Perfectly Matched Layer Boundary 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).

Numerical Simulation of Elastic Wave in Frequency Domain Based on Generalized Finite Difference Method With a Multiaxial Convolutional Perfectly Matched Layer Boundary

Numerical Simulation of Elastic Wave in Frequency Domain Based on Generalized Finite Difference Method With a Multiaxial Convolutional Perfectly Matched Layer Boundary

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.

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.

RF wave propagation simulation for ICRF antenna in EAST

ABSTRACT The propagation performance of radiofrequency (RF) waves excited by ICRF antenna in plasma has a great influence on the coupling effect. In this paper, the propagation characteristics of fast wave (FW) and slow wave (SW) under tokamak experimental condition are calculated, and the influence of angular frequency w 0, antenna power spectrum k// and tokamak total magnetic field B 0 is illustrated based on the typical operating parameters in EAST. By applying perfect matched layer (PML) boundary processing method to simulate single-pass absorption and using finite element method (FEM) to solve Maxwell equations in frequency domain, the propagation and coupling simulation of RF waves in cold plasma for EAST ICRF antenna in B-window were carried out to obtain the polarization characteristics of fields and the relationship between the coupling impedance and the gap length from antenna to the FW cut-off layer. The analysis results in this paper provide useful reference and guidance for the study of propagation coupling of ICRF waves in EAST and other magnetic confined fusion devices.

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.

Scattering of ion cyclotron range of frequency waves by filaments and ELMs

The scattering of ion cyclotron range of frequency (ICRF) waves by filaments and ELMs has been comprehensively studied via modeling. The influence of filaments on the propagation of ICRF waves is studied by building a 2D COMSOL model which solves the wave equation. It is benchmarked against the Mie scattering theoretical model. Cases either with perfect matching layer boundary condition or with poloidal periodic boundary condition are considered. Parameter scans, including the filament density, the filament radius, the number of filaments as well as the distance between filaments, are performed. Then, the influence of ELMs on the propagation of ICRF waves in realistic geometry is studied by importing density distributions calculated by 3D non-linear MHD code JOREK into the 3D antenna code RAPLICASOL. The evolution of density and wave fields during an ELM is analyzed for cases with a low and high scrape-off layer density, respectively. Both the COMSOL simulation and the realistic simulation with JOREK and RAPLICASOL show that the wave fields and Poynting flux can be significantly and globally modified by the ELM filaments. Due to the mutual influence of many density filaments, radially elongated and poloidally distributed stripe structures of the wave fields develop, leading to poloidally inhomogeneous wave fields. Furthermore, the influence of ELMs on the antenna power and antenna coupling resistance is investigated with experimental results in ASDEX Upgrade.

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.

Perfectly matched layer absorbing boundary conditions for Euler equations with oblique mean flows modeled with smoothed particle hydrodynamics.

Absorbing boundary conditions (ABCs) play a critical role in the simulation of sound or wave propagation problems. This paper proposes a technique of space-time transformed perfectly matched layer (PML) boundary condition implemented in a widely used mesh-free method called smoothed particle hydrodynamic (SPH) method, to absorb the outgoing sound waves with oblique shear mean flow. Special consideration is given to the particle features of the SPH, and the PMLs are formulated to correct the truncation error of SPH and absorb the outgoing wave at the same time, aiming to reduce the storage and computational cost in the infinite computational domain. Because the group velocity and phase velocity of the outgoing sound waves in the PMLs may be in different directions, exponentially growing pseudo reflections can result. The authors thus employ space-time transformation to eliminate the reflections effectively in PML boundaries for stable solutions. Moreover, a uniform framework of PML absorbing boundary conditions for Euler equations in the cases of arbitrary oblique mean flow and static media is derived. Finally, the present PML-SPH method with this stable absorbing boundary is applied to simulate sound waves propagating with mean flow. The obtained numerical results agree very well with the reference results.

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.

Highly nonlinear bored core hexagonal photonic crystal fiber (BC-HPCF) with ultra-high negative dispersion for fiber optic transmission system.

In this paper, we propose a bored core hexagonal photonic crystal fiber (BC-HPCF) which obtains ultra-high negative dispersion and large nonlinearity simultaneously. The aim of the proposed design is to achieve the desired optical properties by using circular air holes only to make the fiber simple and manufacturable. To investigate the light guiding properties of the proposed BC-HPCF, finite element method (FEM) with circular perfectly matched boundary layer (PML) is used. According to numerical simulation, it is possible to obtain a large value of negative dispersion of -2102 ps·nm-1·km-1 and large value of nonlinearity of 111.6 W-1 · km-1 at optimum wavelength of 1550 nm. In addition, ±2% deviation in optical characteristics is evaluated and reported in order to study the practical feasibility of the proposed BC-HPCF. The large negative dispersion and high nonlinearity of our proposed design make it a strong candidate for optical broadband communication, super continuum generation, and sensing.

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.

An exact PML to truncate lattices with unstructured-mesh-based adaptive finite element method in frequency domain for ground penetrating radar simulation

We present a new approach of unstructured grid adaptive finite element in the frequency domain (AFEFD) based on exact perfect matching layer (EPML) boundary condition for Ground penetrating radar (GPR) simulation. The discrete equations of transverse magnetic mode are derived by using the unstructured Delaunay mesh coupled with linear interpolation basis functions. For the trade off between the computational efficiency and the accuracy of simulation, an h-type adaptive finite element method (AFEM) is employed and, in particular, with less layer thickness and fewer parameters setting, an EPML boundary condition is developed to truncate the AFEM lattices. In addition, the Zienkiewicz-Zhu posterior error estimation, the mesh refinement scheme and the implementation process of AFEM are also elaborated in detail. To testify the validity and practicability of this methodology, a homogeneous medium model of line current radiation field with analytical solution and a complex model of lining fracture disease are considered. The results of frequency-domain slices, transformed time-domain forward profile, together with wavefield snapshots demonstrated that the reflections, diffractions and other codas caused by non-physical factors at the boundary are effectively absorbed, subsequently, the absorbing performance of simulation with AFEM in frequency domain is greatly improved. More importantly, the proposed methodology can automatically control its mesh density according to the features of the complex object, which significantly economize the computing resource of simulation when AFEM is employed.

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.