Xiao-Chun Nie

A fast volume-surface integral equation solver for scattering from composite conducting-dielectric objects

This paper presents a fast hybrid volume-surface integral equation approach for the computation of electromagnetic scattering from objects comprising both conductors and dielectric materials. The volume electric field integral equation is applied to the material region and the surface electric field integral equation is applied on the conducting surface. The method of moments (MoM) is used to convert the integral equation into a matrix equation and the precorrected-FFT (P-FFT) method is employed to reduce the memory requirement and CPU time for the matrix solution. The present approach is sufficiently versatile in handling problems with either open or closed conductors, and dielectric materials of arbitrary inhomogeneity, due to the combination of the surface and volume electric field integral equations. The application of the precorrected-FFT method facilitates the solving of much larger problems than can be handled by the conventional MoM.

Precorrected-FFT solution of the volume Integral equation for 3-D inhomogeneous dielectric objects

This work presents a fast solution to the volume integral equation for electromagnetic scattering from three-dimensional inhomogeneous dielectric bodies by using the precorrected-fast Fourier transform (FFT) method. The object is modeled using tetrahedral volume elements and the basis functions proposed by Schaubert et al. are employed to expand the unknown electric flux density. The basis functions are then projected onto a fictitious uniform grid surrounding the nonuniform mesh, enabling the FFT to be used to speed up the matrix-vector multiplies in the iterative solution of the matrix equation. The resultant method greatly reduces the memory requirement to O(N) and the computational complexity to O(NlogN), where N is the number of unknowns. As a result, this method is capable of computing electromagnetic scattering from large complex dielectric objects.

A fast analysis of scattering and radiation of large microstrip antenna arrays

An accurate and efficient method that combines the precorrected fast Fourier transform (FFT) method and the discrete complex image method (DCIM) is presented to characterize the scattering and radiation properties of arbitrarily shaped microstrip patch antennas. In this method, the mixed potential integral equation (MPIE) is discretized in the spatial domain by means of the discrete complex image method. The resultant system is solved iteratively using the generalized conjugate residual method (GCR) and the precorrected-FFT technique is used to speed up the matrix-vector multiplication. The precorrected-FFT eliminates the need to generate and store the usual square impedance matrix and thus leads to a significant reduction in memory requirement and computational cost. Numerical results are presented for arbitrarily shaped microstrip antenna arrays to demonstrate the accuracy and efficiency of this technique.

Analysis of probe-fed conformal microstrip antennas on finite grounded substrate

A method based on the volume-surface-wire integral equation and precorrected-fast Fourier transform (FFT) method is presented for accurate analysis of probe-fed microstrip antennas on arbitrarily-shaped, finite-sized ground plane and substrate. The method of moments (MoM) is used to solve the integral equation. Three triangular-type basis functions are used to represent the unknown currents in the substrates, on the conducting surfaces, and probes respectively. The connection of a vertical probe feed to the patch is rigorously modeled by an attachment mode at the junction. The precorrected-FFT method is applied to reduce the memory requirement and computational cost of the traditional MoM to facilitate analysis of large antenna arrays.

A fast combined field volume integral equation solution to EM scattering by 3-D dielectric objects of arbitrary permittivity and permeability

A fast solution to the combined field volume integral equation (CFVIE) for electromagnetic scattering by large three-dimensional dielectric bodies of arbitrary permittivity and permeability is presented. The CFVIE is formulated in the region of the scatterers by expressing the total fields as the sum of the incident wave and the radiated wave due to both the electric and magnetic polarization currents. The resultant integral equation is solved using the method of moments (MoM). Then the precorrected fast Fourier transform (P-FFT) method is applied to reduce the memory requirement and accelerate the matrix-vector multiplication in the MoM solution. In the implementation of the P-FFT method, two sets of projection operators are constructed respectively for the projections of the electric sources and magnetic sources. In addition, two sets of interpolation operators are also applied respectively for the computation of the vector/scalar potentials and the curl of the vector potentials in the support of the testing functions. The resultant method has a memory requirement of O(N) and a computational complexity of O(NlogN) respectively, where N denotes the number of unknowns

Fast Analysis of Electromagnetic Transmission through Arbitrarily Shaped Airborne Radomes Using Precorrected-FFT Method

A fast technique based on the Poggio, Miller, Chang, Harrington and Wu (PMCHW) formulation and the precorrected- FFT method is presented for accurate and efficient analysis of electromagnetic transmission through dielectric radomes of arbitrary shape (including airborne radomes). The method of moments is applied to solve the integral equations in which the surfaces of the radomes are modeled using surface triangular patches and the integral equations are converted into a linear system in terms of the equivalent electric and magnetic surface currents. Next, the precorrected- FFT method, a fast approach associated with O(N 1.5 log N) or less complexity, is used to eliminate the requirement of generating and storing the square impedance matrix and to speed up the matrix-vector product in each iteration of the iterative solution. Numerical results are presented to validate the implementation and illustrate the accuracy of the method.

ANALYSIS OF SCATTERING FROM COMPOSITE CONDUCTING AND DIELECTRIC TARGETS USING THE PRECORRECTED-FFT ALGORITHM

A precorrected‐FFT algorithm is presented for the calculation of electromagnetic scattering from conducting objects coated with lossy materials. The problem is formulated using an EFIE‐PMCHW formulation, which employs the electric field integral equation (EFIE) for conducting objects and the PMCHW formulation for dielectric objects. The integral equations are then discretized by the method of moments (MoM), in which the conducting and dielectric surfaces are represented by triangular patches and the unknown equivalent electric and magnetic currents are expanded using the RWG basis functions. The resultant matrix equation is solved iteratively and the precorrected‐FFT method is used to speed up the matrix‐vector products in iterations as well as to reduce the memory requirement. Numerical examples are presented to validate the implementation and to demonstrate the accuracy of the method.

RCS Computation of Composite Conducting-Dielectric Objects with Junctions using the Hybrid Volume-Surface Integral Equation

The hybrid volume-surface integral equation (VSIE) combined with the Method of Moments (MoM) is applied to the analysis of scattering from arbitrarily composite conducting-dielectric objects withconducting-dielectric or dielectric-dielectric junctions. The electric field volume integral equation is applied to the material region and the electric field surface integral equation is enforced over the conducting surface. Compared to the surface integral equation (SIE), the VSIE is more efficient and convenient since the formulation of the VSIE retains the same simple form regardless of the complexity of the object and materials, and no extra treatment is required when dealing withjunction problems.

A precorrected-FFT approach for capacitance extraction of general three-dimensional structures

In the design of high performance integrated circuits and integrated circuit packaging, there are many cases where the self and coupling capacitances are important for determining final circuit speeds or functionality. The traditional boundary-element technique and Gaussian elimination for solving the integral equation associated with the capacitance extraction problem require O(N/sup 3/) operations and O(N/sup 2/) memory storage. These approaches become computationally intractable when a large number of elements are used, thus limiting the size of the problem that can be analyzed. In this paper, a generalized conjugate residual iterative technique is used to solve the linear system arising from the discretization, and a precorrected-FFT method is then employed to accelerate the matrix-vector products in the iterates. This technique requires O(NlogN) operations and O(N) memory storage to perform a potential calculation.

Temasek laboratories efficient full-wave EMC (TLEFEMC V 1.0) code for analysis of antennas mounted on large and complex platform: Introduction, validation, and application

Fast and accurate full-wave analysis of antennas mounted on large and complex platform is very useful and yet a challenging area in electromagnetic compatibility (EMC) assessment. This paper introduces our Temasek Laboratories (TL) efficient full-wave EMC (TLEFEMC V1.0) code for attempting to solve this challenging problem up to a certain frequency of interest. This code is a great effort made by a team in TL at National University of Singapore (TL@NUS) in collaboration with DSO National Laboratories. The technical core of the TLEFEMC V1.0 code is the combination of surface-wire integral equation (SWIE) and precorrected-FFT (P-FFT) algorithm. Extensively numerical validation for small problems as well as applications to realistic targets has illustrated the capability of the developed code.