Zhenhong Fan

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.

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.

A Novel Hierarchical Two-Level Spectral Preconditioning Technique for Electromagnetic Wave Scattering

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 solved by method of moments. The hierarchical two-level spectral preconditioning technique is developed for the generalized minimal residual iterative method, in which the multilevel fast multipole method is used to accelerate matrix-vector product. The sparse approximate inverse (SAI) preconditioner based on the higher order hierarchical basis functions is used to damp the high frequencies of the error and the low frequencies is eliminated by a spectral preconditioner in a two-level manner defined on the lower order basis functions. The spectral preconditioner is combined with SAI preconditioner to obtain a hierarchical two-level spectral preconditioner. Numerical experiments indicate that the new preconditioner can significantly reduce both the iteration number and computational time.

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.

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.

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.

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.