non-rectangular computational domain. In this paper, we propose a perfectly matched layer (PML) boundary condition for a mesh-free FD solution of the elastic wave equation, which can be applied to the boundaries of the non-rectangular velocity model. The performance of the PML is, however, severely reduced for near-grazing incident waves and low-frequency waves. We thus also propose the complex-frequency-shifted PML (CFS-PML) boundary condition for a mesh-free FD solution of the elastic wave equation. For two PML boundary conditions, we derive unsplit time-domain expressions by constructing auxiliary differential equations, both of which require less memory and are easy for programming. Numerical experiments demonstrate that these two PML boundary conditions effectively eliminate artificial boundary reflections in mesh-free FD simulations. When compared with the PML boundary condition, the CFS-PML boundary condition results in better absorption for near-grazing incident waves and evanescent waves.

Plasmon induced transparency and refractive index sensing in two nanocavities and double nanodisk resonators

Two novel implementations for plasmon-induced transparency (PIT) based on two rectangular nanocavities coupled to a bus waveguide and two nanodisk resonators have been studied and simulated with Finite Difference Time Domain (FDTD) method with Perfectly Matched Layer (PML) boundary conditions. It is shown that the wavelength, transmission and width of the PIT peaks can be tuned by changing the radii of the nanodisk resonators and the gap width. Benefitting from the narrow-appeared transparency windows, the proposed PIT-structures can act as nanosensors with refractive index sensitivity and a figure of merit equal to 800 nm. RIU−1 and 61.55 RIU−1, respectively. The proposed devices have potential nanophotonic applications due to simple geometry, compactness and their resistance to the oxidation.

Frequency-domain elastic wavefield simulation with hybrid absorbing boundary conditions

AbstractThe frequency-domain seismic modeling has advantages over the time-domain modeling, including the efficient implementation of multiple sources and straightforward extension for adding attenuation factors. One of the most persistent challenges in the frequency domain as well as in the time domain is how to effectively suppress the unwanted seismic reflections from the truncated boundaries of the model. Here, we propose a 2D frequency-domain finite-difference wavefield simulation in elastic media with hybrid absorbing boundary conditions, which combine the perfectly matched layer (PML) boundary condition with the Clayton absorbing boundary conditions (first and second orders). The PML boundary condition is implemented in the damping zones of the model, while the Clayton absorbing boundary conditions are applied to the outer boundaries of the damping zones. To improve the absorbing performance of the hybrid absorbing boundary conditions in the frequency domain, we apply the complex coordinate stretching method to the spatial partial derivatives in the Clayton absorbing boundary conditions. To testify the validity of our proposed algorithm, we compare the calculated seismograms with an analytical solution. Numerical tests show the hybrid absorbing boundary condition (PML plus the stretched second-order Clayton absorbing condition) has the best absorbing performance over the other absorbing boundary conditions. In the model tests, we also successfully apply the complex coordinate stretching method to the free surface boundary condition when simulating seismic wave propagation in elastic media with a free surface.

Trapezoid coordinate finite difference modeling of acoustic wave propagation using the CPML boundary condition

Due to compaction of clastic sedimentary rocks caused by gravitational forces, the wave propagation velocity tends to gradually increase with depth. Based on this observation, a trapezoid coordinate system is built to integrate the general velocity variation, and an acoustic wave equation is derived in the new coordinate system. Numerically, a conventional uniform rectangular grid FD scheme can be evoked to solve the new equation. Physically, a variable grid mesh is used: that is, fine grids for shallow areas with low velocity and coarse grids for deep areas with high velocity. This method is free of artificial reflections caused by the transition of different grid sizes. Furthermore, the Convolutional Perfectly Matched Layer (CPML) boundary condition is adapted to eliminate artificial boundary reflections. A homogeneous velocity model is used to verify the effectiveness of the CPML boundary. Tests using the Marmousi benchmark model show that with the demonstrated comparable accuracy, the proposed method is 2.9 times as fast as the conventional physical uniform grid FD algorithm while saving as much as 75% of the computer memory.

Complex Frequency Shifted Perfectly Matched Layer Boundary Conditions for Frequency-Domain Elastic Wavefield Simulations

To absorb unwanted seismic reflections caused by the truncated boundaries, various absorbing boundary conditions have been developed for seismic numerical modeling in both time and frequency domains. Among the various types of perfectly matched layer (PML) boundary conditions, complex frequency shifted PML (CFS-PML) has attracted much attention in time-domain wavefield simulations because it can better handle evanescent and grazing waves. In this paper, we extend the CFS-PML boundary condition to frequency-domain finite-difference seismic modeling, which has several advantages over time-domain modeling including the convenient implementation of multiple sources and a straightforward extension of adding attenuation factors. A comparison with an analytical solution is used to investigate the validity of the proposed CFS-PML algorithm. CFS-PML shows better absorbing behavior than the classical PML boundary condition in our model tests. We further implement CFS-PML for seismic wavefield simulations in an elongated elastic model and a complex model (Marmousi-II) with a free surface boundary condition.

Non-Split PML Boundary Condition for Finite Element Time-Domain Modeling of Ground Penetrating Radar

As a highly efficient absorbing boundary condition, Perfectly Matched Layer (PML) has been widely used in Finite Difference Time Domain (FDTD) simulation of Ground Penetrating Radar (GPR) based on the first order electromagnetic wave equation. However, the PML boundary condition is difficult to apply in GPR Finite Element Time Domain (FETD) simulation based on the second order electromagnetic wave equation. This paper developed a non-split perfectly matched layer (NPML) boundary condition for GPR FETD simulation based on the second order electromagnetic wave equation. Taking two-dimensional TM wave equation as an example, the second order frequency domain equation of GPR was derived according to the definition of complex extending coordinate transformation. Then it transformed into time domain by means of auxiliary differential equation method, and its FETD equation is derived based on Galerkin method. On this basis, a GPR FETD forward program based on NPML boundary condition is developed. The merits of NPML boundary condition are certified by compared with wave field snapshots, signal and reflection errors of homogeneous medium model with split and non-split PML boundary conditions. The comparison demonstrated that the NPML algorithm can reduce memory occupation and improve calculation efficiency. Furthermore, numerical simulation of a complex model verifies the good absorption effects of the NPML boundary condition in complex structures.

Evanescent field boundary conditions for modelling of light propagation

In this work, we introduce a straightforward and original approach for evanescent field boundary conditions (EBCs), which can be, in principle, applied in both Beam Propagation Method (BPM) and Finite Difference Time Domain Method (FDTD) numerical simulations. Importantly, suggested method may serve as an efficient alternative to typically applied ones, such as transparent boundary conditions (TBCs), absorbing boundary conditions (ABCs) or perfectly matched layer (PML) boundary conditions, giving comparable or even better results in terms of smaller reflections and of shorter computation time. Definition of proposed evanescent function, a way of its practical implementation, as well as an influence of its parameters on the light beam propagation in the free-space and in exemplary photonic structures are described in detail. In addition, results of EBCs application are compared with those achieved for Dirichlet, TBC and PML boundary conditions used in analogous arrangement of the physical systems.

A novel three-ring-core few-mode fiber with large effective area and low nonlinear coefficient

A novel three-ring-core few-mode fiber with large effective area and low nonlinear coefficient is proposed in this paper. The fiber characteristics based on the full-vector finite element method (FEM) with perfect matched layer boundary conditions show that four supermodes with large effective area, low nonlinear coefficient and low differential mode group delay (DMGD) are achieved. With the increase of input wavelength, the effective areas of three-ring-core few-mode fiber are increased, and the nonlinear coefficients are decreased. The bending losses are increased with the increase of input wavelength, and are decreased with the increase of bending radius. Moreover, the proposed fiber performs a nonlinear coefficient and DMGD flattened profile at a large wavelength range.

The Perfectly Matched Layer absorbing boundary for fluid–structure interactions using the Immersed Finite Element Method

In this work, a non-reflective boundary condition, the Perfectly Matched Layer (PML) technique, is adapted and implemented in a fluid–structure interaction numerical framework to demonstrate that proper boundary conditions are not only necessary to capture correct wave propagations in a flow field, but also its interacted solid behavior and responses. While most research on the topics of the non-reflective boundary conditions are focused on fluids, little effort has been done in a fluid–structure interaction setting. In this study, the effectiveness of the PML is closely examined in both pure fluid and fluid–structure interaction settings upon incorporating the PML algorithm in a fully-coupled fluid–structure interaction framework, the Immersed Finite Element Method. The performance of the PML boundary condition is evaluated and compared to reference solutions with a variety of benchmark test cases including known and expected solutions of aeroacoustic wave propagation as well as vortex shedding and advection. The application of the PML in numerical simulations of fluid–structure interaction is then investigated to demonstrate the efficacy and necessity of such boundary treatment in order to capture the correct solid deformation and flow field without the requirement of a significantly large computational domain.

Design and characterization of a low-loss, dispersion-flattened photonic crystal fiber for terahertz wave propagation

A porous core photonic crystal fiber, based on Topas, with ultra-low effective material loss and near zero flattened dispersion properties is proposed for efficient polarization preserving transmission of terahertz waves. The Finite Element Method (FEM) with a Perfectly Matched Layer (PML) boundary condition is used to compute the modal characteristics of the fiber that confirms a lower Effective Material Loss (EML) of 0.034cm−1, lower confinement loss of the order of 10−3.7cm−1, higher effective mode area of 0.6×106μm2 and a flattened dispersion variation of 0.09ps/THz/cm. In addition, some other characteristics including birefringence, single mode operation, core power fraction and Figure of Merit (FOM) of the proposed fiber are also discussed. To simplify the fabrication process, only circular shaped air holes with a conventional hexagonal structure in the cladding is deployed. It is anticipated that, this newly proposed waveguide will open a new window for further terahertz research and broadband transmission of terahertz radiation.