Integral Equation

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Weng Cho Chew - One of the best experts on this subject based on the ideXlab platform.

  • augmented electric field Integral Equation for inhomogeneous media
    IEEE Antennas and Wireless Propagation Letters, 2017
    Co-Authors: Yanlin Li, Weng Cho Chew
    Abstract:

    The augmented electric-field Integral Equation is extended for the analysis of inhomogeneous media at low frequencies. The internal surface Integral Equation for inhomogeneous region is derived from the vector potential ( ${{\mathbf A}}$ ) and the scalar potential ( ${{\mathbf \Phi }}$ ) Equations, which are free of low-frequency breakdown. In the new Equations, Green's functions of ${{\mathbf A}}$ and ${{\mathbf \Phi }}$ for inhomogeneous media are incorporated. Due to the absence of the analytic solutions, Green's functions for ${{\mathbf A}}$ and ${{\mathbf \Phi }}$ are solved numerically with the finite-element method and represented in matrix forms. Numerical examples are presented to demonstrate the validity of the proposed scheme in the study of inhomogeneous objects at low frequencies.

  • theory of characteristic modes based on potential based Integral Equation
    URSI International Symposium on Electromagnetic Theory, 2016
    Co-Authors: Qin S Liu, Weng Cho Chew, Sheng Sun, Qi I Dai, Li Jun Jiang
    Abstract:

    The characteristic mode analysis is presented based on the potential-based Integral Equation, where the vector potential Equation and the scalar potential are formulated separately and solved in tandem. Accordingly, the theory of the characteristic modes, originated from the electrical field Integral Equation (EFIE), can be analyzed for the novel potential-based Integral Equation system with the contributions from different components in EFIE.

  • an enhanced augmented electric field Integral Equation formulation for dielectric objects
    IEEE Transactions on Antennas and Propagation, 2016
    Co-Authors: Tian Xia, Weng Cho Chew, Hui Gan, Zhiguo Qian, Michael Wei, Henning Braunisch, Kemal Aygun, Alaeddin Aydiner
    Abstract:

    A full-wave surface Integral Equation (SIE) method based on the augmented electric-field Integral Equation (A-EFIE) for dielectric objects with low-frequency stability is presented in this paper. Motivated by the A-EFIE formulation for perfect electric conductor (PEC), the internal and external problems are both augmented with the current continuity Equation and renormalized to eliminate the low-frequency breakdown. Although the magnetic-field Integral Equation operator $\mathcal{K}$ is free of low-frequency breakdown, its matrix form is ill-conditioned and unsolvable if the traditional Rao–Wilton–Glisson (RWG) basis function is used as the testing and basis functions. As a remedy, the Buffa–Christiansen (BC) basis function is introduced to alleviate this testing issue. After this treatment, the matrix form of operator $\mathcal{K}$ is well conditioned. To solve problems with a large number of unknowns, a preconditioning scheme is introduced to accelerate the convergence and the mixed-form fast multipole algorithm (FMA) is adopted to accelerate the matrix vector product.

  • characteristic mode theory based on combined field Integral Equation
    International Symposium on Antennas and Propagation, 2015
    Co-Authors: Qi I Dai, Weng Cho Chew, Qin S Liu, Hui Gan, Sheng Sun
    Abstract:

    Characteristic mode theory is usually formulated on top of the electric field Integral Equation. We present in this paper a combined field Integral Equation based characteristic mode theory which is immune to the internal resonance corruption when the characteristic modes of closed perfectly conducting surfaces are iteratively solved for. Numerical results are presented to validate the proposed formulation. This work may offer efficient solutions to characteristic mode analysis which involves electrically large closed surfaces.

  • combined field Integral Equation based theory of characteristic mode
    IEEE Transactions on Antennas and Propagation, 2015
    Co-Authors: Qi I Dai, Qin S Liu, Hui Gan, Weng Cho Chew
    Abstract:

    Conventional electric field Integral Equation-based theory is susceptible to the spurious internal resonance problem when the characteristic modes (CMs) of closed perfectly conducting objects are computed iteratively. In this paper, we present a combined field Integral Equation-based theory to remove the difficulty of internal resonances in CMs analysis. The electric and magnetic field Integral operators are shown to share a common set of nontrivial characteristic pairs (values and modes), leading to a generalized eigenvalue problem which is immune to the internal resonance corruption. Numerical results are presented to validate the proposed formulation. This work may offer efficient solutions to CM analysis which involves electrically large closed surfaces.

Vladimir Okhmatovski - One of the best experts on this subject based on the ideXlab platform.

  • novel single source surface Integral Equation for scattering problems by 3 d dielectric objects
    IEEE Transactions on Antennas and Propagation, 2018
    Co-Authors: Farhad Sheikh Hosseini Lori, Anton Menshov, Reza Gholami, Jamiu Mojolagbe, Vladimir Okhmatovski
    Abstract:

    A new single-source Integral Equation is proposed for the solution of electromagnetic wave scattering problems. The traditional volume electric field Integral Equation is reduced to the new single-source surface Integral Equation by representing the electric field inside the scatterer as a superposition of spherical waves emanating from its boundary. Such new Integral Equation formulation has been previously developed for the scalar and vector cases of 2-D scattering problems. In this paper, the 3-D form of this new single-source surface Integral Equation for scattering on homogeneous nonmagnetic dielectrics is proposed. Detailed description of the method of moments (MoMs) discretization and its resultant matrices is presented. In order to validate the new Integral Equation formulation and verify the accuracy of its MoMs discretization, its solution is compared against the analytical Mie series solution and fields computed using the commercial electromagnetic analysis software.

  • surface volume surface electric field Integral Equation for magneto quasi static analysis of complex 3 d interconnects
    IEEE Transactions on Microwave Theory and Techniques, 2014
    Co-Authors: Anton Menshov, Vladimir Okhmatovski
    Abstract:

    A novel single-source surface-volume-surface Integral Equation is proposed for accurate broadband resistance and inductance extraction in 3-D interconnects. The new Equation originates in the volume Integral Equation (VIE) traditionally used for magneto-quasi-static modeling of current flow in 3-D wires. The latter is reduced to a surface Integral Equation by representing the electric field inside each conductor segment as a superposition of cylindrical waves emanating from the conductor's boundary. As no approximation is utilized and all underlying boundary conditions and pertinent Equations are satisfied in the reduction, the new Integral Equation is rigorously equivalent to the solution of the traditional volume electric field Integral Equation. The rigorous nature of the proposed single-source surface Integral Equation is corroborated numerically. In this paper, a detailed description of the method of moments discretization for the proposed surface Integral Equation is also presented. Numerical solution of the proposed surface Integral Equation for a 12-conductor bond-wire package is used to demonstrate the accuracy of the method and its computational benefits compared to the traditional solution based on the VIE.

Anton Menshov - One of the best experts on this subject based on the ideXlab platform.

  • novel single source surface Integral Equation for scattering problems by 3 d dielectric objects
    IEEE Transactions on Antennas and Propagation, 2018
    Co-Authors: Farhad Sheikh Hosseini Lori, Anton Menshov, Reza Gholami, Jamiu Mojolagbe, Vladimir Okhmatovski
    Abstract:

    A new single-source Integral Equation is proposed for the solution of electromagnetic wave scattering problems. The traditional volume electric field Integral Equation is reduced to the new single-source surface Integral Equation by representing the electric field inside the scatterer as a superposition of spherical waves emanating from its boundary. Such new Integral Equation formulation has been previously developed for the scalar and vector cases of 2-D scattering problems. In this paper, the 3-D form of this new single-source surface Integral Equation for scattering on homogeneous nonmagnetic dielectrics is proposed. Detailed description of the method of moments (MoMs) discretization and its resultant matrices is presented. In order to validate the new Integral Equation formulation and verify the accuracy of its MoMs discretization, its solution is compared against the analytical Mie series solution and fields computed using the commercial electromagnetic analysis software.

  • surface volume surface electric field Integral Equation for magneto quasi static analysis of complex 3 d interconnects
    IEEE Transactions on Microwave Theory and Techniques, 2014
    Co-Authors: Anton Menshov, Vladimir Okhmatovski
    Abstract:

    A novel single-source surface-volume-surface Integral Equation is proposed for accurate broadband resistance and inductance extraction in 3-D interconnects. The new Equation originates in the volume Integral Equation (VIE) traditionally used for magneto-quasi-static modeling of current flow in 3-D wires. The latter is reduced to a surface Integral Equation by representing the electric field inside each conductor segment as a superposition of cylindrical waves emanating from the conductor's boundary. As no approximation is utilized and all underlying boundary conditions and pertinent Equations are satisfied in the reduction, the new Integral Equation is rigorously equivalent to the solution of the traditional volume electric field Integral Equation. The rigorous nature of the proposed single-source surface Integral Equation is corroborated numerically. In this paper, a detailed description of the method of moments discretization for the proposed surface Integral Equation is also presented. Numerical solution of the proposed surface Integral Equation for a 12-conductor bond-wire package is used to demonstrate the accuracy of the method and its computational benefits compared to the traditional solution based on the VIE.

Giuseppe Vecchi - One of the best experts on this subject based on the ideXlab platform.

  • Dual-Surface Electric Field Integral Equation Solution of Large Complex Problems
    IEEE Transactions on Antennas and Propagation, 2016
    Co-Authors: Muhammad Zubair, Matteo Alessandro Francavilla, Deping Zheng, Francesca Vipiana, Giuseppe Vecchi
    Abstract:

    The Integral Equation analysis of large perfect electric conductor bodies is commonly formulated in terms of combined field Integral Equations (CFIE) that avoid spurious internal resonances. The dual-surface electric field Integral Equation (DSEFIE) is a less employed alternative approach; we discuss here how to cure its shortcomings and enhance its advantages over the CFIE for large bodies of nontrivial geometrical complexity. We study the convergence and accuracy of the DSEFIE also with respect to the current state of the art in the testing of the magnetic field Integral Equation. Examples of applications to large and realistic composite structures show the effectiveness of the proposed approach.

Pasi Ylaoijala - One of the best experts on this subject based on the ideXlab platform.

  • discretization of volume Integral Equation formulations for extremely anisotropic materials
    IEEE Transactions on Antennas and Propagation, 2012
    Co-Authors: Johannes Markkanen, Pasi Ylaoijala, Ari Sihvola
    Abstract:

    A stable volume Integral Equation formulation and its discretization for extremely anisotropic materials is presented. The volume Integral Equations are written in terms of the volume equivalent currents. The equivalent currents are expanded with piecewise constant basis functions, and the Galerkin's scheme is applied for testing the Equations. Numerical results show that the behavior of the formulation is more stable than the behaviors of the more conventional volume Integral Equation formulations based on fluxes or fields, when the scatterer is extremely anisotropic. Finally, the developed method is applied to analyze a highly anisotropic material interface which approximates the ideal DB boundary.

  • current and charge Integral Equation formulation
    IEEE Transactions on Antennas and Propagation, 2006
    Co-Authors: Matti Taskinen, Pasi Ylaoijala
    Abstract:

    A new stable frequency domain surface Integral Equation formulation is proposed for the three dimensional electromagnetic scattering of composite metallic and dielectric objects. The developed formulation does not suffer from the low frequency breakdown and leads to a well balanced and stable system on a wide frequency band. Surface charge densities are used as unknowns in addition to the traditional surface current densities. The balance of the system is achieved by using normalized field quantities and by enforcing the continuity of the fields across the boundaries with carefully chosen scaling factors. The linear dependence between the currents and charges is taken into account with an Integral operator, and the linear dependence in charges is removed with the deflation method. A combined field Integral Equation form of the formulation is proposed to remove the internal resonance problem associated to the closed metallic objects. Due to the good balance in the new formulation, fast converging iterative solutions on a very wide frequency band can be obtained. The new formulation and its convergence is verified with numerical examples.

  • surface Integral Equation method for general composite metallic and dielectric structures with junctions
    Progress in Electromagnetics Research-pier, 2005
    Co-Authors: Pasi Ylaoijala, Matti Taskinen, Jukka Sarvas
    Abstract:

    The surface Integral Equation method is applied for the electromagnetic analysis of general metallic and dielectric structures of arbitrary shape. The method is based on the EFIE-CFIE-PMCHWT Integral Equation formulation with Galerkins type discretization. The numerical implementation is divided into three independent steps: First,the electric and magnetic field Integral Equations are presented and discretized individually in each non-metallic subdomain with the RWG basis and testing functions. Next the linearly dependent and zero unknowns are removed from the discretized system by enforcing the electromagnetic boundary conditions on interfaces and at junctions. Finally,the extra Equations are removed by applying the wanted Integral Equation formulation,and the reduced system is solved. The division into these three steps has two advantages. Firstly,it greatly simplifies the treatment of composite objects with multiple metallic and dielectric regions and junctions since the boundary conditions are separated from the discretization and Integral Equation formulation. In particular,no special junction basis functions or special testing procedures at junctions are needed. Secondly,the separation of the Integral Equation formulation from the two previous steps makes it easy to modify the procedure for other formulations. The method is validated by numerical examples.