Aiming Zhu

A study of combined field formulations for material scattering for a locally corrected Nystro/spl uml/m discretization

A study of the error convergence and condition number of three integral-equation formulations derived for penetrable material scattering objects-the Poggio, Miller, Chang, Harrington, Wu and Tsai (PMCHWT), the Mu/spl uml/ller, and the PMCHWT(-) formulations-is presented for a variety of problems when discretized via a locally corrected Nystro/spl uml/m method. The PMCHWT formulation is a first-kind integral equation with a hypersingular operator. The Mu/spl uml/ller formulation leads to a second-kind equation consisting of a diagonal term plus a compact operator. This form is both frequency and mesh stable. However, unlike the PMCHWT formulation, the error grows with the refractive index. The PMCHWT(-) formulation is in the form of a second-kind equation, but has a hypersingular term.

A quadrature-sampled precorrected FFT method for the electromagnetic scattering from inhomogeneous objects

A fast iterative solution for the electromagnetic scattering from inhomogeneous objects computed via the quadrature sampled precorrected fast Fourier transform (QSPCFFT) algorithm is presented. The method is based on a locally corrected Nystrom solution of the volume electric field integral equation. The discontinuous FFT is applied to accelerate the computation of all far interactions. The method preserves the high-order properties of the Nystrom solution, and has a complexity that can scale as O(N log N) and memory that scales as O(N), where N is the number of unknowns.

Modified simply sparse method for electromagnetic scattering by PEC

In this paper, the multilevel simply sparse method (MLSSM) is presented to improve the performance of fast direct solvers for integral equations. The SSM is a general, physically motivated compression algorithm for integral equation formulations of electromagnetic phenomena. An important feature of the algorithm is the ease with which it can be applied to diverse scattering and radiation configurations. In this paper, the MSSM is used to compress various integral equations including the electric field integral equation (EFIE), magnetic field integral equation (MFIE) and combined field integral equation (CFIE). All of these IE were compressed into a sparse format and compared to the compressed format of the MLFMM. Also, the work presented consists of the multilevel implementation of the SSM (MLSSM) that will further reduce the memory usage.

Comparison of the Muller and PMWCHT surface integral formulations for the locally corrected Nystrom method

Two surface integral formulations, the Muller and PMCHWT methods, are compared for the computation of the electromagnetic scattering by composite dielectric objects via the locally corrected Nystrom (LCN) method. The Muller formulation leads to a second-kind integral equation, whereas the PMCHWT formulation leads to a first-kind integral equation with a hypersingular kernel. For the high-order LCN solution of these integral formulations, it is shown that the Muller formulation leads to faster convergence rates and smaller condition numbers, and is more efficient for the same level of accuracy for moderate to low contrast materials. For high contrast materials, while the PMCHWT simulation converges at a slower rate, it can still realize the desired precision with fewer unknowns than a Muller formulation.

High-order pre-corrected FFT solution for electromagnetic scattering

Introduction A high-order pre-corrected FFT algorithm is introduced for the fast, high-order solution of integral equations arising in electromagnetic scattering. The pre-corrected FFT (PCFFT) originally developed by Jacob White [ I ] has been classically applied to quasistatic problems, but is also applicable to dynamic problems. As a fast method, the PCFFT has the advantage over classical fast multipole methods [2, 31 in that the accuracy and effectiveness are based on discretization rather than electrical lengths. However, the use of the FFT requires a discretization of all space. Consequently, the PCFFT method is better suited for the simulation of large problems with a fairly homogenous distribution of unknowns. Some examples would be large, densely packed electrical interconnects in digital or mixed signal systems with tine electrical detail. In this paper, a pre-corrected FFT method based on the quadrature sampled FFT (QSFFT) originally developed by Fan and Lu [4] is used to accelerate a locally corrected Nystrom (LCN) formulation [ 5 ] . The QSFFT maintains the high-order properties of the LCN.

Mixed-order basis functions for the locally-corrected Nystro/spl uml/m method

The paper presents a thorough study of the application of the mixed-order basis proposed by F. Caliskan and A.F. Peterson (see IEEE Antennas and Wireless Propag. Lett., vol.2, p.72-3, 2003) for the locally corrected Nystrom (LCN) method when analyzing electromagnetic scattering by targets composed of both dielectric and conducting materials. The integral formulation is based on a superposition of the classical combined field integral equation (CFIE) operator (Peterson et al., 1998) for metallic surfaces and a Muller formulation for penetrable objects (Muller, C., 1969; Mautz, J.R. and Harrington, R.F., 1979). It is demonstrated that for general scattering objects, mixed-order basis functions accelerate the convergence of the LCN solution, eliminate spurious charges for singular geometries, and can significantly reduce the condition number of the impedance matrix.

Fast, high-order, hybrid integral equation solver for electromagnetic scattering

A fast, high-order, hybrid integral equation solver for electromagnetic scattering is presented. The solver is based on a locally corrected Nystrom solution of a hybrid volume integral equation (VIE) and surface integral equation (SIE) formulation. The solution can be accelerated by quadrature-sampled pre-corrected FFT or the multilevel fast multipole method (MLFMM), or a combination of both schemes. The methods are validated in this paper through the study of the electromagnetic scattering of canonical geometries made of a composite of conducting and dielectric materials.

A fast, high-order integral equation solution for the scattering by inhomogeneous objects

A fast solution for the electromagnetic scattering by inhomogeneous objects is presented. The method is based on a locally corrected Nystrom solution of the volume electric field integral equation. The matrix-vector multiplication is accelerated via the quadrature sampled precorrected FFT (QSPCFFT) (Gedney, S.D. et al., 2003). The QSPCFFT method preserves the high-order properties of the Nystrom solution, and has a complexity that scales as O(N log N) and memory that scales as O(N).

Sparse Factorization of the Impedance Matrix in an Overlapped Localizing Basis: TMz Case

It has been observed that localizing current modes provide sparse factorizations of discrete integral equations at low frequencies. This paper extends these results by incorporating overlapping localized modes. For TMz scattering, it is observed that the computational complexity of the resulting factorization algorithm approaches O(NlogN). The memory complexity of the factored representation scales approximately as O(N) for electrically small arrays. Results from the 3-D implementation of these algorithms will be presented separately at this meeting

A novel perfectly matched layer method for an unconditionally stable ADI-FDTD method

Recently an unconditionally stable ADI method was successfully applied to the solution of Maxwells equations using a variation of the FDTD method. The ADI method is most useful for solving problems where the lattice is grossly over discretized spatially (< 10/sup -2//spl lambda//sub min/). For this scheme to be applicable to analyzing practical electromagnetic interaction problems, an efficient absorbing boundary condition that maintains unconditional stability must be derived. In this paper, an absorbing boundary condition using a perfectly matched layer (PML) is introduced. Specifically, the convolutional PML (CPML) method is used with complex frequency shifted scaling coefficients. It is shown that this method maintains unconditional stability. Further, it is demonstrated that the method provides a significant improvement in the reflection error as compared to the originally proposed split-field PML ADI scheme.