Open Region Problems Research Articles

Unconditionally Stable System Incorporated Factorization-Splitting Algorithm for Blackout Re-Entry Vehicle

A high-temperature plasma sheath is generated on the surface of the re-entry vehicle through the conversion of kinetic energy to thermal and chemical energy across a strong shock wave at the hypersonic speed. Such a condition results in the forming of a blackout which significantly affects the communication components. To analyze the re-entry vehicle at the hypersonic speed, an unconditionally stable system incorporated factorization-splitting (SIFS) algorithm is proposed in finite-difference time-domain (FDTD) grids. The proposed algorithm shows advantages in the entire performance by simplifying the update implementation in multi-scale problems. The plasma sheath is analyzed based on the modified auxiliary difference equation (ADE) method according to the integer time step scheme in the unconditionally stable algorithm. Higher order perfectly matched layer (PML) formulation is modified to simulate open region problems. Numerical examples are carried out to demonstrate the performance of the algorithm from the aspects of target characteristics and antenna model. From resultants, it can be concluded that the proposed algorithm shows considerable accuracy, efficiency, and absorption during the simulation. Meanwhile, plasma sheath significantly affects the communication and detection of the re-entry vehicle.

Bandpass leapfrog hybrid implicit–explicit procedure with promoted absorption for obtaining fine geometry in a single direction

For an accurate and efficient calculation of fine geometry along a single direction in open regions, a bandpass one-step hybrid implicit–explicit (HIE) procedure with promoted absorption is implemented in this study. More precisely, the proposed scheme is modified by integrating complex envelope (CE) method, higher order concept, perfectly matched layer (PML) formulation, and one-step leapfrog HIE procedure. Furthermore, by introducing property variables, efficiency can be improved significantly. In addition, the proposed scheme not only overcomes the Courant–Friedrich–Levy stability condition but also solves the efficiency decrement problem of implicit algorithms. The effectiveness of the proposed algorithm is validated and demonstrated both numerically and experimentally. According to the results, we can conclude that the proposed scheme is advantageous in terms of enhanced accuracy, promoted absorption, improved efficiency for fine geometry along a single direction in bandpass open region problems.

One‐step leapfrog alternating direction implicit procedure for left‐handed material in open region problems with enhanced absorption

AbstractBy incorporating higher order formulation and one‐step leapfrog alternating direction implicit (ADI) procedure, unconditionally stable perfectly matched layer implementation is proposed for terminating frequency‐dependent left‐handed material in finite‐difference time‐domain lattice. To be more specific, frequency‐dependent left‐handed material can be calculated by the piecewise linear recursive convolution method. The proposed scheme shows advantages of higher order formulation and one‐step leapfrog ADI procedure in terms of enhancing absorbing performance, improving computational efficiency and simulating open region problems. The effectiveness is demonstrated through the computational domain with dipole antenna model above the left‐handed material slab. From results, it can be concluded that the proposed formulation can obtain considerable absorption, outstanding efficiency, and improved entire performance. Meanwhile, the proposed scheme also keeps its stability when time step far exceeds the Courant‐Friedrich‐Levy condition.

Bandpass approximate Crank-Nicolson implementation for anisotropic gyrotropic plasma open region simulation

For overcoming the Courant-Friedrich-Levy (CFL) stable condition and maintaining the stability of the algorithm, unconditionally stable implementation is proposed for the simulation of anisotropic gyrotropic plasma in bandpass open region problems. To be more accurately, the proposed implementation is based on the complex envelope method, higher order concept, perfectly matched layer formulation and Crank-Nicolson Direct-Splitting procedure which shows advantages over them including accuracy, efficiency and absorption. The gyrotropic plasma with unique anisotropic characteristic can be simulated by the modified approach. For the further illustration of effectiveness, several numerical examples are introduced. Through the results and comparison with previous work, it can be concluded that the entire performance which includes accuracy, efficiency and absorption can be significantly improved. In addition, the mesh size can be no longer limited by the CFL condition rather than the computational accuracy which shows considerable potential in numerical simulation of fine structures. Meanwhile, the time step can be obtained according to the maximum frequency rather than bandwidth resulting in the exponential decrement of running time.

Approximate Crank–Nicolson Algorithm with Higher-Order PML Implementation for Plasma Simulation in Open Region Problems

By incorporating the higher-order concept with the perfectly matched later (PML) scheme, unconditionally stable approximate Crank–Nicolson algorithm is proposed for plasma simulation in open region problems. More precisely, the proposed implementation is based on the CN Direct-Splitting (CNDS) procedure for the finite-difference time-domain (FDTD) unmagnetized plasma simulation. The unmagnetized plasma can be regarded as frequency-dependent media which can be calculated by the piecewise linear recursive convolution (PLRC) method. The proposed implementation shows the advantages of higher-order concept, CNDS procedure, and PLRC method in terms of improved absorbing performance, enhanced computational efficiency, and outstanding calculation accuracy. Numerical examples are introduced to indicate the effectiveness and efficiency. It can be concluded from results that the proposed scheme shows considerable efficiency, accuracy, absorption, and unconditional stability.

Complex Envelope Approximate Crank-Nicolson Method and Its Open Boundary Implementation for Bandpass Problem

To efficiently simulate the bandpass electromagnetic problems by employing the finite-difference time-domain (FDTD) algorithm, unconditionally stable implementation is proposed based upon the complex envelope method and the Crank-Nicolson Direct-Splitting (CNDS) algorithm. To further absorb outgoing waves and reduce wave reflections in open region problems, absorbing boundary condition with improved absorption is proposed by incorporating the proposed scheme with the higher order perfectly matched layer (PML) formulation. The proposed scheme takes advantage of the complex envelope method, the CNDS algorithm and the higher order PML formulation in terms of simulating bandpass signals and enhancing absorption and improving computational efficiency. Numerical examples are carried out to further demonstrate the effectiveness and efficiency. Through the resultants, it can be illustrated that the proposed scheme can not only obtain considerable accuracy, favorable absorbing performance, outstanding efficiency in the simulation of bandpass open region problems but also maintain the stability of the algorithm when the time step surpasses far beyond the Courant-Friedrich-Levy condition.

Computationally Efficient Locally One-Dimensional Algorithm for Open Region Ground Penetrating Radar Problem With Improved Absorption

By incorporating higher order formulation with perfectly matched layer (PML) implementation, unconditionally stable computationally efficient locally one-dimensional (LOD) algorithm with improved absorption is proposed for simulating ground penetrating radar and its open region problems in finite-difference time-domain (FDTD) algorithm. To take advantages of these methods, the proposed implementation shows characteristics of maintaining considerable accuracy, enhancing computational efficiency and improving the entire absorption. These above-mentioned advantages are illustrated through the ground penetrating radar related problem in open regions. It can be concluded from the calculation results that the proposal shows advantages of higher order formulation, PML implementation and LOD procedure which are efficient in remarkable accuracy, considerable efficiency and improved absorption with increment of CFLNs. Meanwhile, the simulation results also indicate that the proposal is an unconditionally stable procedure with the dissatisfaction of Courant-Friedrichs-Levy stability condition.

Efficient Enhanced Hybrid Implicit-Explicit Procedure to Gyrotropic Plasma in Open Regions With Fine Geometry Details Along Single Direction

For the simulation of gyrotropic plasma structure with fine geometry details along a single direction in open regions, the hybrid implicit-explicit (HIE) algorithm with improved absorbing boundary condition is modified based on the finite-difference time-domain (FDTD) algorithm. More precisely, incorporating the perfectly matched layer (PML) formulation, the higher order concept and the HIE procedure, the proposed implementation shows its significant superiority in terms of efficiency, accuracy and absorption. To simulate the unique anisotropic characteristic inside the gyrotropic plasma regions, the bilinear transform (BT) method is employed during the calculation. The effectiveness can be further demonstrated theoretically and numerically. Through the results, it can be concluded that the proposed scheme exhibits remarkable behaviors in the gyrotropic plasma open region problems. It can not only obtain considerable accuracy compared with the theoretical solution but also receive better absorption and efficiency compared with the published work. In addition, the results also indicate that the proposed scheme can maintain the stability of the algorithm with dissatisfaction of the Courant-Friedrichs-Levy condition between time step and mesh size.

Computationally efficient complex envelope approximate Crank–Nicolson scheme and its open region problem for anisotropic gyrotropic plasma

By incorporating a complex envelope (CE) method, higher order formulation, and approximate Crank–Nicolson (CN) procedure, unconditionally stable complex frequency shifted perfectly matched layer (CFS-PML) implementation is proposed for anisotropic gyrotropic plasma bandpass simulation in open region problems. More precisely, the CE based higher order CN approximate-factorization-splitting (AFS) PML implementation is introduced to terminate the unbounded finite-difference time-domain (FDTD) lattice. The proposed implementation can not only improve computational efficiency but also enhance the absorption at boundaries during the whole bandpass simulation. Numerical examples which include plasma slab models and ridge waveguide structures are introduced to further demonstrate accuracy, absorption, and efficiency. It can be concluded in the results that our proposal can achieve considerable performance in modeling bandpass signals, improving computational efficiency, enhancing absorption, and maintaining remarkable accuracy. Meanwhile, it can be observed that the proposed implementation is stable when the time step surpasses far beyond the Courant–Friedrichs–Lewy condition.

Higher-Order Finite Element Electromagnetics Code for HPC environments

In this communication, an electromagnetic software developed to work in High-Performance Computing (HPC) environments is presented. The software is mainly based on the Finite Element Method (FEM) making use of a number of numerical techniques developed by its authors including its own family of higher-order curl-conforming elements and a non-standard mesh truncation methodology for the analysis of open region problems such as those of scattering and radiation. The code is written in FORTRAN 2003 and it adopts from scratch parallel programming paradigms such as Message Passing Interface (MPI) and Open Multi-Processing (OpenMP). It also includes an in-house development to ease the use of remote computer systems and HPC environments. Initially designed for single-user multicore machines and small cluster environments, a number of modifications have been included in the code in order to make it capable of running on large-scale computer systems and hence, be able to deal with larger problems in terms of number of unknowns. Details of the implementation are shown. Numerical results obtained on an HPC system corresponding to the analysis of a few illustrative challenging problems are also shown.

Self-adaptive [formula omitted] finite element method with iterative mesh truncation technique accelerated with Adaptive Cross Approximation

To alleviate the computational bottleneck of a powerful two-dimensional self-adaptive hp finite element method (FEM) for the analysis of open region problems, which uses an iterative computation of the Integral Equation over a fictitious boundary for truncating the FEM domain, we propose the use of Adaptive Cross Approximation (ACA) to effectively accelerate the computation of the Integral Equation. It will be shown that in this context ACA exhibits a robust behavior, yields good accuracy and compression levels up to 90%, and provides a good fair control of the approximants, which is a crucial advantage for hp adaptivity. Theoretical and empirical results of performance (computational complexity) comparing the accelerated and non-accelerated versions of the method are presented. Several canonical scenarios are addressed to resemble the behavior of ACA with h, p and hp adaptive strategies, and higher order methods in general.

A DGTD Scheme for Modeling the Radiated Emission From DUTs in Shielding Enclosures Using Near Electric Field Only

To meet the electromagnetic interference regulation, the radiated emission from device under test such as electronic devices must be carefully manipulated and accurately characterized. Instead of resorting to the direct far-field measurement, in this paper, a novel approach is proposed to model the radiated emission from electronic devices placed in shielding enclosures by using the near electric field only. Based on the Schelkkunoff's equivalence principle and Raleigh–Carson reciprocity theorem, only the tangential components of the electric field over the ventilation slots and apertures of the shielding enclosure are sufficient to obtain the radiated emissions outside the shielding box if the inside of the shielding enclosure was filled with perfectly electric conductor (PEC). In order to efficiently model wideband emission, the time-domain sampling scheme is employed. Due to the lack of analytical Green's function for arbitrary PEC boxes, the radiated emission must be obtained via the full-wave numerical methods by considering the total radiated emission as the superposition between the direct radiation from the equivalent magnetic currents in free space and the scattered field generated by the PEC shielding box. In this study, the state-of-the-art discontinuous Galerkin time-domain (DGTD) method is utilized, which has the flexibility to model irregular geometries, keep high-order accuracy, and more importantly involves only local operations. For open-region problems, a hybridized DGTD and time-domain boundary integration method applied to rigorously truncate the computational domain. To validate the proposed approach, several representative examples are presented and compared with both analytical and numerical results.

A New 3-D Nonspurious Discontinuous Galerkin Spectral Element Time-Domain (DG-SETD) Method for Maxwell’s Equations

A new discontinuous Galerkin spectral element time-domain (DG-SETD) method for Maxwell's equations based on the field variables E and B is proposed to analyze three-dimensional (3-D) transient electromagnetic phenomena. Compared to the previous SETD method based on the field variables E and H (the EH scheme), in which different orders of interpolation polynomials for electric and magnetic field intensities are required, the newly proposed method can eliminate spurious modes using basis functions with the same order interpolation for electric field intensity and magnetic flux density (the EB scheme). Consequently, it can reduce the number of unknowns and computation load. Domain decomposition for the EB scheme SETD method is completed via the DG method. In addition, the EB scheme SETD method is extended to the well-posed time-domain perfectly matched layer (PML) to truncate the computation domain when solving open-region problems. The effectiveness and advantages of the new DG-SETD method are validated by eigenvalue analysis and numerical results.

Systematic wave-equation finite difference time domain formulations for modeling electromagnetic wave-propagation in general linear and nonlinear dispersive materials

In this paper, systematic wave-equation finite difference time domain (WE-FDTD) formulations are presented for modeling electromagnetic wave-propagation in linear and nonlinear dispersive materials. In the proposed formulations, the complex conjugate pole residue (CCPR) pairs model is adopted in deriving a unified dispersive WE-FDTD algorithm that allows modeling different dispersive materials, such as Debye, Drude and Lorentz, in the same manner with the minimal additional auxiliary variables. Moreover, the proposed formulations are incorporated with the wave-equation perfectly matched layer (WE-PML) to construct a material independent mesh truncating technique that can be used for modeling general frequency-dependent open region problems. Several numerical examples involving linear and nonlinear dispersive materials are included to show the validity of the proposed formulations.

A preconditioned dual–primal finite element tearing and interconnecting method for solving three-dimensional time-harmonic Maxwell's equations

A new preconditioned dual–primal nonoverlapping domain decomposition method is proposed for the finite element solution of three-dimensional large-scale electromagnetic problems. With the aid of two Lagrange multipliers, the new method converts the original volumetric problem to a surface problem by using a higher-order transmission condition at the subdomain interfaces to significantly improve the convergence of the iterative solution of the global interface equation. Similar to the previous version, a global coarse problem related to the degrees of freedom at the subdomain corner edges is formulated to propagate the residual error to the whole computational domain at each iteration, which further increases the rate of convergence. In addition, a fully algebraic preconditioner based on matrix splitting is constructed to make the proposed domain decomposition method even more robust and scalable. Perfectly matched layers (PMLs) are considered for the boundary truncation when solving open-region problems. The influence of the PML truncation on the convergence performance is investigated by examining the convergence of the transmission condition for an interface inside the PML. Numerical examples including wave propagation and antenna radiation problems truncated with PMLs are presented to demonstrate the validity and the capability of this method.

One-Step Leapfrog ADI-FDTD Method in 3-D Cylindrical Grids With a CPML Implementation

A three-dimensional (3-D) unconditionally stable one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method in the cylindrical coordinate system is presented. It is more computationally efficient while preserving the properties of the two-step scheme. By reusing the auxiliary variable, it also uses less memory than the two-step scheme. In contrast with the one-step leapfrog ADI-FDTD method in the Cartesian coordinate system, some implicit equations of the one-step leapfrog ADI-FDTD method in the cylindrical coordinate system are not tridiagonal equations. The Sherman Morrison formula is used to solve them efficiently. To solve open region problems, convolutional perfectly matched layer (CPML) for the one-step leapfrog scheme is proposed. Numerical results are presented to validate them.

SURFACE AND VOLUME INTEGRAL EQUATION METHODS FOR TIME-HARMONIC SOLUTIONS OF MAXWELL'S EQUATIONS (Invited Paper)

During the last two-three decades the importance of computer simulations based on numerical full-wave solutions of Maxwell's has continuously increased in electrical engineering. Software products based on integral equation methods have an unquestionable importance in the frequency domain electromagnetic analysis and design of open-region problems. This paper deals with the surface and volume integral equation methods for finding time-harmonic solutions of Maxwell's equations. First a review of classical integral equation representations and formulations is given. Thereafter we briefly overview the mathematical background of integral operators and equations and their discretization with the method of moments. The main focus is on advanced techniques that would enable accurate, stable, and scalable solutions on a wide range of material parameters, frequencies and applications. Finally, future perspectives of the integral equation methods for solving Maxwell's equations are discussed.

A split-step-scheme-based precise integration time domain method for solving wave equation

Purpose – This paper aims to present a modified precise integration time domain (PITD) method for the numerical solution of 2D scalar wave equation. Design/methodology/approach – The split step (SS) scheme is applied to factorize the conventional PITD calculation into two sub-steps procedures and then field components can be updated along one spatial direction only in each sub-step. The perfectly matched layer (PML) absorber is extended to this method for modeling open region problems by using the stretched coordinate approach. Findings – It is shown that this method requires less computation time and storage space in comparison with the conventional PITD method, yet maintains the numerical stability despite using large time steps. Research limitations/implications – The WE-PITD method requires the divergence free region, which may be a limit on its usage. Hence, there is a challenge of using this technique in the 3D problems. Originality/value – Based on the SS scheme, the PITD method is used to solve the scale wave equation rather than Maxwell's equations, leading to a significant reduction in the computation time and memory usage.

Recent New Trends for Solving Open-Region Problems with Refinement of Taylor Polynomial Order [EM Programmer's Notebook

An important issue for solving open-region problems using the Finite-Difference Time-Domain (FDTD) Method is the truncation of the computational domain. This article experimentally demonstrates an efficient and simple perfectly matched layer (PML) absorbing boundary condition (ABC) implementation using Berenger's split-field scheme. The method relies on approximating the exponential function present in PML field-updating coefficients with a low-order Taylor series. It was observed that with a reduced PML thickness - which represented a good balance between error reduction and computer burden - the numerical reflection that a PML absorbing boundary condition produced was less with the low-order Taylor's series approximation than that resulting from a higher-order approximation.

Integral-Based Exponential Time Differencing Algorithms for General Dispersive Media and the CFS-PML

Two efficient integral-based exponential time differencing (ETD) algorithms for general dispersive media in the finite-difference time domain (FDTD) are introduced. The first employs a linear approximation for the field over an integral time step in the integrand (denoted Algorithm I), and the second employs a Taylor series for approximating the field over the integral time step (denoted Algorithm II). Compared with the auxiliary differential equation (ADE) method and the piecewise linear recursive convolution (PLRC) method, the proposed algorithms have the same second-order accuracy but can lead to a substantial saving in both the memory space and CPU time consumption. To complete the scheme for the open region problems, a novel integral-based ETD implementation of the complex frequency shifted perfectly matched layer (CFS-PML) is proposed. Compared with the well-known recursive convolution implementation of the CFS-PML (CPML), this new implementation can lead to a substantial saving in the CPU time and a significant improvement of around 20 dB in the absorbing performance. And through the integral-based ETD algorithm, a much simpler interpretation of the CPML is presented.