Rushan Chen

Application of the SSOR preconditioned CG algorithm to the vector FEM for 3D full-wave analysis of electromagnetic-field boundary-value problems

The symmetric successive overrelaxation (SSOR) preconditioning scheme is applied to the conjugate-gradient (CG) method for solving a large system of linear equations resulting from the use of edge-based finite-element method (FEM). For this scheme, there is no additional computing time required to construct the preconditioning matrix and it contains more global information of the coefficient matrix when compared with those of the banded-matrix preconditioning scheme. The efficient implementation of this preconditioned CG (PCG) algorithm is described in details for complex coefficient matrix. With SSOR as the preconditioner and its efficient implementation in the CG algorithm, this PCG approach can reach convergence in five times CPU time shorter than CG for several typical structures. By comparison with other preconditioned techniques, these results demonstrate that SSOR preconditioning strategy is especially effective for CG iterative method when an edge FEM is applied to solve large-scale time-harmonic electromagnetic-field problems.

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.

Nested Equivalent Source Approximation for the Modeling of Multiscale Structures

We introduce a method to compress the impedance matrix of the method of moments (MoM) for the modeling of high-fidelity multiscale structures at low- to moderate-frequencies. We start from a method recently proposed to compress static (scalar) problems, proved to have O(N) computational complexity. We represent far coupling between groups through equivalent source distributions on properly defined, automatically generated equivalence surfaces. The equivalent sources are obtained via an inverse-source process that enforces equivalence of radiated fields on testing surfaces within a prescribed accuracy, and are intrinsically multiscale. This results in an O(N) complexity scaling of matrix-vector products, but reduces multiplicative constants (i.e., reduces time and memory requirements) for all structures. It affords an improved representation of couplings in multiscale structures, resulting in a fast convergence of iterative solvers. Our approach is Greens function independent and easy to be implemented in existing MoM codes; the present version is based on the electric field integral equation (EFIE). Numerical results prove the effectiveness of the proposed algorithm for complex multiscale structures.

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.

An efficient method to analyze the H-plane waveguide junction circulator with a ferrite sphere

This paper presents an approximate, but efficient field treatment of the new easy-to-fabricate ferrite-sphere-based H-plane waveguide circulator for potentially low-cost millimeter-wave communication systems. A new three-dimensional modeling strategy using a self-inconsistent mixed-coordinates-based mode-matching technique is developed, i.e., the solutions of the Helmholtz wave equations in the ferrite sphere and in the surrounding areas are deduced in the form of infinite summation of spherical, cylindrical, and general Cartesian modes, respectively. The point-matching method is then used on the interface between the ferrite sphere and air within the cylindrical junction, as well as the interface between the junction and waveguides to numerically obtain the coefficients of different orders of basis functions of the field. Therefore, the field distributions, as well as the characteristics of the circulator, are numerically calculated and good agreement is observed between the numerical results and measured data.

Efficient Analysis of EM Scattering From Bodies of Revolution via the ACA

In this communication, the adaptive cross approximation (ACA) algorithm is utilized to analyze the scattering from arbitrary metallic bodies of revolution (BoRs) that is formulated by the electric field integral equation approach. For a given mode, a multilevel partitioning is used to group the basis functions of the BoRs along the longitudinal dimension. The interactions of the adjacent groups are calculated directly by the method of moments (MoM), and the interactions of well-separated groups are compressed by the ACA algorithm. The memory requirement and CPU time consumption are reduced drastically.

An Efficient Algorithm for Implementing the Crank–Nicolson Scheme in the Mixed Finite-Element Time-Domain Method

In this paper, an efficient algorithm for implementing Crank-Nicolson scheme in the finite-element time-domain (FETD) method is presented. Based on a direct discretization of the first-order coupled Maxwell curl equations, this algorithm employs edge elements (Whitney 1-form) to expand the electric field and face elements (Whitney 2-form) for the magnetic field. Since the curl of an edge-element is the linear combination of those face elements whose faces contain the given edge, only the Maxwell-Ampere equation composes a sparse linear matrix equation for the electric field update; the Maxwell-Faraday equation is explicit. The Crank-Nicolson scheme is implemented leading to an unconditionally stable vector FETD method and the matrix inverse is not required to be computed explicitly. Therefore, only one matrix equation is required to be solved at each time step. Numerical results demonstrate that the proposed method is efficient when compared with the conventional leap-frog mixed FETD method and the Crank-Nicolson FDTD method.

Spectral Two-Step Preconditioning of Multilevel Fast Multipole Algorithm for the Fast Monostatic RCS Calculation

A new spectral two-step preconditioning of multilevel fast multipole algorithm (MLFMA) is proposed to solve large dense linear systems with multiple right-hand sides arising in monostatic radar cross section (RCS) calculations. The first system is solved with a deflated generalized minimal residual (GMRES) method and the eigenvector information is generated at the same time. Based on this eigenvector information, a spectral preconditioner is defined and combined with a previously constructed sparse approximate inverse (SAI) preconditioner in a two-step manner, resulting in the proposed spectral two-step preconditioner. Restarted GMRES with the newly constructed spectral two-step preconditioner is considered as the iterative method for solving subsequent systems and the MLFMA is used to speed up the matrix-vector product operations. Numerical experiments indicate that the new preconditioner is very effective with the MLFMA and can reduce both the iteration number and the computational time significantly.

Electromagnetic Scattering for Multiple PEC Bodies of Revolution Using Equivalence Principle Algorithm

An equivalence principle algorithm (EPA) method is extended to analyze the electromagnetic scattering from multiple bodies of revolution (MBoR) with the axes arbitrarily oriented. Equivalence spheres are used to enclose each BoR and the equivalence currents are expanded by the basis functions of bodies of revolution (BoR). To obtain the scattering operators and translation operators of EPA for Fourier modes independently, the rotational symmetry systems are established in local BoR coordinate systems. The origin of the local BoR coordinate system is located at the center of the equivalence sphere and the z-axis coincides with the axis of the enclosed BoR to obtain the scattering operator of each equivalence sphere, whereas the origin is located at the observation sphere and z-axis passes through the center of the source sphere to obtain the translation operator of each pair of equivalence spheres. The current coefficient transformation algorithm is used to transform the equivalence currents among local BoR coordinate systems. The total equation is iteratively solved in the global coordinate system. The proposed scheme is especially efficient for the analysis of scattering from MBoR randomly distributed in electrically large scale region. Numerical results are given to demonstrate the efficiency.