D. Z. Ding

A Multiresolution Curvilinear Rao–Wilton–Glisson Basis Function for Fast Analysis of Electromagnetic Scattering

A new set of multiresolution curvilinear Rao-Wilton-Glisson (MR-CRWG) basis functions is proposed for the method of moments (MoM) solution of integral equations for three-dimensional (3-D) electromagnetic (EM) problems. The MR-CRWG basis functions are constructed as linear combinations of curvilinear Rao-Wilton-Glisson (CRWG) basis functions which are defined over curvilinear triangular patches, thus allowing direct application on the existing MoM codes that using CRWG basis. The multiresolution property of the MR-CRWG basis can lead to the fast convergence of iterative solvers merely by a simple diagonal preconditioning to the corresponding MoM matrices. Moreover, the convergence of iterative solvers can be further improved by introducing a perturbation from the principle value term of the magnetic field integral equation (MFIE) operator to construct diagonal preconditioners for efficient iterative solution of the electric field integral equation (EFIE). Another important property of the MR-CRWG basis is that the MoM matrices using the MR-CRWG basis can be highly sparsified without loss of accuracy. The MR-CRWG basis has been applied to the 3-D electromagnetic scattering problems and the numerical results indicate that the MR-CRWG basis performs much better than the CRWG basis.

Preconditioning Matrix Interpolation Technique for Fast Analysis of Scattering Over Broad Frequency Band

A hybrid interpolation method is proposed for the fast analysis of the radar cross-section (RCS) over a broad frequency band by use of the matrix interpolation method. In order to efficiently compute electromagnetic scattering, the general minimal residual (GMRES) iterative solver is applied to compute the coefficients of Rao-Wilton-Glisson (RWG) basis functions and the sparse approximate inversion (SAI) preconditioning technique is used to accelerate the iterative solver. Moreover, both the near field impedance and SAI preconditioning matrices are interpolated at intermediate frequencies over a relatively large frequency band with rational function interpolation technique. Therefore, a lot of time can be saved for the calculation of both the near field impedance and preconditioning matrices. Numerical results demonstrate that this hybrid method is efficient for wideband RCS calculation with high accuracy.

Solution of PMCHW Integral Equation for Transient Electromagnetic Scattering From Dielectric Body of Revolution

The transient EM scattering from a homogeneous dielectric body of revolution (BOR) is formulated in terms of the time-domain PMCHW (TD-PMCHW) integral equation. Triangular functions along the generatrix of the BOR and weighted Laguerre polynomials are used as the spatial and temporal basis functions, respectively, to expand the unknown equivalent surface electric/magnetic current densities. In this way, both the memory requirement and the CPU time can be reduced largely since the matrix equation for each Fourier mode can be solved independently. Numerical results are presented to demonstrate the feasibility of the proposed method. Moreover, the convergence is discussed for both the weighted Laguerre polynomials and the Fourier mode.

Application of multiresolution preconditioner technique for scattering problem in a half space

In this paper, a modified multilevel fast multipole method (MLFMM) is presented to compute the scattering problem of the arbitrary perfect electric conductors (PECs) above a lossy half space. The half-space MLFMM algorithm is validated through comparison with authoritative literature results. Further the multiresolution (MR) preconditioner is used to precondition the modified MLFMM, the results show the MR preconditioner can speed up the convergence rate quite well.

Application of perturbed multiresolution preconditioner technique combined with MLFMA for scattering problem

A new multiresolution (MR) preconditioner is presented in this paper, and it is combined with the multilevel fast multipole algorithm (MLFMA) for the analysis of electromagnetic scatters; Furthermore, the MR preconditioner is modified to be more effective by including a perturbation which is constructed from the principle value term of the magnetic field integral equation (MFIE) operator for solving the electric field integral equation (EFIE), and the modified MR preconditioner is named perturbed MR preconditioner. The MR preconditioner is a physics-based preconditioning scheme for the Method-of- Moments (MoM) methods, which is derives from the generation of a MR basis. And the MR basis functions are constructed as linear combinations of Rao-Wilton-Glisson (RWG) basis functions. Unlike other preconditioners, the perturbed MR preconditioner requires a low memory occupation and computational cost for its generation and application. The use of the perturbed MR preconditioner combined with the MLFMA can speeds up the convergence rate of the iterative solvers effectively.

Analysis of Transient EM Scattering From Penetrable Objects by Time Domain Nonconformal VIE

A marching-on-in-time (MOT)-based nonconformal volume integral equation (VIE) is proposed to analyze the transient electromagnetic scattering from the inhomogeneous penetrable objects. The gradient-gradient operator is acted on the Greens function to realize the nonconformal tetrahedral meshes discretization. Half Schaubert-Wilton-Glisson (SWG) basis functions are chosen for the trail and test spatial functions, meanwhile the piecewise polynomial Lagrange interpolation functions are applied for temporal expansion. In addition, the quasi-explicit scheme is introduced to accelerate the calculation of conventional implicit MOT system. Numerical results are given to demonstrate the flexibility and validity of the proposed scheme.

Augmented EFIE with Adaptive Cross Approximation Algorithm for Analysis of Electromagnetic Problems

The augmented electric field integral equation (A-EFIE) with charge neutrality enforcement provides a stable formulation to conquer low-frequency breakdown characteristic of conventional EFIE. It is augmented with additional charge unknowns through current continuity equation. The A-EFIE combined with the multilevel adaptive cross-approximation (MLACA) algorithm is developed to further reduce the memory requirement and computation time for analyzing electromagnetic problems. Numerical examples are given to demonstrate the accuracy and efficiency of the proposed method.

Augmented MLFMM for solving the electromagnetic scattering problems with fine structures

MLFMM augmented with a Greens function interpolation method is proposed to efficiently solve the electromagnetic scattering problems. One well-known shortcoming of the traditional mid-frequency MLFMM method is that the finest box size must be at least 0.25 wavelength to ensure the accuracy. However, there exists a myriad of real targets having fine structure, and it usually produces a large number of unknowns in each finest box when discretizing these targets in the MLFMM implemetation, which leads to a large mount of storage of near-field interactions. In this article, a Greens function interpolation method (MLGFIM) is proposed to attack this kind of problem, the MLGFIM can make the finest box size reduced to as small as 0.1 wavelength or even smaller, and it enables a significant reduction in memory and complexity against the MLFMM. Numerical examples are presented to validate the proposed scheme.

Application of Iterative Solvers in 3D Crank-Nicolson FDTD Method for Simulating Resonant Frequencies of the Dielectric Cavity

In this paper, several Krylov subspace iterative algorithms are proposed as the solvers for the unconditionally stable three-dimensional Crank-Nicolson finite-difference time- domain (3D CN-FDTD) method. To demonstrate features of this method, a resonant cavity is analyzed. Numerical results indicate that the GMRES method is the most efficient solver for the dielectric cavity. And while the time step size excessively larger than the Courant-Friedrich-Levy (CFL) limit, the CN-FDTD maintained accuracy compared with the exact solutions.

Marching-on-in-Degree Method With Delayed Weighted Laguerre Polynomials for Transient Electromagnetic Scattering Analysis

The large cost of computing resources has become a bottleneck of the marching-on-in-degree (MOD) solver of time-domain integral equation (TDIE). A set of delayed weighted Laguerre polynomials is proposed to address this problem in this paper. By incorporating the phase propagation information into itself, the proposed temporal basis function can model the phase variation of the induced current at different places of the scatterer, leading to a great reduction in the spatial unknowns. Moreover, the curvilinear Rao-Wilton-Glisson (CRWG) basis functions are adopted for the spatial discretization to improve the modeling precision of curve surfaces. Numerical results show that the proposed method can greatly reduce the mesh density of the scatterer and save the computing resources. It is both stable and efficient for the transient scattering analysis of perfect electrically conducting (PEC) objects with large smooth surfaces.