Hanru Shao

Hybrid Tangential Equivalence Principle Algorithm with MLFMA for Analysis of Array Structures

In this paper, a novel technique is proposed to solve the electromagnetic scattering by large flnite arrays by combining the tangential equivalence principle algorithm (T-EPA) with multilevel fast multipole algorithm (MLFMA). The equivalence principle algorithm (EPA) is a kind of domain decomposition scheme for the electromagnetic scattering and radiation problems based on integral equation (IE). For the array with same elements, only one scattering matrix needs to be constructed and stored. T-EPA has better accuracy than the original EPA. But the calculation for the impedance matrix in T-EPA is still time consuming. MLFMA is proposed to speed up the matrix-vector multiplication in T-EPA. Numerical results are shown to demonstrate the accuracy and e-ciency of the proposed technique.

Analyzing Large-Scale Arrays Using Tangential Equivalence Principle Algorithm With Characteristic Basis Functions

In this paper, the tangential equivalence principle algorithm (T-EPA) combined with characteristic basis functions (CBFs) is presented to analyze the electromagnetic scattering of large-scale antenna arrays. The T-EPA is a kind of domain decomposition scheme for the electromagnetic scattering and radiation problems based on integral equation (IE). CBFs are macrobasis functions which are constructed by conventional local basis functions. By utilizing CBFs together with the T-EPA, the scattering analysis of large-scale arrays will be much more efficient with decreased unknowns compared with the original T-EPA. Further, the multilevel fast multipole algorithm (MLFMA) is applied to accelerate the matrix-vector multiplication in the T-EPA. Numerical results are shown to demonstrate the accuracy and efficiency of the proposed technique.

Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations

Hierarchical (-) matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE-) based computational electromagnetics, -matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solve -matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure of -matrices are also available along with high efficiency and accuracy, which is a unique advantage compared to other fast algorithms. In this paper, a novel sparse approximate inverse (SAI) preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solving -matrices system in electromagnetic applications, and a group of parallel fast direct solvers are developed for dealing with multiple right-hand-side cases. Finally, numerical experiments are given to demonstrate the advantages of the proposed multilevel preconditioner compared to conventional “single level” preconditioners and the practicability of the fast direct solvers for arbitrary complex structures.

Fast Simulation of Array Structures Using T-EPA With Hierarchical LU Decomposition

In this letter, a novel technique that combines the tangential equivalence algorithm (T-EPA) with hierarchical (H-) LU decomposition is proposed to solve the electromagnetic problems of large arrays. The T-EPA is a kind of domain decomposition method based on integral equation. The characteristic basis functions (CBFs) have been used on equivalence surface to reduce the number of unknowns. Multilevel fast multipole algorithm (MLFMA) has also been used to accelerate the matrix-vector multiplication. However, the inversion of dense matrix required in T-EPA is very time-consuming. Here, an efficient H-LU decomposition based on H-matrix framework is proposed to reduce the computational complexity of the inversion of dense matrix. Numerical results are shown to demonstrate the accuracy and efficiency of the proposed method.

Simulation of multiscale structures using equivalence principle algorithm with grid-robust higher order vector basis

In this paper, equivalence principle algorithm (EPA) with grid-robust higher order vector basis (GRHOVB) is proposed to solve the multi-scale problems. The EPA is a kind of domain decomposition method which transfers the interaction of the objects into interaction between virtual equivalence surfaces. Compared with traditional Curvilinear Rao-Wilton-Glisson (CRWG) function, GRHOVB can be used on the equivalence surface to reduce the number of unknowns and also improve the accuracy. The tap basis is utilized to deal with current continuity when the object is intercepted by an equivalence surface. The equations are simplified further to improve the tap basis scheme. Numerical results are shown to demonstrate the accuracy and efficiency of the proposed method.

Single-Source Equivalence Principle Algorithm for the Analysis of Complex Structures

In this letter, a novel single-source equivalence principle algorithm is presented. In the traditional equivalence principle algorithm (EPA), double sources, which are equivalence electric and magnetic currents, are constructed on the equivalence surface to replace the currents of the enclosed scatterers. According to the extinction theorem, electric current is related to magnetic current. Therefore, only electric or magnetic current, called single-source, is the final unknown on the equivalence surface. The accuracy of two kinds of single-source EPA is investigated. Multilevel Fast Multipole Algorithm (MLFMA) is used to accelerate the couplings between equivalence surfaces. Numerical results demonstrate the accuracy and efficiency of the proposed method.

Electromagnetic Analysis of Large Scale Periodic Arrays Using a Two-Level CBFs Method Accelerated With FMM-FFT

To realize efficient analysis of large scale planar periodic arrays, a two-level characteristic basis functions method accelerated with fast multipole method-fast Fourier transform (FMM-FFT) is developed in this paper. The characteristic basis functions (CBFs) for each element are constructed in a two-level framework, in which the CBFs construction based on plane wave derivation for single element at child level and the CBFs construction based on local interaction between array elements at father level are combined. The number of unknowns is reduced significantly by the two-level CBFs. Further, FMM-FFT is applied to expedite the computation of interaction between elements. Numerical results of large scale planar periodic arrays are given to demonstrate the validity and efficiency of the present method.

Single-source EPA for electromagnetic scattering by array structures

In traditional equivalence principle algorithm (EPA), the unknown currents of the scatterers are replaced by equivalent electric and magnetic currents on the virtual equivalence surface. In this paper, a single electric/magnetic current on the equivalence surface is used to generate the scattered field. According to the extinction theorem, a relation between the equivalence electric current and magnetic current can be established, which is similar to generalized impedance boundary condition (GIBC). Therefore, only the electric/magnetic current is the unknown in the final EPA formulation. Numerical results for the array structures are obtained to demonstrate the accuracy and efficiency of the proposed method.

Solving multi-scale electromagnetic problems by domain decomposition based integral equation method

In this paper, we introduced domain decomposition based integral equation (IE) methods for complicated multi-scale problems. The first multi-scale problem is solving electromagnetic scattering from a perfectly electric conductor with complicated geometry. A hybrid IE-DDM-MLFMA with Gauss-Seidel iteration is developed. As non-overlapping DDM, it has the advantage of flexible dividing domain and no buffer zone. The Gauss-Seidel iteration is proposed to update the currents on each sub-domain in real time, so the number of outer iterations is reduced greatly. The second multi-scale problem is electromagnetic analysis of large antenna array. To realize efficient solution, the tangential equivalence principle algorithm (T-EPA) combined with characteristic basis functions (CBFs) is presented. By utilizing the CBFs together with T-EPA, the analysis of large scale arrays will be more efficient with decreased unknowns compared with original T-EPA. Numerical results are shown to demonstrate the accuracy and efficiency of the present methods.

Multilevel sparse approximate inverse preconditioning for solving dynamic integral equation by H-matrix method

A novel sparse approximate inverse (SAI) preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solving 3D electromagnetic scattering by integral equation. This multilevel formatted preconditioning is derived from the hierarchical data structure of hierarchical (H-) matrix, which overcomes the construction restrict of conventional SAI preconditioner combined with popular fast algorithms like multilevel fast multipole algorithm (MLFMA). Numerical experiments have demonstrated that this proposed preconditioner has a good property, can achieve fast convergence even for very complex structures.