Integral Equation Technique Research Articles

Subdivision based isogeometric analysis technique for electric field integral equations for simply connected structures

The analysis of electromagnetic scattering has long been performed on a discrete representation of the geometry. This representation is typically continuous but not differentiable. The need to define physical quantities on this geometric representation has led to development of sets of basis functions that need to satisfy constraints at the boundaries of the elements/tessellations (viz., continuity of normal or tangential components across element boundaries). For electromagnetics, these result in either curl/div-conforming basis sets. The geometric representation used for analysis is in stark contrast with that used for design, wherein the surface representation is higher order differentiable. Using this representation for both geometry and physics on geometry has several advantages, and is elucidated in Hughes et al. (2005) [7]. Until now, a bulk of the literature on isogeometric methods have been limited to solid mechanics, with some effort to create NURBS based basis functions for electromagnetic analysis. In this paper, we present the first complete isogeometry solution methodology for the electric field integral equation as applied to simply connected structures. This paper systematically proceeds through surface representation using subdivision, definition of vector basis functions on this surface, to fidelity in the solution of integral equations. We also present techniques to stabilize the solution at low frequencies, and impose a Calderón preconditioner. Several results presented serve to validate the proposed approach as well as demonstrate some of its capabilities.

Second Order Effect Induced by a Forced Heaving

Abstract In this paper, the 2 nd order hydrodynamic force effect of heaving submerged circular cylinder is considered, with the linear potential theory. Boundary value problem (BVP) is expanded up to the 2 nd order by using of the perturbation method and the 2 nd order velocity potential is calculated by means of integral equation technique using the classical Green’s function expressed in cylindrical coordinates. The method of solving BVP is based on eigenfunction expansions. With different cylinder heights and heaving frequencies, graphical results are present-ed. As a result of the study, the cause of oscillatory force pattern is analyzed with the occurrence of negative add-ed mass when a top of the cylinder gets closer to the free surface. Keywords: Second order force, Potential theory, Heaving cylinder, Eigen function expansions, Green function, Negative added mass. 1. Introduction When the wave loads on the structure are calculated, velocity potential is calculated through the linearization of the nonlinear free surface boundary condition with a linear potential theory. However, a sudden increase in the demand of the fossil energy has brought an increase in the demand for the offshore structures with a low natural frequency such as Tension leg platforms (TLP) or Gravity base towers. Accordingly, approximated high order solutions using potential theory has been widely studied. 2

Energy transfer in a liquid filled elemental passage of a porous medium for permeability enhancement due to pulsations of a vapor bubble

In this paper, a novel method which has been proposed during the last decade for increasing of the permeability of porous media of petroleum reservoirs by transferring of energy via ultrasound waves is investigated numerically. Increasing of permeability of porous media of petroleum reservoirs results in enhancing of oil recovery. This technique is based on the idea of transferring of energy to the liquid filled porous media via the ultrasound waves and consequently producing of pulsating vapor bubbles. The generated vapor bubbles transfer the energy of ultrasound waves in the liquid filled passages of a porous medium through velocity and pressure fields in the liquid domain and in turn apply impact forces on obstacles which have been made from accumulation of clays inside passages of the porous medium around the wellbore of an oil well after a long operating time. Removing of these obstacles, results in increasing of permeability of the porous medium and enhancing of oil recovery. The boundary integral equation technique is employed for numerical simulation of the growth and collapse of the cavitation bubbles and transferring of energy in the liquid domain by the bubbles pulsations. Three different geometries have been proposed as elemental passages of a porous medium. Numerical results show that the controlled growth and collapse of vapor bubbles induced by emission of the ultrasound waves in a liquid filled porous medium could lead to a powerful technology for enhancing oil recovery and consequently for industrial and economical development of the nations and countries having petroleum and other liquid reservoirs.DOI: http://dx.doi.org/10.5755/j01.mech.22.1.14238

Transient Electromagnetic Scattering of a Metallic Object Buried in Underwater Sediments

In this paper, we study the electromagnetic scattering of a conducting and permeable sphere buried in sea sediments. Instead of taking a uniform conducting medium in the previous work, we model marine environments as a layered medium that consists of the air, the sea, and the sediment. We adopt an integral equation technique to compute time-harmonic solutions for background and scattered fields under fundamental source excitations, i.e., vertical and horizontal magnetic dipoles. The corresponding transient scattering responses to causal step waveform are computed through the digital sine transform. The derived fundamental solutions provide convenient formulas tailored for three-layer medium modeling. The numerical experiments demonstrate that the scattered responses computed in the different backgrounds are approaching almost to the same decays at late times. However, the background fields can significantly mask the scattered responses. Subtracting assumed uniform background responses from “measured” total fields in the three-layered medium cannot provide a correct scattering response in the interested time range, i.e., 0.1–25 ms. To remove the background fields, we propose a conceptual gradiometer system that has receiver cubes installed radially symmetric with respect to a transmitting antenna. The results demonstrate that the suitable differential combinations are able to yield the scattering responses that well agree with those of a free space as the layered background fields in these combined receivers are equal and their influence are automatically canceled out.

The dual reciprocity boundary integral equation technique to solve a class of the linear and nonlinear fractional partial differential equations

In this paper, we apply the boundary integral equation technique and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of linear and nonlinear time‐fractional partial differential equations (TFPDEs). The main aim of the present paper is to examine the applicability and efficiency of DRBEM for solving TFPDEs. We employ the time‐stepping scheme to approximate the time derivative, and the method of linear radial basis functions is also used in the DRBEM technique. This method is improved by using a predictor–corrector scheme to overcome the nonlinearity that appears in the nonlinear problems under consideration. To confirm the accuracy of the new approach, several examples are presented. The convergence of the DRBEM is studied numerically by comparing the exact solutions of the problems under investigation. Copyright © 2015 John Wiley & Sons, Ltd.

Wave interaction with dual circular porous plates

In this paper we investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green’s integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cum-collocation method using the behaviour of the potential functions at the tips of the plates. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.

Efficient and Accurate Computational Electromagnetics Approach to Precipitation Particle Scattering Analysis Based on Higher-Order Method of Moments Integral Equation Modeling

AbstractA new full-wave computational electromagnetics (CEM) approach to precipitation particle scattering analysis based primarily on a higher-order method of moments (MoM) for solving surface integral equations (SIEs) is proposed, as an alternative and addition to the conventionally used tools in this area. This is a well-established CEM approach that has not been applied, evaluated, discussed, or compared with other approaches in the scattering analysis of precipitation particles so far. Several characteristic examples of scattering from precipitation particles of various shapes demonstrate the capabilities and potential of the presented numerical methodology, and discuss its advantages over both discrete dipole approximation (DDA) and -matrix methods in cases considered. In particular, it is shown that the higher-order MoM-SIE approach is much faster, more accurate, and more robust than the DDA method, and much more general and versatile than the -matrix method. In addition, the paper illustrates problems with the convergence of the DDA method in some cases with high-contrast dielectric materials and large electrical sizes of particles and with the convergence of the -matrix method in some cases with electrically large or geometrically complex (viz., with a large aspect ratio) particles. For simulations of continuously inhomogeneous scatterers (e.g., melting ice particles), a higher-order MoM volume integral equation (VIE) technique is used, as the study’s secondary methodology. The results also indicate the necessity for numerically rigorous and computationally efficient realistic precipitation particle modeling in weather scattering applications, which is becoming even more important as the sensor frequencies of radar/radiometric systems are increasing.

Calculation of effective parameters of high permittivity integrated artificial dielectrics

An analysis is presented of the effective electromagnetic parameters of high-permittivity, anisotropic artificial dielectrics which are built by stacking arrays of metallic elements and conventional dielectric films, with adjacent arrays shifted with respect to each other. The effective parameters of the artificial dielectric are extracted from the scattering coefficients of plane electromagnetic waves which are normally or obliquely incident on a slab of the artificial material with finite thickness. These coefficients are derived from the generalised scattering matrix of a single layer of metallic elements which is computed using the integral equation technique. Both two-dimensional and three-dimensional configurations are considered. Calculations demonstrate the feasibility of artificial dielectric films with extremely high values of effective relative permittivity (several thousands) in the plane of the film at millimetre-wave (mm-wave) frequencies. These artificial dielectrics have a high potential for application in microwave and mm-wave integrated circuits because of their high-permittivity and planar layout. As a potential application, the authors propose an artificial dielectric waveguide integrated on a silicon substrate.

Thermal shock fracture of a cylinder with a penny-shaped crack based on hyperbolic heat conduction

This paper studies the thermal shock fracture of a cracked cylinder based on the hyperbolic heat conduction. The crack faces are subjected to a sudden anti-symmetric thermal flux and a sudden symmetric thermal flux, respectively. By Laplace transform and dual integral equation technique, the mode II stress intensity factor and the mode I stress intensity factor are developed at the crack front for the two cases, respectively. Numerical results of stress intensity factor for selected thermal relaxation time and crack size are shown graphically. It is found that the stress intensity factor is considerably enhanced for large thermal relaxation time (which is a material constant) or small crack radius. In addition, the stress intensity factor at the crack front increases with the thermal relaxation time. For the case of anti-symmetric thermal flux, the mode II stress intensity factor increases rapidly with crack size. Whereas for the case of symmetric thermal flux, with increasing crack size, the mode I stress intensity factor increases slowly.

Determination of position and orientation of conducting rod using a neural network

The problem of electromagnetic wave diffraction by a conducting rod has been solved using the integral equation technique. The diagram of backward scattering has been plotted. A wavelet packet decomposition of the obtained characteristic has been carried out. Based on the values of Shannon entropy for decomposition components we have constructed the feature vector. We have trained a neural network based on radial basis elements, which allows one to determine the position of a rod and its spatial orientation based on the feature vector. Numerical simulation and statistical analysis of the numerical results have been carried out.

Highly efficient full‐wave electromagnetic analysis of 3‐D arbitrarily shaped waveguide microwave devices using an integral equation technique

AbstractA novel technique for the full‐wave analysis of 3‐D complex waveguide devices is presented. This new formulation, based on the Boundary Integral‐Resonant Mode Expansion (BI‐RME) method, allows the rigorous full‐wave electromagnetic characterization of 3‐D arbitrarily shaped metallic structures making use of extremely low CPU resources (both time and memory). The unknown electric current density on the surface of the metallic elements is represented by means of Rao‐Wilton‐Glisson basis functions, and an algebraic procedure based on a singular value decomposition is applied to transform such functions into the classical solenoidal and nonsolenoidal basis functions needed by the original BI‐RME technique. The developed tool also provides an accurate computation of the electromagnetic fields at an arbitrary observation point of the considered device, so it can be used for predicting high‐power breakdown phenomena. In order to validate the accuracy and efficiency of this novel approach, several new designs of band‐pass waveguides filters are presented. The obtained results (S‐parameters and electromagnetic fields) are successfully compared both to experimental data and to numerical simulations provided by a commercial software based on the finite element technique. The results obtained show that the new technique is specially suitable for the efficient full‐wave analysis of complex waveguide devices considering an integrated coaxial excitation, where the coaxial probes may be in contact with the metallic insets of the component.

Matrix models, Toeplitz determinants and recurrence times for powers of random unitary matrices

The purpose of this paper is to study the eigenvalues [Formula: see text] of Ut where U is a large N×N random unitary matrix and t > 0. In particular we are interested in the typical times t for which all the eigenvalues are simultaneously close to 1 in different ways thus corresponding to recurrence times in the issue of quantum measurements. Our strategy consists in rewriting the problem as a random matrix integral and use loop equations techniques to compute the first-orders of the large N asymptotic. We also connect the problem to the computation of a large Toeplitz determinant whose symbol is the characteristic function of several arc segments of the unit circle. In particular in the case of a single arc segment we recover Widom's formula. Eventually we explain why the first return time is expected to converge toward an exponential distribution when N is large. Numerical simulations are provided along the paper to illustrate the results.

Integral Equation Analysis of Multilayered Waveguide Bends Using Complex Images Green's Function Technique

In this paper, a new approach for analyzing multilayered waveguide bends using an integral equation technique is introduced. The equivalence principle is employed to form a combined field integral equation (CFIE). The use of complex images Green's functions in the method of moments solution of the developed CFIE formulation results in a highly accurate and fast solution of the problem and simultaneously, reduces computational complexity. The proposed method is applied to a general 2-D optical bend. The accuracy of the results is verified by comparison with the physical optics method.

Lagrange‐type modeling of continuous dielectric permittivity variation in double‐higher‐order volume integral equation method

AbstractA novel double‐higher‐order entire‐domain volume integral equation (VIE) technique for efficient analysis of electromagnetic structures with continuously inhomogeneous dielectric materials is presented. The technique takes advantage of large curved hexahedral discretization elements—enabled by double‐higher‐order modeling (higher‐order modeling of both the geometry and the current)—in applications involving highly inhomogeneous dielectric bodies. Lagrange‐type modeling of an arbitrary continuous variation of the equivalent complex permittivity of the dielectric throughout each VIE geometrical element is implemented, in place of piecewise homogeneous approximate models of the inhomogeneous structures. The technique combines the features of the previous double‐higher‐order piecewise homogeneous VIE method and continuously inhomogeneous finite element method (FEM). This appears to be the first implementation and demonstration of a VIE method with double‐higher‐order discretization elements and conformal modeling of inhomogeneous dielectric materials embedded within elements that are also higher (arbitrary) order (with arbitrary material‐representation orders within each curved and large VIE element). The new technique is validated and evaluated by comparisons with a continuously inhomogeneous double‐higher‐order FEM technique, a piecewise homogeneous version of the double‐higher‐order VIE technique, and a commercial piecewise homogeneous FEM code. The examples include two real‐world applications involving continuously inhomogeneous permittivity profiles: scattering from an egg‐shaped melting hailstone and near‐field analysis of a Luneburg lens, illuminated by a corrugated horn antenna. The results show that the new technique is more efficient and ensures considerable reductions in the number of unknowns and computational time when compared to the three alternative approaches.

Simple and complex forms of disorder in ionic liquids

An analysis of the structural features of high and room temperature liquids is proposed, which attempts to explain the differences in disorder between these two types of systems by the particles shape and the ratio of the molecular size to the temperature. This is achieved by the study of different types of models, by computer simulations and liquid state integral equation techniques. The comparative study of the correlation functions and structure factors explains the origin of the pre-peak observed in room temperature ionic liquids, and clarifies the respective roles of the electrostatic and neutral part of the various atom–atom interactions. The study equally clarifies the differences between the fluctuations, and in particular critical fluctuations, and the structural micro-heterogeneity. The excellent agreement between the theory and the simulations, as opposed to the poorer agreement often observed in case of associated molecular liquids (such as water and alcohols), illustrates the conceptual difference between free and bound charges, ionic and molecular liquids. It is argued herein that different forms of disorders are associated to this underlying difference.

End-fire ultrawideband low profile dipole-slot antenna

This paper presents a simple end-fire ultrawideband dipole-slot antenna, which consists of a single plate dipole located above the screen and loaded by two slots, that are formed by three metal sheets. The results of numerical investigation of its matching and radiation characteristics using integral equations technique for the current and the charge are demonstrated in the article. An optimized variant of the antenna has a low profile (0.17λmax) and in the frequency range with bandwidth ratio 3.2:1 it provides VSWR<2in the case of excitation by the 50Ω feeder, and also it provides almost unalterable shape of the radiation pattern for the wavelengths, which are close to the λ/2 distance to the screen, what cannot be obtained for the dipole antenna above the screen. It has been shown that such an effect is achieved due to the in-phase combining of the radiations emitted by the dipole-slot system and by the screen in the front half-space.

Bridged defects in continuously and discretely reinforced solids

The paper examines problems that relate to defects in elastic solids that are reinforced by aligned fibres. The category of problems deals with flaw bridging that can occur as a result of continuity of fibres across the defect in the matrix region. The defects can be a flaw of finite dimensions or cracks in the conventional sense. The presence of fibre continuity across a flaw exerts a displacement-dependent boundary condition at the faces of the crack that can alter the stress state at the boundary of the defect and contribute to fracture generation. The analysis of both a spheroidal flaw with fibre bridging and an idealized penny-shaped crack with fibre continuity across the faces of the crack leads to the conclusion that the stress amplification usually associated with extension of the flaw is suppressed by the fibre continuity. The second type of problem deals with the mechanics of flaws that can emanate from the extremities of an isolated cylindrical fibre in an elastic matrix of infinite extent. The problem is examined using a computational approach based on the boundary integral equation technique. The modelling is used to examine the role of the fibre–matrix elasticity mismatch on the stress intensity factors at the tip of penny-shaped cracks emanating from the ends of the fibre.

Electromagnetic Wave Scattering Analysis From 2-D Periodic Rough Surfaces Using Complex Images Technique

The integral equation technique, in combination with the method of moments, is widely used for treating the electromagnetic scattering from periodic rough surfaces. This method, however, requires the computation of a kernel (a periodic Green's function) that consists of a slowly converging infinite series of conventional Green's functions. To accelerate the convergence of this series, different methods have been proposed in literature. In this paper, we use a complex image (CI) technique to find a closed-form expression for the periodic Green's function, which is then used to analyze the electromagnetic scattering from arbitrary periodic rough surfaces. The resulting CI Green's function consists of a finite number of terms corresponding to real and complex sources. Moreover, the CI Green's function in the Hankel form (evanescent waves) is used if the observation and source points are close. In the far-field region, the series in the plane-wave form (propagating Floquet modes) caused by the extraction of poles are sufficient and necessary. The results indicate that the presented CI Green's function leads to numerical efficiency yet having a rather high level of accuracy.

Analysis of eddy current formulations in two-dimensional domains with cracks

In this paper, the eddy current problem in a two-dimensional conductor containing a crack is studied. The decomposition of the electric field into a piecewise regular part and a singular part deriving from scalar potentials localized at the crack tip and at the crack mouth is proved. At the crack mouth, the electric field is shown to have standard singularities inside the conductor, but presents a singularity outside the conductor that does not belong to the classical L 2 -space. Well-posedness of the E-based model and the A � ψ-formulation of combined potentials are proved and an un-gauged discretization of the latter formulation is discussed. The present paper is concerned with the analysis of eddy currents in the presence of cracks. Eddy current simulations have become an important research area due to numerous applications in electrical engineering. Eddy current testing, for example, as a particular technique of non destructive testing, remains one of the most popular tools in the quality control of conducting test pieces, and an important number of papers in the electric engineering community, mostly based on integral equation techniques, is devoted to numerical methods for crack detection (see e.g. (11, 12, 14, 15, 27)). In a typically configuration of eddy current testing, a coil carrying an alternative current is placed in proximity to the conducting test piece. The coil's magnetic field induces the eddy currents in the conductor which generate measurable variations of the impedance of the coil. In the presence of a crack, the eddy currents are deviated and the electromagnetic response allows for the detection of the defect. Due to the limited penetration depth of the currents, eddy current testing is mostly used to detect cracks that are situated near the surface. In the mathematical community, eddy current models have gathered much interest in relation with the topological properties of the device. Several formulations for the eddy current problem have been suggested (see

An Efficient Single-Source Integral Equation Solution to EM Scattering From a Coated Conductor

The single-source integral equation (SSIE) technique is presented to analyze electromagnetic scattering from an arbitrarily shaped three-dimensional conducting object coated by a homogeneous dielectric body. The external and interior surface equivalence principles combined with the continuity of the tangential components of the total electric and magnetic fields on the surface of the dielectric and zero tangential component of the total electric field on the surface of the conductor are used to formulate the single-source electric and magnetic field integral equations. With a localization procedure, the Calderon preconditioned single-source electric field integral equation (SSEFIE) is constructed and combined with single-source magnetic field integral equation (SSMFIE) to produce a single-source combined field integral equation (SSCFIE), which is free from spurious resonance and dense-mesh breakdown. Numerical results validate the good performance of the proposed algorithm.