Dazhi Ding

GPU Accelerated Unconditionally Stable Crank-Nicolson FDTD Method for the Analysis of Three-Dimensional Microwave Circuits

The programmable graphics processing unit (GPU) is employed to accelerate the unconditionally stable Crank-Nicolson flnite-difierence time-domain (CN-FDTD) method for the analysis of microwave circuits. In order to e-ciently solve the linear system from the CN-FDTD method at each time step, both the sparse matrix vector product (SMVP) and the arithmetic operations on vectors in the bi-conjugate gradient stabilized (Bi-CGSTAB) algorithm are performed with multiple processors of the GPU. Therefore, the GPU based BI-CGSTAB algorithm can signiflcantly speed up the CN-FDTD simulation due to parallel computing capability of modern GPUs. Numerical results demonstrate that this method is very efiective and a speedup factor of 10 can be achieved.

Electromagnetic Scattering by Conducting Bor Coated with Chiral Media Above a Lossy Half-Space

Electromagnetic scattering by conducting bodies of revolution (BOR) coated with homogeneous chiral media above a lossy half-space is formulated in terms of the Poggio-Miller-ChangHarrington-Wu surface integral equation combined with combined field integral equation. A field decomposition scheme is utilized to split a chiral media into two equivalent homogeneous media. The spatial domain half-space Green’s functions are obtained via the discrete complex image method. Due to the rotational symmetry property of BOR, the method of moment for BOR (BORMoM) is applied to the linear system solved by the multifrontal direct solver. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.

Weak Form Nonuniform Fast Fourier Transform Method for Solving Volume Integral Equations

Electromagnetic scattering problems involving inhomogeneous objects can be numerically solved by applying a method of moment’s discretization to the hypersingular volume integral equation in which a grad-div operator acts on a vector potential. The vector potential is a spatial convolution of the free space Green’s function and the contrast source over the domain of interest. For electrically large problems, the direct solution of the resulting linear system is expensive, both computationally and in memory use. Conventionally, the fast Fourier transform method (FFT) combined Krylov subspace iterative approaches are adopted. However, the uniform discretization required by FFT is not ideal for those problems involving inhomogeneous scatterers and sharp discontinuities. In this paper, a nonuniform FFT method combined weak form integral equation technique is presented. The method performs better in terms of speed and memory use than FFT on the configuration involving both the electrically large and fine structures. This is illustrated by a representative numerical test case.

SSOR PRECONDITIONED INNER-OUTER FLEXIBLE GMRES METHOD FOR MLFMM ANALYSIS OF SCATTERING OF OPEN OBJECTS

To efficiently solve large dense complex linear system arising from electric field integral equations (EFIE) formulation of electromagnetic scattering problems, the multilevel fast multipole method (MLFMM) is used to accelerate the matrix-vector product operations. The inner-outer flexible generalized minimum residual method (FGMRES) is combined with the symmetric successive over- relaxation (SSOR) preconditioner based on the near-part matrix of the EFIE in the inner iteration of FGMRES to speed up the convergence rate of iterative methods. Numerical experiments with a few electromagnetic scattering problems for open structures are given to demonstrate the efficiency of the proposed method.

An Efficient Sai Preconditioning Technique for Higher Order Hierarchical MLFMM Implementation

A new set of higher order hierarchical basis functions based on curvilinear triangular patch is proposed for expansion of the current in electrical field integral equations (EFIE) solved by method of moments (MoM). The multilevel fast multipole method (MLFMM) is used to accelerate matrix-vector product. An improved sparse approximate inverse (SAI) preconditioner in the higher order hierarchical MLFMM context is constructed based on the near- field matrix of the EFIE. The quality of the SAI preconditioner can be greatly improved by use of information from higher order hierarchical MLFMM implementation. Numerical experiments with a few electromagnetic scattering problems for open structures are given to show the validity and efficiency of the proposed SAI preconditioner.

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.

Meshed ground microstrip antennas with low radar cross section

It is proposed that the radar cross section (RCS) of a microstrip antenna can be effectively reduced over a broad frequency band by utilizing a well-designed meshed ground plane. The radiation characteristic of the microstrip antenna is only slightly influenced by cutting slots on the ground plane. The calculated results suggest that the meshed microstrip ground antenna has much lower RCS than the solid ground one over a band 1–18GHz, with a maximum reduction of 15dB, while the radiation performance of the microstrip antenna, such as gain, impedance bandwidth and so on, remains almost the same as that of the solid antenna.

Application of Two-Step Spectral Preconditioning Technique for Electromagnetic Scattering in a Half Space

To e-ciently solve large dense complex linear system arising from electric fleld integral equations (EFIE) formulation of half-space electromagnetic scattering problems, the multilevel fast multipole algorithm (MLFMA) is used to accelerate the matrix- vector product operations. The two-step spectral preconditioning is developed for the generalized minimal residual iterative method (GMRES). The two-step spectral preconditioner is constructed by combining the spectral preconditioner and sparse approximate inverse (SAI) preconditioner to speed up the convergence rate of iterative methods. Numerical experiments for scattering from conducting objects above or embeded in a lossy half-space are given to demonstrate the e-ciency of the proposed method.

Efficient analysis of multilayer microstrip structures by matrix decomposition algorithm — Singular value decomposition

In order to efficiently and accurately analyze the scattering of multilayer microstrip structures, the matrix decomposition algorithm — singular value decomposition (MDA-SVD) is used to accelerate the matrix-vector multiplication operations. MDA-SVD is purely algebraic; hence, its formulation and implementation are integral equation kernel independent. It utilizes the SVD algorithm to reduce the memory requirement and solution time of the matrix decomposition algorithm. The numerical results demonstrate the efficiency of the proposed method.