Approximate Boundary Conditions Research Articles

Method for Calculating Radiation Characteristics of Dual-Reflector Antennas with Resonance Size Reflectors of Finite Thickness and Conductivity

The paper presents a method for calculating the radiation patterns (RP) of dual-reflector antenna systems taking into account the electrodynamic interaction between reflectors. This method is suitable for use in the resonance range of wavelengths with respect to the main dimensions of reflectors. The method is based on the iteration procedure proposed by the authors. Each iteration involves the use of the method for calculating the scattering of electromagnetic wave by unclosed screens of finite thickness and conductivity that is suitable for use in resonance range. The specified method is based on applying the E-field integral equation that takes into account the Leontovich approximate boundary conditions on impedance surface and makes it possible to take into account the real thickness and conductivity of antenna’s reflectors. The paper presents the results of calculating RP of dual-reflector antennas built in accordance with the Gregorian scheme for different sizes of small reflector aperture and different arrangements of feeder at the fixed size of large reflector. The paths of reducing the level of the first side lobes of RP are shown. The specified reduction is achieved at the expense of the feeder proper placing with respect to the small reflector of antenna.

Construction of boundary conditions for hyperbolic relaxation approximations I: The linearized Suliciu model

Starting with this paper, we intend to develop a program aiming at construction of boundary conditions (BCs) for hyperbolic relaxation systems. Physically, such BCs are not always available. The construction is based on the assumption that the relaxation systems and well-posed BCs for the corresponding equilibrium systems are given. This paper focuses on the linearized Suliciu model. We obtain strictly dissipative and compatible BCs for the linearized model with different non-characteristic boundaries. Moreover, the effectiveness of the constructed BCs is shown by resorting to formal asymptotic solutions and energy estimates.

Diffraction of Electromagnetic Waves by Multilayer Graphene Metasurfaces in the Terahertz Frequency Band

We perform mathematical modeling of diffraction of plane electromagnetic waves by multilayer metasurfaces comprised by elements of graphene nanoribbons. The modeling is based on solving the three-dimensional boundary value diffraction problem by three methods, specifically, those of self-contained units with Floquet channels, the volume integro-differential equation, and approximate boundary conditions. The coefficients of reflection, transmission, and absorption of s- and p-polarized waves by metasurfaces made of elements of rectangular graphene nanoribbons are calculated as functions of the frequency and the incidence angle for various values of the chemical potential with allowance for the geometric and dimensional effects in the terahertz frequency band. It is shown that at the resonant frequencies of the surface plasmon polariton, multilayer metasurfaces comprised by two graphene strips in an elementary cell on substrates, which contain layers of a dielectric and graphene, are electrically controlled efficient wideband terahertz absorbers and polarizers in the reflection regime that are insensitive to incidence angles.

Dispersion Characteristics of Spin-Electromagnetic Waves in Planar Multiferroic Structures with Coplanar Transmission Line

Introduction. The distinctive feature of a coplanar transmission line with thin ferrite and ferroelectric films is the absence of undesirable irregularities in dispersion for relatively low frequencies when the wavelength approaches the thickness of ferroelectric layer, in contrast to the open ferrite-ferroelectric wave-guiding structure without metallization. Aim. The purpose of this paper is twofold: (i) to develop a theory of the wave spectra in the multiferroic structures based on the coplanar lines; (ii) using this theory to find ways to enhance the electric tuning range. Materials and methods . The dispersion relation for spin-electromagnetic waves was derived through analytical solution of the full set of the Maxwell's equations utilizing a method of approximate boundary conditions. Results. A theory of spin-electromagnetic wave spectrum has been developed for the thin-film ferrite-ferroelectric structure based on a coplanar transmission line. According to this theory, dispersion characteristics of the spin-electromagnetic waves were described and analyzed for different parameters of the structure. The obtained results show that the investigated structure demonstrates a dual electric and magnetic field tunability of wave spectra. Its efficiency increases with an increase in the thicknesses of the ferrite and ferroelectric films and with a decrease in the width of the central metal strip. Conclusion. The distinctive features of the proposed coplanar waveguides are the thin-film planar topology and dual tunability of the wave spectra. All these advantages make the proposed structures perspective for development of new microwave devices.

Приближенные граничные условия для задачи нахождения оптических коэффициентов ультратонких металлических пленок в СВЧ и ТГЦ диапазонах

Approximate boundary conditions for a problem of calculating the optical coefficients of a system composed of inhomogeneous ultrathin metallic film with an arbitrary thickness dependence of conductivity deposited on dielectric substrate are obtained. The derivation of the boundary conditions is based on the Picard method of successive approximations. Analytical expressions for the errors in calculating the optical coefficients with use of the proposed approximate boundary conditions are presented. It is shown that the error increases with the frequency and the film thickness increasing. The maximum error for films of 10 nm-thickness does not exceed 10.7% at 1 THz. As an example, the complex optical coefficients of a system similar to Fabry-Perot etalon and a metal film without a substrate with model thickness dependence of conductivity are calculated. The coincidence between the results of numerical simulation and calculations performed with approximate boundary conditions is shown. The possibility of direct calculating the average conductivity of a film from experimentally measured reflection and transmission coefficients is demonstrated.

Analysis of an observer strategy for initial state reconstruction of wave-like systems in unbounded domains

We are interested in reconstructing the initial condition of a wave equation in an unbounded domain configuration from measurements available in time on a subdomain. To solve this problem, we adopt an iterative strategy of reconstruction based on observers and time reversal adjoint formulations. We prove the convergence of our reconstruction algorithm with perfect measurements and its robustness to noise. Moreover, we develop a complete strategy to practically solve this problem on a bounded domain using artificial transparent boundary conditions to account for the exterior domain. Our work then demonstrates that the consistency error introduced by the use of approximate transparent boundary conditions is compensated by the stabilization properties obtained from the use of the available measurements, hence allowing to still be able to reconstruct the unknown initial condition.

Transparent boundary conditions for higher-order finite-difference schemes of the Schrödinger equation in (1+1)D

A systematic development of discrete transparent boundary conditions (TBCs) for higher-order finite-difference approximations to Schrödinger-type equations is formulated and tested numerically. The finite-range interaction scheme for the original wave function is transformed into an equivalent nearest-neighbour coupling scheme for unit cells represented by multi-component spinors. This nearest-neighbour scheme lends itself to an established approach: the single-cell translation matrix for the extended spinor is constructed in Z space and cast into Jordan form. TBCs are obtained by setting out-bound growing spinor contributions equal to zero. Specifically we consider unitary extensions to the Crank–Nicolson time-propagation scheme for the time-dependent Schrödinger equation in (1+1)D. Numerical examples are given for selected higher-order propagation schemes. Finally, a simplified formulation based on a single, dominant growth factor is discussed and tested numerically.

An element free Galerkin method for static behavior of a magneto-electro-elastic beam in thermal environments

In this article, an element free Galerkin method (EFGM) has been used for the static analysis of a magneto-electro-elastic (MEE) beam in thermal environments. The influence of pyro effects (pyroelectric and pyromagnetic) on the physical characteristics (displacements and the potentials) of the MEE beam under plane strain conditions in various thermal conditions are studied. The system governing equations of MEE structures are derived from the Hamilton principle and constitutive equations of linear coupling between elastic, electric, magnetic and thermal properties of MEE materials. In EFGM, the moving least squares (MLS) method is utilized to generate shape functions. Since it does not satisfy the principle of Kronecker delta, the penalty method is implemented to impose approximate boundary conditions. The result is verified and applied to reveal the effects of thermo-magnetic and thermo-electric coupling by MEE column. Further, a comparative study is made to evaluate the variations of physical characteristics along the longitudinal direction of the MEE beam in different thermal environments. Numerical results demonstrate the efficiency and accuracy of the EFG formulation to multi-physics simulation of MEE structures in thermal environments.

Efficient Near-Field Analysis of the Electromagnetic Scattering Based on the Dirichlet-to-Neumann Map

This paper proposes an efficient technique to solve the electromagnetic scattering problem, in the near zone of scatterers illuminated by external fields. The technique is based on a differential formulation of the Helmholtz equation discretized in terms of a finite element method (FEM). In order to numerically solve the problem, it is necessary to truncate the unbounded solution domain to obtain a bounded computational domain. This is usually done by defining fictitious boundaries where absorbing conditions are imposed, for example by applying the perfect matching layer (PML) approach. In this paper, these boundary conditions are expressed in an analytical form by using the Dirichlet-to-Neumann (DtN) operator. Compared to classical solutions such as PML, the proposed approach based on the DtN: (i) avoids the errors related to approximated boundary conditions; (ii) allows placing the boundary in close proximity to the scatterers, thus, reducing the solution domain to be meshed and the related computational cost; (iii) allows dealing with objects of arbitrary shapes and materials, since the shape of the boundary independent from those of the scatterers. Case-studies on problems related to the scattering from cable bundles demonstrate the accuracy and the computational advantage of the proposed technique, compared to existing ones.

A modified analytical model for stress analysis of adhesively bonded stepped-lap joints under tensile load

A modified analytical model with closed-form solution is proposed in this study to investigate interfacial shear and normal stresses in adhesively bonded double-lap joints with stepped outer adherend, subjected to tensile loading. By extending some researchers' prior related works, explicit expressions for adhesive interfacial shear and normal stresses are derived, with considerations of shear deformation in the adherends and plasticity in the adhesive layer. Continuity conditions are introduced to fit the variation of the outer adherend thicknesses. To obtain unknown constants of general solutions for adhesive normal stress, some approximate boundary conditions are reconstructed and several simplifications are imposed. The adhesive stress distributions along the bondline are obtained to investigate the effects of joint's material properties and geometric parameters. Adhesive with elastic-perfect plastic behavior is also considered in the analyses. The results obtained from the present model show an excellent agreement with corresponding finite element results. The present method is applicable to implement parametric analysis and optimal design for adhesively bonded double-lap joint.

Wind field simulation over complex terrain under different inflow wind directions

Accurate numerical simulation of wind field over complex terrain is an important prerequisite for wind resource assessment. In this study, numerical simulation of wind field over complex terrain was further carried out by taking the complex terrain around Siu Ho Wan station in Hong Kong as an example. By artificially expanding the original digital model data, Gambit and ICEM CFD software were used to create high-precision complex terrain model with high-quality meshing. The equilibrium atmospheric boundary layer simulation based on RANS turbulence model was carried out in a flat terrain domain, and the approximate inflow boundary conditions for the wind field simulation over complex terrain were established. Based on this, numerical simulations of wind field over complex terrain under different inflow wind directions were carried out. The numerical results were compared with the wind tunnel test and field measurement data for land and sea fetches. The results show that the numerical results are in good agreement with the wind tunnel data and the field measurement data which can verify the accuracy and reliability of the numerical simulation. The near ground wind field over complex terrain is complex and affected obviously by the terrain, and the wind field characteristics should be fully understood by numerical simulation when carrying out engineering application on it.

Parametric model updating with frequency and MAC combined objective function of port crane structure based on operational modal analysis

Abstract In FE modeling of port crane structures, errors may be caused due to the simplification of complicated components, unclear physical properties, local approximation and inaccurate boundary conditions. So it is very important to update the FE model accuracy according to the experiment model and results. However there are two major problems when solving the model updating of port crane structure, the one is the difficulty of collecting the structure modal parameters with traditional modal experiment method because of the large scale of port crane structure, the other is mismatching problem while updating processing due to most of the model updating method currently constructing the objective function only by frequency. In this paper, an operational modal analysis is adopted to estimate the modal parameters of port crane structure based on the operational condition. A parametric model updating methodology of finite element (FE) model is proposed to solve port crane structure model updating: a series of design parameters of the FE model of port crane structure are selected as the main factors based on the sensitivity analysis, the objective function is built by considering the frequency correlation and the modal assurance criterion (MAC) together, and finally a zero-order/first-order combination algorithm is utilized to get the final accurate FE model of port crane structure. Research results showed that methodology proposed in this paper has satisfied updating accuracy for port crane structure, which verifies that the proposed method is suitable for model updating problem of this kind of structure.

Engine characterization using experimental method and prediction of insertion loss of the exhaust system

The evaluation of the acoustic performance of an exhaust system at the design stage requires a correlated engine model and reasonably approximate input boundary conditions to simulate the end results, both of which are not easily available. It is known that the input boundary conditions for insertion loss analysis require two engine parameters, namely, source impedance and source strength spectra. This study describes experimental measurements for these parameters using in-duct measurement via the multi-load method for a six-cylinder diesel engine and calculation for insertion loss using GT-Power. The research discusses the approach taken to select the acoustic load cases considered for the multi-load method and then the execution of the test plan for different engine operating conditions The time domain data sets were processed to obtain the frequency spectra and was used to get the impedance of the acoustic load cases and finally the source impedance and source strength spectra for different engine operating conditions. The results obtained using all the acoustic load cases were optimized by filtering out unacceptable load cases and then re-evaluating the source characteristics to use them as input boundary conditions for insertion loss analysis. The analysis results were then compared to the experimental insertion loss.

Transparent numerical boundary conditions for evolution equations: Derivation and stability analysis

The aim of this article is to propose a systematic study of transparent boundary conditions for finite difference approximations of evolution equations. We try to keep the discussion at the highest level of generality in order to apply the theory to the broadest class of problems.

Theory of Spin-Electromagnetic Waves in Planar Thin-Film Multiferroic Heterostructures Based on a Coplanar Transmission Line and Its Application for Electromagnonic Crystals

A theory of spin-electromagnetic wave spectrum has been developed for the thin-film ferrite-ferroelectric structure based on a coplanar transmission line (TL). The dispersion relation was derived through analytical solution of the full set of Maxwell’s equations utilizing a method of approximate boundary conditions. The theory was used for numerical simulation of the transmission characteristics of the periodic multiferroic heterostructures containing the coplanar TL with a periodic variation of its width. We named these heterostructures “electromagnonic crystals.” The transmission characteristics of the electromagnonic crystals were calculated by the transfer-matrix method. The obtained results show that a high microwave signal rejection of more than 30 dB appears in the electromagnonic crystals due to the Bragg reflections. The distinctive features of the proposed electromagnonic crystals are the thin-film planar topology and dual tunability of the electromagnonic band-gap positions.

CO2 Injection Monitoring Using Transient Electromagnetic in Ground-Borehole Configuration

Using geophysical methods, specifically transient electromagnetic (TEM), for CO2 monitoring is an effective way to detect CO2 diffusion. In this work, a multi-scale finite-difference time-domain (FDTD) algorithm was established to monitor CO2 by defining new iterative relations and approximating boundary conditions, which achieves unification in the time and space domain. The response curve characteristics of different forms of CO2 were acquired by changing the receiver's depth and position, CO2 resistivity, scale, and injection stage. Different models considering a planar, tilted, and large-scale CO2 bodies, which were established to test the capacity of TEM monitoring for CO2. The TEM response of injected CO2 bodies had obvious characteristics and the response curve had distinguishable differences from background. This phenomenon could provide reference models for real TEM CO2 monitoring.

Prediction of nontidal sea level variations in the Persian Gulf using data assimilation techniques

ABSTRACTThe regular pattern of tidal water level fluctuation in the open seas is often deviated by the effect of weather systems. The stochastic behavior of these systems makes it difficult to predict the nontidal residuals (NTR) precisely. The hydrodynamic models as efficient tools for the simulation of NTR may suffer from lack of accuracy due to approximate boundary conditions and forcings. Data Assimilation (DA) techniques combine hydrodynamic model predictions with available field observations to improve the predictions. In this study, a number of DA methods were employed to improve the NTR predictions in a semienclosed basin. The results have shown the studied DA techniques, which are originally developed for weather prediction problems, can be improved by considering the physical mechanisms of NTR generation. A new formula was introduced for the calculation of weight factors of the existing methods. Application of the proposed method increased the accuracy of NTR predictions significantly so that the correlation coefficient of the NTR predictions increased from 0.660 to 0.896 and the root mean square error decreased from 5.22 cm to 2.51 cm. In addition, so it is concluded among the studied DA schemes, Barnes method has better efficiency for prediction of NTR in the region.

An iterative approach for analyzing cracks in two-dimensional piezoelectric media with exact boundary conditions

An iterative approach is proposed for analyzing cracks in two-dimensional piezoelectric media based on the sub-region boundary element formulation with exact boundary conditions on the crack face. In this approach, the opening crack cavity is treated as one of the sub-regions governed by the Poisson equation of electric potential. The real crack opening, the crack cavity region, and the field in the cavity region are determined for the geometrically nonlinear problem. The widely used approximate crack models corresponding to three approximate boundary conditions are evaluated based on the proposed approach. The proposed approach is implemented efficiently to analyze problems with very thin domains, such as the crack opening cavity, and employing the intelligent adaptive algorithms in the Mathematica software means that nearly singular integrals require no special treatment.

Flexible and Accurate Simulation of Radiation Cooling with FETD Method

Thermal management and simulation are becoming increasingly important in many areas of engineering applications. There are three cooling routes for thermal management, namely thermal conduction, thermal convection and thermal radiation, among which the first two approaches have been widely studied and applied, while the radiation cooling has not yet attracted much attention in terrestrial environment because it usually contributes less to the total amount of thermal dissipation. Thus the simulation method for radiation cooling was also seldom noticed. The traditional way to simulate the radiation cooling is to solve the thermal conduction equation with an approximate radiation boundary condition, which neglects the wavelength and angular dependence of the emissivity of the object surface. In this paper, we combine the heat conduction equation with a rigorous radiation boundary condition discretized by the finite-element time-domain method to simulate the radiation cooling accurately and flexibly. Numerical results are given to demonstrate the accuracy, flexibilities and potential applications of the proposed method. The proposed numerical model can provide a powerful tool to gain deep physical insight and optimize the physical design of radiation cooling.

Wall-Modeled Large-Eddy Simulation for Complex Turbulent Flows.

Large-eddy simulation (LES) has proven to be a computationally tractable approach to simulate unsteady turbulent flows. However, prohibitive resolution requirements induced by near-wall eddies in high-Reynolds number boundary layers necessitate the use of wall models or approximate wall boundary conditions. We review recent investigations in wall-modeled LES, including the development of novel approximate boundary conditions and the application of wall models to complex flows (e.g., boundary-layer separation, shock/boundary-layer interactions, transition). We also assess the validity of underlying assumptions in wall-model derivations to elucidate the accuracy of these investigations, and offer suggestions for future studies.