Shifei Tao

A Higher-Order Solution of Volume Integral Equation for Electromagnetic Scattering From Inhomogeneous Objects

A higher-order solution of volume integral equation is proposed for the analysis of electromagnetic (EM) scattering from inhomogeneous objects. The higher-order basis functions used in this solution are defined in curvilinear tetrahedron elements, in which the Lagrange interpolation polynomials are utilized to construct the basis functions for representing the unknown volume electric current density. The proposed higher-order solution is implemented with point matching for the method of moments (MoM) of the volume electric field integral equation (VEFIE). Several numerical examples are presented to validate the higher-order convergence and great efficiency to analyze the electromagnetic scattering from inhomogeneous objects.

Electromagnetic Scattering Analysis of a Conductor Coated by Multilayer Thin Materials

In this letter, an efficient numerical approach for the electromagnetic scattering analysis of the conductor coated by multilayer thin materials for closed bodies is proposed. Only the induced current on the conductor is needed to be discretized as the unknowns, so the number of unknowns is independent with the number of dielectric coating layers. For the model of a conductor coated by multilayer thin materials, the electric field integral equation (EFIE) is presented and the multilevel fast multipole method (MLFMM) is utilized to speed up the matrix vector product after these equations converted to matrix equations with Galerkin testing. To validate this approach, several numerical examples are presented.

Fast analysis of finite and curved frequency selective surfaces using the VSIE with MLFMA

In this paper, the hybrid volume-surface integral-equation(VSIE) approach is proposed to analyze the transmission and reflection characteristics of finite and curved frequency-selective surfaces (FSS) structures. The surface current and electric flux density is expanded by surface RWG and volume SWG basis functions, respectively. The multilevel fast multipole algorithm (MLFMA) is applied to reduce the computational complexity. Simulated results are given to demonstrate the accuracy and efficiency of the proposed method.

A Time-Domain Thin Dielectric Sheet (TD-TDS) Integral Equation Method for Scattering Characteristics of Tunable Graphene

A time-domain thin dielectric sheet (TD-TDS) integral equation method is presented to analyze the transient scattering of thin graphene films with the electrostatic bias. In this method, the volume integral of the time-domain volume integral equation is transformed to surface integral to reduce the scale of calculation. In this method, the Rao–Wilson–Glisson basis function and the pulse functions are employed as a spatial basis function while the fourth-order Lagrangian basis functions are employed as temporal basis functions. The main advantages of the TD-TDS method are: 1) this method provides a new way for the simulation of graphene device; 2) only the surfaces of the targets need to be meshed when the targets are modeled as surfaces instead of volumes. As a result, the computational resources and time are greatly reduced; 3) broadband electromagnetic response characteristics can be obtained only after one time computation; and 4) this TD-TDS method is suitable for analyzing the dispersive dielectric material whose permittivity is a Drude model with a time convolution operation. Numerical examples are demonstrated to show the accuracy and efficiency of the TD-TDS method.

An Efficient Algorithm for Surface Integral Equation Based on Mesh-Free Scheme

An efficient algorithm for solving surface integral equation based on mesh-free scheme is proposed. The surface current is represented by a set of shape functions instead of conventional Rao-Wilton-Glisson (RWG) basis functions in the method of moments (MoM). The shape functions are constructed on some distributed nodes without explicitly requiring continuity conditions. Unlike the RWG, the basis function in this letter is not reliant on the tessellation and can be used with nonconformal meshes. In addition, it can be used flexibly to mix different discretization scales of grids. Numerical results demonstrate that scattering from objects can be computed efficiently with the multilevel fast multipole method (MLFMM) combined with adaptive cross approximation (ACA).

Efficient method for evaluation of second-harmonic generation by surface integral equation

A frequency-domain method based surface integral equation of the tangential Poggio–Miller–Chang–Harrington–Wu–Tsai formulation is presented as a full wave analysis to evaluate surface second-harmonic generation from noble metal nanoparticles of virtually arbitrary shape. According to the similar solution of fields and boundary conditions at fundamental and second-harmonic frequency, we get the derivation of surface integral equation formulations with only half unknowns compared with the conventional surface integral equation method. Simultaneously, the condition number of impedance matrix has been sharply declined. Numerical examples of gold nanospheres of different radius are presented to demonstrate the accuracy and efficiency of the proposed method. To further research the distribution of surface nonlinear polarization and properties of the second-harmonic radiation, we apply our method to a noncentrosymmetric L-shaped gold nanoparticle studied experimentally. This method provides an efficient and promising approach for evaluation of nonlinear optical radiation generated from metal nanoparticles array and optimization design of nonlinear nanoantennas.

Complex Source Beam Method for EM Scattering From PEC Objects

This letter proposes a fast method that combines the complex-source beam (CSB) and multilevel fast multipole algorithm (MLFMA) for electromagnetic (EM) scattering problems. The CSB for the MLFMA is obtained by introducing an imaginary part for the independent variable of the spherical Hankel function in the translation operator, which makes the translation operator directional. Furthermore, a window function is introduced in the translation operator to make it more directional. A large part of the angular translation operators are then discarded with an angle threshold. Numerical examples demonstrate that the translation operator memory cost can be reduced significantly compared to the MLFMA, and more accurate results can be obtained compared to the ray-propagation multilevel fast multipole algorithm (RP-MLFMA).

Numerical analysis of metal targets in the terahertz and infrared

The Drude model is used to describe the equivalent relative permittivity of metal, which varies the frequency and determines the value of the surface impedance. The surface integral equation method is applied to solve electromagnetic scattering by arbitrarily shaped three dimensional metallic objects modeled with the impedance boundary condition (IBC). Several metal spheres are analyzed which are composed by three different metals. The computed results are all compared with the perfect electric conductor (PEC) case, which show that there are big differences of the electromagnetic properties for different metals.

Electromagnetic analysis of electrically large and arbitraried shaped FSS using hybrid VSIE combined with parallelized MLFMM

A numerical scheme of computing the reflection coefficient and transmission coefficient of the finite and arbitraried shaped frequency selective surfaces (FSS) is proposed. The volume-surface integral equation (VSIE) sovler in conjunction with the parallel multilevel fast multipole method (MLFMM) is applied to calculate the transmission and reflection coefficient of two typical finite size frequency selective surfaces. A number of results are given to prove the accuracy and efficiency of the proposed scheme.