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A VIE-based algebraic domain decomposition for analyzing electromagnetic scattering from inhomogeneous isotropy/anisotropy dielectric objects
摘要： A VIE-based domain decomposition method (DDM) is proposed for analyzing EM scattering from inhomogeneous electrically large dielectric objects. The volume integral equation (VIE) still uses tetrahedra to model the entire body and uses the SWG basis functions to expand the equivalent electric ?ux density. This new DDM is established by dividing the unknowns on the whole electrically large body into groups, serving as subdomains. Through necessary symmetry treatment of standard MoM impedance matrix, the DDM using subdomain-decoupling technology can be combined with the VIE model to reduce memory requirement. Actually, this is an algebraic DDM, not a geometric DDM. In other words, it has no requirement of physical location of basis functions belonging to the same subdomain. This decoupling procedure is completely eliminating the coupling impact of the primary subdomain with the rest of the dielectric body, until every subdomain is independent with each other. In this work, when solving ultimate decoupled impedance subdomain matrix, the LU decomposition process for solving interpolating coef?cients of multiple right sides is accelerated by GPU parallel technology to signi?cantly decrease CPU time. In brief, this paper ?rst time combines the algebraic DDM with the conventional VIE model (including both isotropy and anisotropy VIE model) to signi?cantly decrease the requirement of memory. At last, a few representative numerical examples are provided to demonstrate validity, ef?ciency and stability of the new method.
关键词： MoM,volume integral equation,domain decomposition
更新于2025-09-23 15:23:52
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Numerical Analysis of the Integral Equation Method for the Computation of the Electromagnetic Field in a Nonhomogeneous Medium
摘要： The article considers mathematical modeling of the electromagnetic field in a nonhomogeneous medium by the integral equation method. The case of high-contrast conducting media is studied in detail, with the conducting nonhomogeneity embedded in a poorly conducting medium. The analysis of the integral equation, in this case, has shown that the solution deteriorates when the conducting nonhomogeneity is inside a low-conductivity layer. It is shown that this effect can be overcome by Dmitriev’s method of elevated background conductivity. The contrast effect is most pronounced for the H-polarized two-dimensional electromagnetic field in a nonhomogeneous medium. The numerical experiment has accordingly been conducted for this particular case. The solution computed by the integral equation method with elevated background conductivity is compared with the solution computed by the finite-difference method. The results of the two methods show excellent fit.
关键词： integral equation method,electromagnetic sounding,nonhomogeneous medium,Maxwell equations
更新于2025-09-23 15:22:29
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Coupling of Characteristic Modes on PEC and Lossy Dielectric Structures
摘要： Surface integral equation based theory of characteristic modes (TCM) is presented for structures including perfect electric conductors (PEC) and lossy dielectric bodies. The formulation is a combination of the classical TCM formulation for PEC structures and a recently developed one for penetrable bodies. The potential of the methodology for practical antenna design problems is demonstrated by studying coupling of the modes on a PEC plate (antenna ground plane) and an adjacent highly lossy dielectric block (user’s hand). This analysis reveals existence of different types of modes having weak or strong interactions between the PEC and dielectric parts.
关键词： Characteristic modes,dielectric losses,mobile handset antenna,surface integral equation structure
更新于2025-09-23 15:22:29
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[IEEE 2019 IEEE High Power Diode Lasers and Systems Conference (HPD) - Coventry, United Kingdom (2019.10.9-2019.10.10)] 2019 IEEE High Power Diode Lasers and Systems Conference (HPD) - Applications of thermoreflectance imaging to high-power diode laser diagnostics
摘要： A time-domain electric ?eld volume integral equation (TD-EFVIE) solver is proposed for characterizing transient electromagnetic wave interactions on high-contrast dielectric scatterers. The TD-EFVIE is discretized using the Schaubert–Wilton–Glisson (SWG) and approximate prolate spherical wave (APSW) functions in space and time, respectively. The resulting system of equations cannot be solved by a straightforward application of the marching on-in-time (MOT) scheme since the two-sided APSW interpolation functions require the knowledge of unknown “future” ?eld samples during time marching. Causality of the MOT scheme is restored using an extrapolation technique that predicts the future samples from known “past” ones. Unlike the extrapolation techniques developed for MOT schemes that are used in solving time-domain surface integral equations, this scheme trains the extrapolation coef?cients using samples of exponentials with exponents on the complex frequency plane. This increases the stability of the MOT-TD-EFVIE solver signi?cantly, since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme. Numerical results demonstrate that the proposed MOT solver maintains its stability even when applied to analyzing wave interactions on high-contrast scatterers.
关键词： extrapolation,electric ?eld volume integral equation (EFVIE),transient analysis,time-domain analysis,Band-limited interpolation,marching on-in-time (MOT) method
更新于2025-09-23 15:19:57
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[IEEE 2019 8th International Conference on Renewable Energy Research and Applications (ICRERA) - Brasov, Romania (2019.11.3-2019.11.6)] 2019 8th International Conference on Renewable Energy Research and Applications (ICRERA) - Effects of Price Developments on Photovoltaic Panel to Inverter Power Ratios
摘要： A time-domain electric ?eld volume integral equation (TD-EFVIE) solver is proposed for characterizing transient electromagnetic wave interactions on high-contrast dielectric scatterers. The TD-EFVIE is discretized using the Schaubert–Wilton–Glisson (SWG) and approximate prolate spherical wave (APSW) functions in space and time, respectively. The resulting system of equations cannot be solved by a straightforward application of the marching on-in-time (MOT) scheme since the two-sided APSW interpolation functions require the knowledge of unknown “future” ?eld samples during time marching. Causality of the MOT scheme is restored using an extrapolation technique that predicts the future samples from known “past” ones. Unlike the extrapolation techniques developed for MOT schemes that are used in solving time-domain surface integral equations, this scheme trains the extrapolation coef?cients using samples of exponentials with exponents on the complex frequency plane. This increases the stability of the MOT-TD-EFVIE solver signi?cantly, since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme. Numerical results demonstrate that the proposed MOT solver maintains its stability even when applied to analyzing wave interactions on high-contrast scatterers.
关键词： transient analysis,Band-limited interpolation,time-domain analysis,extrapolation,marching on-in-time (MOT) method,electric ?eld volume integral equation (EFVIE)
更新于2025-09-23 15:19:57
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[IEEE 2019 IEEE 46th Photovoltaic Specialists Conference (PVSC) - Chicago, IL, USA (2019.6.16-2019.6.21)] 2019 IEEE 46th Photovoltaic Specialists Conference (PVSC) - The role of financing in realizing ultra-low solar electricity prices in the Middle East
摘要： A hybrid approach is proposed to signal integrity analysis of trace and vias in plate pair with an in?nitely large dimension. By using the domain decomposition method, trace domain and via domain are divided from the plate domain. Each individual domain of via and trace structure is modeled by the 3-D full-wave tool HFSS as a multimode network composed of TEM mode waveguide ports at top/bottom antipad interfaces and vertical lumped ports on the segmentation interfaces. The plate domain is dominated by TMZ 0 modes and network parameters are solved by boundary integral method. Connection of network of each domain enforces the ?eld continuity conditions along the segmentation interfaces and yields the ?nal S parameter of trace and via as well as trace/via to trace/via coupling. Once the via pattern and trace routing are determined, the coupling can be ef?ciently modeled by the proposed hybrid approach and the layouts of via structures and trace routing in a plate pair are ef?ciently optimized.
关键词： trace/via to trace/via coupling,domain decomposition method (DDM),Contour integral equation
更新于2025-09-23 15:19:57
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COMPUTATIONAL ASPECTS OF 2D-QUASI-PERIODIC-GREEN-FUNCTION COMPUTATIONS FOR SCATTERING BY DIELECTRIC OBJECTS VIA SURFACE INTEGRAL EQUATIONS
摘要： We describe a surface integral-equation (SIE) method suitable for computation of electromagnetic ?elds scattered by 2D-periodic high-permittivity and plasmonic scatterers. The method makes use of fast evaluation of the 2D-quasi-periodic Green function (2D-QPGF) and its gradient using a tabulation technique in combination with tri-linear interpolation. In particular we present a very e?cient technique to create the look-up tables for the 2D-QPGF and its gradient where we use to our advantage that it is very e?ective to simultaneously compute the QPGF and its gradient, and to simultaneously compute these values for the case in which the role of source and observation point are interchanged. We use the Ewald representation of the 2D-QPGF and its gradient to construct the tables with pre-computed values. Usually the expressions for the Ewald representation of the 2D-QPGF and its gradient are presented in terms of the complex complementary error function but here we give the expressions in terms of the Faddeeva function enabling e?cient use of the dedicated algorithms to compute the Faddeeva function. Expressions are given for both lossy and lossless medium parameters and it is shown that the expression for the lossless case can be evaluated twice as fast as the expression for the lossy case. Two case studies are presented to validate the proposed method and to show that the time required for computing the method of moments (MoM) integrals that require evaluation of the 2D-QPGF becomes comparable to the time required for computing the MoM integrals that require evaluation of the aperiodic Green function.
关键词： Faddeeva function,surface integral-equation (SIE) method,Ewald representation,method of moments (MoM),2D-quasi-periodic Green function (2D-QPGF)
更新于2025-09-23 15:19:57
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Fast algorithms for integral formulations of steady-state radiative transfer equation
摘要： We investigate integral formulations and fast algorithms for the steady-state radiative transfer equation with isotropic and anisotropic scattering. When the scattering term is a smooth convolution on the unit sphere, a model reduction step in the angular domain using the Fourier transformation in 2D and the spherical harmonic transformation in 3D significantly reduces the number of degrees of freedoms. The resulting Fourier coefficients or spherical harmonic coefficients satisfy a Fredholm integral equation of the second kind. We study the uniqueness of the equation and proved an a priori estimate. For a homogeneous medium, the integral equation can be solved efficiently using the FFT and iterative methods. For an inhomogeneous medium, the recursive skeletonization factorization method is applied instead. Numerical simulations demonstrate the efficiency of the proposed algorithms in both homogeneous and inhomogeneous cases and for both transport and diffusion regimes.
关键词： FFT,radiative transfer,Fredholm integral equation,anisotropic scattering,Fast algorithm,recursive skeletonization
更新于2025-09-19 17:15:36
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Roblems, Methods, and Algorithms in Models of Physical Fundamentals of Elements of Optical Computers
摘要： This paper considers two variants of problems that arise in developing optical computers. The first variant is related to the mathematical analysis of problems of optical bistability in the case of multibeam interaction of laser radiation in nonlinear media. The existence of optical bistability is confirmed by the results of solving the boundary value problem for a system of nonlinear ordinary differential equations. In the general case of an arbitrary nonstationary process, the problem is reduced to solving a system of two nonlinear integral equations with respect to complex amplitudes describing interference patterns. The second variant of problems is devoted to studying the absorption and scattering of light by nanomaterials. As a result, a multidimensional integral equation was obtained for the complex amplitude of the electric field. A fundamentally important feature of this equation is its singularity inside a nanoparticle.
关键词： optical computer,laser interaction,mathematical model,bistability,integral equation
更新于2025-09-19 17:15:36
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A singularity free and derivative free approach for Abel integral equation in analyzing the laser-induced breakdown spectroscopy
摘要： In order to make a detailed analysis of the laser-induced breakdown spectroscopy (LIBS), we present a new approach which has advantages of singularity free and derivative free for solving the Abel integral equation. After presenting the model describing the LIBS, a collocation method is applied and two main steps are introduced. First, the Abel integral equation is transformed to a singularity free and derivative free integral equation. Then, by expanding the solution of the integral equation to a polynomial of degree n, the solution can be approximated by a linear system established by the collocation method. Our approach is suitable for dealing with LIBS problem for any form of the measured intensity. In particular, the method is insensitive to the noisy intensity data. A convergence analysis is also given to show the validity of the method and numerical examples are provided to show its efficiency and accuracy.
关键词： spectrum,laser-induced breakdown spectroscopy (LIBS),Abel integral equation,plasma
更新于2025-09-19 17:13:59