Equivalence Principle Algorithm Research Articles

Research on electromagnetic scattering and radio wave propagation algorithm based on machine learning in half-space

In this paper, to investigate the problem of radio wave propagation in complex environments, a new algorithm is proposed based on the equivalence principle algorithm and the domain decomposition method to rapidly and accurately predict electromagnetic scattering and radio wave propagation in half-space. First, equivalent surfaces are introduced to decompose the obstacle region and replace the scattering effect of obstacles within the equivalent surfaces with equivalent input and output electromagnetic currents. Then, the operator S, representing the relationship between the input and output equivalent electromagnetic currents on the equivalent surfaces, and the operator T, representing the interactions between the equivalent electromagnetic currents on each equivalent surface, are derived; this allows the calculation process of the overall spatial field in a complex environment to be simplified to the iterative calculation process of operators S and T. To reduce the complexity of calculating S, a neural network embedded with physical information is introduced to replace the calculation process. Finally, the training results are applied to an example and compared with the theoretical numerical results yielded by the method of moments in different cases with obstacles. The results reveal that the new method proposed in this paper is highly accurate and achieves a substantial improvement in calculation speed. Therefore, our proposed algorithm provides a new and reliable method for calculating the spatial field in complex environments.

Reduced-order models for array structures mounted on platforms with parameters variations

A hybrid model order reduction (MOR) method is developed to calculate the electromagnetic characteristic of array structures mounted on platforms with parameters variations. The reduced-order model (ROM) of the platform is generated as a reduced-order input-output matrix during the offline stage. Using the equivalence principle algorithm (EPA), the ROM of array is generated by transferring the unknowns on the elements to equivalence surfaces. The frequency and material independent reactions (FMIR) method is applied to support the sweep of array material parameters. In the online stage, when the array positions vary in the input region, both of the array and platform ROMs can be used repeatedly. When the array materials vary in the input region, the platform ROM and geometry dependent matrices of EPA are reusable. Therefore, the computational cost can be reduced significantly. Comparing the proposed method to commercial solver, two numerical results are given to show the efficiency.

Fast Frequency and Material Parameters Sweep for the Calculation of Array Structures

In this letter, an efficient hybrid method is proposed to analyze array structures when frequency and material parameters sweep. Using the frequency and material independent reactions method, the impedance matrix is split into the product of a geometry dependent matrix and a wavenumber dependent factor. The geometry dependent matrix needs to be solved and stored only once when parameters sweep. However, the memory requirement will be very huge for electrically large objects such as array structures. To deal with this problem, the equivalence principle algorithm is used to decompose the array into subdomains and transfer unknowns on the subdomains to the unknowns on the equivalence surfaces. Furthermore, the characteristic basis functions are constructed on the equivalence surfaces to reduce the number of unknowns and matrix storage significantly. Several numerical results are shown to demonstrate the accuracy and efficiency of the proposed method.

Modeling of Multiscale Wave Interactions Based on an Iterative Scheme of MoM-PO-EPA Algorithm

Electromagnetic modeling of multiscale wave interactions is a challenging task. This is because wave physics exhibit different characteristics at different length scales that require suitable modeling algorithms. Combining these algorithms to model multiscale wave physics requires careful design and tuning. In this study, we investigated a hybrid algorithm based on the method of moment (MoM), iterative physical optics (IPO) approximation, and the equivalence principle algorithm (EPA). EPA modeled targets with details, MoM modeled targets with moderate scales, and IPO modeled electrically large scatterers. The virtual equivalence surfaces in EPA worked as interfaces between relatively large and small scatterers. An iterative scheme is used to solve the targets instead of a matrix equation with large dimensions. This algorithm achieved a good balance between accuracy and efficiency. Numerical examples of modeling the plane-wave scattering of multiscale targets verify its performance for 2D and 3D problems. The iterative scheme can become faster and need less memory usage when solving the multiscale scatterers.

An Efficient Integral Equation Model-Order Reduction Method for Complex Radiation Problem

In this letter, an efficient integral equation model-order reduction method is proposed to analyze complex radiation problem. In the offline stage, the randomized singular value decomposition and discrete empirical interpolation method are used to construct a reduced-order model (ROM) for the platform. In the online stage, the equivalence principle algorithm is used to transfer unknowns on the antenna to the unknowns on the equivalence surface. The modified tap basis scheme is applied to decompose the antenna from the platform and solve the current continuity challenge when the platform is cut off by equivalence surface. When the antenna position is changed in the input region, only the tap region needs to be remeshed and resolved. The ROM of platform, antenna, and equivalence surface are reusable in the online computation, which can reduce the computational complexity significantly. Numerical results demonstrate the accuracy and efficiency of the proposed method.

Fast Computation of Electromagnetic Scattering From a Metal–Dielectric Composite and Randomly Distributed BoRs Cluster

An efficient equivalence principle algorithm with spherical equivalent source (SEPA) is proposed to analyze the electromagnetic scattering from a metal–dielectric composite and randomly distributed bodies of revolution (BoRs) cluster, which is called SEPA-CBoR for short. Due to the rotationally symmetrical property, the electromagnetic currents on the BoRs and the equivalence spheres (ESs) are all expanded by the basis functions of BoR. In this way, the self-action and the interaction can be both calculated by using the method of moment for BoR (BoR-MoM). With the repeatability fully used, the self-action for the BoRs with the same size just needs to be calculated once. Moreover, the interaction can also be got once when the size and relative displacement vector of their corresponding ESs are the same. Since these self-action/interaction matrices are constructed in mutually orthogonal Fourier modes, the entire problem is eventually solved by a couple of small matrix equations independently. As a result, the SEPA-CBoR method can greatly save the memory requirement and solution time. Several numerical examples are presented to demonstrate the accuracy and efficiency for the composite BoRs cluster problems. Especially, it is helpful to distinguish the fake targets with the accurate echo signs obtained from the efficient SEPA-CBoR method.

Electromagnetic scattering from an arbitrarily shaped PEC object coated by spherical dielectric material using equivalence principle algorithm

A new method is presented for the analysis of electromagnetic scattering from arbitrarily shaped PEC object coated by homogeneous spherical dielectric material. The analysis of the internal PEC objects is performed using the equivalence principle algorithm (EPA). First, the scattering operator of EPA is evaluated for the PEC object in terms of RWG basis functions where the background is filled by coating material. Then a translation procedure is introduced to translate scattering operator evaluated in terms of RWG basis functions to a new scattering operator in terms of spherical wave harmonics (SWHs). This new scattering operator relates SWH coefficients of the scattered wave by internal PEC to those of the incident wave. By invoking the boundary conditions on the surface of spherical coating using the mode-matching technique, the coefficients of the scattered wave outside the coating material are evaluated. Since the scattering operator is independent from the coating radius, the problem may be solved by only analysis of boundary conditions on the surface of spherical coating for various values of coating radii without needing to repeat the analysis of internal PEC object. Several numerical examples are investigated to evaluate validity and efficiency of the proposed method.

Generalized Solver Hybridization Using Equivalence Principle Algorithm

The simulation of antennas often necessitates modeling the effect of nearby electrically large structures. Such structures are often unsuitable for modeling with the same technique as used on the antenna because of the prohibitive required unknown count. First-principles models of antennas (or other key features) must then be augmented with approximate models of the larger auxiliary structures, usually with high-frequency asymptotic models. The surface equivalence principle is applied to linear-media multiple scattering without regard to the formulations used for each contained domain. A Schur complement is then applied to convert the homogeneous medium equivalent problem into a inhomogeneous medium equivalent problem. The Schur complement form supports application of approximate models and makes the scattering physics plain. The results are provided for two cases modeled with the equivalence principle algorithm (EPA) hybridized with physical optics (PO) approximation.

Application of Equivalence Principle for EM Scattering From Irregular Array of Arbitrarily Oriented PEC Scatterers Using Both Translation and Rotation Addition Theorems

Electromagnetic scattering from irregular array of arbitrarily oriented PEC scatterers is investigated using a novel domain decomposition method based on equivalence principle algorithm (EPA) in conjunction with addition theorems for spherical wave harmonics (SWHs). Each element is considered to be enclosed by a spherical equivalence surface as a single domain. The primary unknowns on each element are replaced by the equivalent electric and magnetic current distributions on the equivalence sphere in terms of RWG basis functions. From these current distributions, the scattered field outside its equivalence sphere is evaluated in terms of SWHs in the local coordinates system fixed to each element body. The SWHs in rotated local coordinates are translated as a new set of SWHs in other local coordinates with the same origin but axes parallel to the global coordinate’s axes using the rotation addition theorem. Furthermore, the mutual coupling effects among the separated domains are considered using the translation addition theorem for parallel local coordinate systems. It is shown that the proposed method effectively reduces the computational costs by reducing the number of unknowns versus the conventional EPA. The efficiency and validity of the proposed method are investigated through several numerical examples.

Implementation of the Equivalence Principle Algorithm for Potential Integral Equations

A novel implementation of the equivalence principle algorithm (EPA) employing potential integral equations (PIEs) is presented. EPA is generalized to be compatible with PIEs that are used to formulate inner problems inside equivalence surfaces. Based on the stability of PIEs, the resulting EPA-PIE implementation is suitable for low-frequency problems involving dense discretizations with respect to wavelength. Along with the formulation and a clear demonstration of the EPA-PIE mechanism, high accuracy, stability, and efficiency of the implementation are presented on canonical problems.

Electromagnetic Multiple PEC Object Scattering Using Equivalence Principle and Addition Theorem for Spherical Wave Harmonics

A novel domain decomposition procedure is presented to analyze the electromagnetic wave multiple scattering among separate PEC objects. The method is based on the equivalence principle algorithm (EPA) that transfers the primary unknowns on the objects to the unknowns on the equivalence surfaces. Each equivalence surface is considered to be a spherical surface encompassing a PEC object. Inside the equivalence spheres, the analysis is performed based on the Rao–Wilton–Glisson (RWG) basis functions where the electromagnetic interactions outside them are considered by means of the addition theorem for spherical wave harmonics (SWHs). The translation procedures are presented to translate the RWG basis functions to SWHs and vice versa. The reduction of unknowns in the presented method versus the conventional EPA (which uses translation operators among equivalence surfaces) shows its efficiency. Some numerical examples are presented to evaluate the efficacy of the proposed approach. The acceptable consistency among the results of the proposed method and the conventional EPA as well as the direct method of moments validates the proposed method.

Improved Generalized Single-Source Tangential Equivalence Principle Algorithm with Contact-Region Modeling Method for Array Structures

An improved generalized single-source tangential equivalence principle algorithm (GSST-EPA) is proposed for analyzing array structures with connected elements. In order to use the advantages of GSST-EPA, the connected array elements are decomposed and computed by a contact-region modeling (CRM) method, which makes that each element has the same meshes. The unknowns of elements can be transferred onto the equivalence surfaces by GSST-EPA. The scattering matrix in GSST-EPA needs to be solved and stored only once due to the same meshes for each element. The shift invariant of translation matrices is also used to reduce the computation of near-field interaction. Furthermore, the multilevel fast multipole algorithm (MLFMA) is used to accelerate the matrix-vector multiplication in the GSST-EPA. Numerical results are shown to demonstrate the accuracy and efficiency of the proposed method.

Volume integral equation equivalence principle algorithm domain decomposition with body of revolution equivalence surface

A novel equivalence principle algorithm (EPA) domain decomposition method previously for the surface integral equation is explored for volume integral equation in this work. The whole object is decomposed into several subdomains, the equivalence spheres are automatically produced to enclose each subdomain. The Rao–Wilton–Glisson (RWG) and body of revolution (BoR) basis functions are defined on the equivalence sphere surface. The equivalence currents defined on the RWG basis functions are evaluated with multilevel fast multipole algorithm, and then the currents defined on the RWGs can be projected onto the BoR basis functions. Compared with surface integral equation EPA-BoR algorithm, the ratio of the number of average original unknowns in each subdomain with respect to the equivalence unknowns is relatively larger, which leads to significant reduction of computations. Numerical simulations validate the accuracy and efficiency of the proposed method.

Solution box: SOLBOX-09, SOLBOX-10

Periodicity is a major property of many structures in electromagnetic applications, such as antenna arrays [1], frequency-selective surfaces, metamaterials [2], and photonic crystals [3]. Array elements (unit cells, antennas, etc.) are periodically arranged in order to enhance the response of a single element or to gain new capabilities due to interactions between them. Naturally, electromagnetic simulations of periodic structures have a long history in the literature. This is still an active area as the structures become more complicated and require more sophisticated (accurate, efficient, stable) tools for precise analysis. When the structure is infinitely large, and particularly when the periodicity is sub-wavelength, there are excellent tools based on Fourier series and finite-diff erence models, e.g., see [4] and [5]. Similarly, when the elements can be represented pointwise with or without interactions, there are analytical (e.g., using array factor) and semi-analytical (e.g., using lumped elements and/or transmission-line models) techniques. On the other hand, challenges arise when each element is a complex electromagnetic problem itself while it needs to interact with other complex elements. In addition, if the finiteness is an important geometric parameter of a periodic structure, its full-wave models may lead to large-scale problems that can be difficult to solve numerically. In such cases, it is tempting to substitute high-order mathematical models for the elements [6], specifically by isolating their inner dynamics to derive the required equivalence [7] within the decomposed models. A well-known method in this path is called the Equivalence-Principle Algorithm (EPA), which has been used and improved (e.g., hybridized with or used in other methods) by numerous researchers [7–11].

Space mapping optimisation of 2D array elements arrangement to reduce the radar cross‐scattering

The authors propose a novel aggressive space mapping (ASM) algorithm for the two-dimensional antenna array elements arrangement to reduce the antenna array radar cross-scattering; meanwhile, to ensure the radiation performance. The coarse model is evaluated with genetic algorithm and analytic formulations, the fine model verification is computed with the full wave method of moments (MoMs) enhanced by the equivalence principle algorithm (EPA). The high-order basis functions and matrix compression technique are employed in the EPA-MoM for further accelerations. Only small number of iterations in the ASM optimisation is required for the fine model verification, to achieve the optimisation requirements. Numerical tests of the horn antenna array optimisation with moderate time are presented to show the efficiency of the proposed algorithm.

Full Wave Modeling of Array Structures Using Generalized Single-Source Tangential Equivalence Principle Algorithm

The generalized single-source tangential equivalence principle algorithm (GSST-EPA) is proposed to solve the electromagnetic scattering of array structures with very small distance or even connected elements. For the traditional EPA scheme, it is difficult to deal with those situations. Based on source reconstruction method (SRM), the new GSST-EPA can be used to solve this problem efficiently. This scheme can also reduce the number of unknowns by half via the extinction theorem and keep the good accuracy by using tangential field projection. Furthermore, the multilevel fast multipole algorithm (MLFMA) is used to accelerate the matrix-vector multiplication in the GSST-EPA. Several numerical results are given to demonstrate the accuracy and efficiency of the proposed method.

Improving the Accuracy of Single-Source Equivalence Principle Algorithm by Using Tangential Field Projection Scheme

ABSTRACTThe single-source equivalence principle algorithm has been proposed as an efficient solution for analyzing large array structures. However, due to the discretization error of the identity operator, the accuracy of single-source equivalence principle algorithm is not good. In this paper, a single-source tangential equivalence principle algorithm is proposed to improve the accuracy by using the tangential field projection scheme. Based on this scheme and extinction theorem, a new relation between equivalence electric current and magnetic current can be established which has more accurate discretization. Moreover, it is demonstrated that the single-source equivalence principle algorithm can be derived from one type of single-source tangential equivalence principle algorithm. Numerical examples are designed to demonstrate the accuracy improvement of the proposed method.

Analysis of connected structures using equivalence principle algorithm with source reconstruction method

ABSTRACTA new domain decomposition scheme based on equivalence principle algorithm (EPA) is proposed for analyzing electromagnetic scattering from connected structures. The EPA transforms the unknown of inside scatterers to the unknown on the equivalence surfaces which enclose the scatterers. The challenge arises when the equivalence surface intercepts the connected scatterers, because the current will be singular at the connection that is hard to model. In this paper, a new scheme based on source reconstruction method (SRM) is introduced to deal with the connected problems. This scheme can avoid the current singularity and keep the good convergence of EPA equations. Furthermore, generalized EPA (GEPA) is proposed to improve the theory of EPA and the ability to solve real life problems. Numerical results demonstrate the accuracy and efficiency of the proposed method.

An Efficient Marching-on-in-Degree Solution of Transient Multiscale EM Scattering Problems

A marching-on-in-degree (MOD)-based time-domain domain decomposition method is proposed to efficiently analyze the transient electromagnetic scattering from electrically large multiscale targets. The algorithm starts with an octree that divides the whole scattering target into several subdomains. Then using the equivalence principle algorithm, each subdomain is enclosed by an equivalence sphere (ES), where both the RWG and BoR spatial basis functions are employed to expand the unknown currents. The interactions of the near-field subdomains are directly calculated by the method of moments, while the far-field interactions can be converted into the interactions of corresponding ESs. This scheme implicitly satisfies the current continuity condition, and the convergence can be accelerated as well. By harnessing the rotational symmetry of the ESs, the computational resources are reduced significantly compared with the traditional MOD method. Several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed algorithm.

Hybridization of Periodic Equivalence Principle Algorithm, Equivalence Principle Algorithm, and Physical Optics for Analysis of Large Finite Antenna Array with Perfect Electrically Conducting Object

ABSTRACTIn the solution of a radiation problem on a large-scale antenna array with a large perfect electrically conducting object, the equivalence principle algorithm hybridized with physical optics has been used to accelerate the calculation. However, the efficiency of this hybridization will be low if the number of elements in the antenna array is large. This article proposes a novel method to speed up the equivalence principle algorithm hybridized with physical optics by introducing the periodic equivalence principle algorithm. The calculation of the couplings among the elements will be simplified, and the elapsed time will decrease. At the same time, the total memory required will be saved.