Mur Absorbing Boundary Condition Research Articles

Statement of absorbing Mur boundary conditions of the first order of accuracy for solving problems of electrodynamics by the method of finite differences in the time domain

Problem statement. The accuracy and convergence of calculations for solving problems of electrodynamics by the finite difference method in the time domain significantly depends on the correct choice of parameters and the correct setting of the absorbing boundary conditions (ABC). Two main types of absorbing boundary conditions are known: Mur ABC; Beranger ABC. It is believed that the Mur ABC is less effective at absorbing spherical waves than the Beranger ABC, but they do not require the introduction of additional parameters (the so-called "Beranger fields"), which simplifies the implementation of program code and saves computer RAM. Calculations have shown that the efficiency of the Mur ABC will depend on their thickness. On the one hand, an increase in the thickness of the ABC layers will lead to an increase in the accuracy of calculations, on the other hand, to an increase in the size of the calculation area and, as a result, an increase in RAM. The problem arises of determining the criterion for evaluating the efficiency of ABC to determine their optimal thickness. Goal. Identification of new factors that make it possible to use the Mur ABC as efficiently as the Beranger ABC, while significantly saving computer resources. Result. The expressions for the ABC are presented, taking into account the interaction of all components of the electromagnetic field within a single cell of the FDTD. Calculations of the reflection coefficient – a criterion for evaluating the efficiency of the ABC, are presented. Practical significance. Calculations are presented that allow automating the selection of ABC parameters for their stable operation in solving electrodynamic problems.

Improved ADI iterative algorithm with two‐step Gauss–Seidel procedure for efficientLaguerre‐based BOR–FDTD method

An improved alternating-direction-implicit (ADI) algorithm for an efficient Laguerre-based body-of-revolution finite-difference time-domain (BOR–FDTD) method is presented. A new correction equation for Eρ*q is added to the linear equations to speed up the convergence, and the two-step Gauss–Seidel procedure instead of the one-step procedure in the existing algorithm is introduced in the entire iterative algorithm. To validate the accuracy and efficiency of the proposed algorithm, which is applied to the BOR structure, two scattering examples are provided to demonstrate the algorithm. At the same time, the relative reflection error of the perfectly matched layer (PML) is calculated for comparisons with Mur's absorbing boundary condition.

A Paralleling-in-Order Unconditionally Stable AH FDTD in Cylindrical Coordinates System

The unconditionally stable associated Hermite (AH) finite-difference time domain (FDTD) with Mur's absorbing boundary condition is extended into the cylindrical coordinates system. With AH expansion and paralleling-in-order scheme, the time-domain Maxwell's equations in cylindrical coordinates are transformed to AH domain five-point equations. And, Ampere's law is applied to treat the central axis formulation by using the AH differential operator. The numerical results demonstrate a good accuracy and higher efficiency for the proposed method when compared with the conventional FDTD method.

A Circuit Particle-in-Cell Coupled Simulation of a Magnetically Insulated Transmission Line System

We have developed a circuit particle-in-cell (PIC) coupled model for simulating a pulsed power system, based on a circuit algorithm of a pulsed power supply and a PIC simulation for a magnetically insulated transmission line (MITL) system. The coupled algorithm comprises an external circuit algorithm based on BERTHA and a coupled algorithm for the PIC and circuit interface based on the Mur absorbing boundary condition. In this paper, a simple coaxial MITL with a single linear transformer driver (LTD) was simulated to validate the coupled model compared with PSPICE and BERTHA simulations. The numerical results show that the circuit–PIC coupled model achieved almost the same outputs on the load. The coupled model was then applied to an MITL system driven by ten LTD cavities. The simulation results and experimental results were in agreement, which confirms that the circuit–PIC coupled model could provide a reference for the structural design of experimental apparatuses.

Application of Symplectic Partitioned Runge-Kutta Method and Total-Field Scattered-Field Formulation to Simulation of GPR Data

The second-order Lobatto IIIA-IIIB symplectic partitioned RungeKutta (SPRK) method, combining with the first-order Mur absorbing boundary condition, is developed for the simulation of ground penetrating radar wave propagation in layered pavement structure. For 2-dimetional case, a significant advantage of this method is that only two functions need to be calculated at each time step. The total-field/scattered-field technique is used for plane wave excitation. Numerical examples are presented to verify the accuracy and efficiency of the proposed algorithm. The results illustrate that the reflected signal calculated by the SPRK method is in good agreement with that obtained using the finite difference time domain (FDTD) scheme, but the CPU time consumed by proposed algorithm is reduce about 20% of the FDTD scheme. In addition, an actual field test is conducted to evaluate the further performance of the SPRK method. It is found that the simulated waveform fits well with the measured signal in many aspects, especially in the peak amplitude and time delay.

Transient modelling of a linear induction launcher-type coil gun with two-dimensional cylindrical finite-difference time domain method

Two-dimensional (2D) simulation of a linear induction launcher-type coil gun is performed by the cylindrical finite-difference time domain (FDTD) method. Maxwell's equations in cylindrical coordinates are used to formulate the problem. Circular symmetry is assumed for reducing the 3D problem to a 2D one. A singularity that appeared at r=0 is extracted by using the integral formulation of the FDTD method. A special quasi-static approximation of the FDTD method is applied in the cylindrical problem space which is terminated with the second-order Mur absorbing boundary condition. The armature movement in the FDTD method is treated by the quasi-steady-state method. An experimental model was built, and the muzzle velocity was measured for comparison with the calculated value. Good agreement was obtained.

Mur Absorbing Boundary Condition for Three-Step 3-D LOD-FDTD Method

A consistent implementation of Mur first-order absorbing boundary condition (ABC) for three-step 3-D locally 1-D finite-difference time- domain (LOD-FDTD) method is presented. Numerical examples are included to validate the proposed scheme in comparison with Mur ABC for the standard FDTD and two other Mur ABC schemes for the LOD-FDTD. The numerical results illustrate that the proposed scheme can achieve good wave-absorbing capability.

An Improvement of Absorbing Boundary Condition Based on Algorithm of Constrained Interpolation Profile Method for Finite-Difference Time-Domain Acoustic Simulation

In this study we examined an improved reasonable absorbing boundary condition (ABC). We examined ABC on the basis of the algorithm of the constrained interpolation profile (CIP) method for finite-difference time-domain (FDTD) acoustic simulation. Analysis of one-dimensional sound propagation with CIP-ABC was implemented. The results obtained in this study clarified that improved CIP-ABCs have better absorption performance than first-order Mur's ABC. That is, CIP-ABCs maintain a reflection coefficient that is lower than that of Mur's ABC in all frequency ranges.

Mur Absorbing Boundary Condition for Efficient Fundamental 3-D LOD-FDTD

This letter presents the implementations of Mur first-order absorbing boundary condition (ABC) for efficient fundamental scheme of 3-D locally one-dimensional finite-difference time-domain (LOD-FDTD) method. The Mur ABC is incorporated into the efficient fundamental scheme using consistent implementation and a novel implementation with lower reflection coefficient. Both implementations in the efficient fundamental scheme are compared and validated with the conventional LOD-FDTD scheme. By comparing the CPU time of both conventional and efficient fundamental schemes, it is ascertained that substantial gain in the overall efficiency may be achieved for the latter even with Mur ABC incorporated.

Anisotropic-medium PML for efficient Laguerre-based FDTD method

An anisotropic-medium perfectly matched layer (PML) for efficient Laguerre-based finite-difference time-domain (FDTD) method is presented. To verify the validity of the presented method, a numerical example of scattering from a two-dimensional rectangular conductor is given. Compared with Mur's absorbing boundary condition, the presented PML shows better absorbing performance.

Leaky mode analysis of optical waveguides by Legendre and Laguerre pseudospectral method

AbstractIn this letter, an efficient multidomain pseudospectral method is implemented to solve leaky waveguides. The exterior subdomains with the evanescent and oscillatory mode shapes, the optical fields are, respectively, expanded by Laguerre‐Gauss functions and Legendre polynomials incorporating simple Mur's absorbing boundary condition. Numerical results verify the effectiveness of the present approach and are in good agreement with exact data. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 2507–2509, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23748

Stability analysis of the Mur's absorbing boundary condition in the alternating direction implicit finite-difference method

The stability analysis of the Mur's first order absorbing boundary condition (ABC) in the alternating direction implicit finite-difference time-domain (ADI-FDTD) method is presented. The theoretical stability analysis of this scheme is studied by deriving the amplification matrix. The effect of wave propagation direction on the stability of this scheme is investigated. From the stability analysis, it is found that the Mur's first order ABC in the ADI-FDTD method will be unstable. The instability of the scheme is validated by means of actual numerical simulations.

Numerical calculations of ARROW structures by pseudospectral approach with Mur’s absorbing boundary conditions

The pseudospectral method, proposed in our previous work, has not yet been constructed for optical waveguides with leaky modes or anisotropic materials. Our present study focuses on antiresonant reflecting optical waveguides (ARROWS) made by anisotropic materials. In contrast to the fields in the outermost subdomain expanded by Laguerre-Gaussian functions for guided mode problems, the fields in the high-index outermost subdomain are expanded by the Chebyshev polynomials with Mur's absorbing boundary condition (ABC). Accordingly, the traveling waves can leak freely out of the computational window, and the desirable properties of the pseudospectral scheme, i.e., provision of fast and accurate solutions, can be preserved. A number of numerical examples tested by the present approach are shown to be in good agreement with exact data and published results achieved by other numerical methods.

3D scalar FDTD method for waveguides with circular symmetry

AbstractA 3D scalar finite‐difference time‐domain (FDTD) method in cylindrical coordinates is formulated in order to analyze the wave propagation in circularly symmetric waveguides. The 2nd‐order Mur's absorbing boundary condition (ABC) is provided as well. This method can be used to simulate the propagation and coupling between the modes in a multimode waveguide structure. An isotropic point source propagating in either a symmetric medium or multimode step‐index fiber and a plane‐source propagation in multimode fiber are simulated in this paper. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 45: 218–221, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20774

A study on an improved absorbing boundary condition for a multimode waveguide analysis using the FDTD method

AbstractWhen the FDTD method is applied to the analysis of a multimode waveguide, a problem is the treatment of the absorbing boundary corresponding to the matching at the termination. In the present study, the electromagnetic field in the cross section of the waveguide one cell inward from the termination is expressed as a linear combination of the eigenmodes of the waveguide. For the propagating mode, Mur's absorbing boundary condition is applied by means of the modal phase velocity, and the electromagnetic field at the termination is derived for each nonpropagating mode analytically by means of the modal attenuation constant. Finally, a linear combination is created at the termination to make a simple absorbing boundary. As a specific application, this procedure is applied to a waveguide with an H‐plane discontinuity for which the modal transmitted power is calculated, demonstrating the effectiveness of the procedure. Since the present technique is based on waveguide eigenmode expansion in the frequency domain, it can be used only for single‐frequency analysis. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 87(12): 1–9, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20110

An efficient numerical interface between FDTD and haar MRTD-formulation and applications

A hybrid finite-difference time-domain (FDTD)/Haar multiresolution time-domain (MRTD) technique for the time-domain analysis of microwave structures is proposed in this paper. The salient features of the presented algorithm are, first, its inherent stability that stems from the matching of the dispersion properties of FDTD and Haar MRTD and, second, its applicability to arbitrarily high wavelet order MRTD schemes. Thus, the application of the MRTD technique to the modeling of open structures and inhomogeneous circuit geometries is facilitated. In particular, the straightforward implementation of perfectly matched layer type and Mur's absorbing boundary conditions is attained. The fact that the proposed interface involves no spatial or temporal interpolations or extrapolations indicates its potential to efficiently connect FDTD and Haar MRTD.

On analytical absorbing boundary conditions in FDTD

AbstractIn this Letter a new algorithm to compute the corner‐point field components of a two‐dimensional (2‐D) Mur absorbing boundary condition (ABC) in the finite‐difference–time‐domain (FDTD) method is presented. It is shown that field value calculation at the corner points of the truncation domain affects the accuracy of the FDTD. The proposed scheme overcomes the drawbacks of reflection on the truncated boundary and computation divergence that may occur when the existing scheme is used. Numerical examples are illustrated to validate the effectiveness of the proposed scheme. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 33: 437–440, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10344

Time-Domain Analysis of Millimeter Wave Circulation Around a Magnetised Ferrite Sphere

An efficient numerical method has been devised for the study of wave circulated by a magnetised ferrite sphere. It is a finite-difference time-domain formulation that incorporates Mur's absorbing boundary conditions and a perfectly matched layer. The electromagnetic fields inside the ferrite body are calculated using special updating equations derived from the equation of motion of the magnetization vector and Maxwell's curl equations in consistency. The electromagnetic fields inside ferrite and the power-density distribution on the ferrite's surface normal to the bias external magnetic field are obtained in a wide frequency band with a single time domain run. It is observed that an incident plane wave would circulate around the magnetised ferrite body in an open space as if the ferrite were placed inside a waveguide / microstrip junction circulators.

FDTD Analysis of EW Wave Circulating by a Magnetized Ferrite Body in Free Space

An efficient numerical method has been devised for the study of wave circulating by a magnetised ferrite body of an arbitrary shape. It is a finite-difference time-domain formulation that incorporates Mur's absorbing boundary conditions and a perfectly matched layer. Several shapes of interest have been studied, including spheres, circular cylinders. The electromagnetic fields inside ferrite and the power-density distribution on the ferrite's surface normal to the bias external magnetic field are obtained. It is observed that an incident plane wave would circulate around the magnetised ferrite body in an open space as if the ferrite were placed inside a waveguide junction circulator.

FDTD analysis of EM wave circulated by a magnetised ferrite body of arbitrary shape

An efficient numerical method has been devised for the study of a wave circulated by a magnetised ferrite body of an arbitrary shape. It is a finite-difference time-domain formulation that incorporates Mur's absorbing boundary conditions and a perfectly matched layer. Several shapes of interest have been studied, including spheres and circular cylinders. The electromagnetic fields inside the ferrite and the power-density distribution on the ferrite's surface normal to the bias external magnetic field are obtained. It is observed that an incident wave would circulate around the magnetised ferrite body in an open space as if the ferrite were placed inside a waveguide junction circulator. The technique is also extended to analyse the electrical performance of waveguide junction circulators. Various wave circulation characteristics are examined, and good agreement is observed between the numerical results and the measured data.