Lan-Wei Guo

A multiple-grid p-FFT with IE-DDM for analyzing scattering from structures above a half space

In this paper, a multiple-grid precorrected fast Fourier transform (MG-pFFT) based on the integral equation domain decomposition method (IE-DDM) is presented for multi-scale, dynamic electromagnetic scattering problems in half space. In the framework of the IE-DDM, the proposed method employs multiple auxiliary FFT grids in each domain. Numerical experiments validate the reduced complexity and accuracy of this method. It is also shown that the proposed method is an efficient and robust preconditioner for the original IE system in half space.

A Novel JMCFIE-DDM for Analysis of EM Scattering and Radiation by Composite Objects

In this letter, a new integral equation domain decomposition method (IE-DDM) using electric and magnetic current combined-field integral equation (JMCFIE) is proposed for efficient electromagnetic analysis of composite objects. This method provides a flexible way to decompose a complex composite domain into several easily solvable nonoverlapping subdomains. In order to obtain a good approximation of the global solution, both electric and magnetic field interactions are considered at the subdomain interfaces, in addition to the traditional Robin-type transmission conditions. In this manner, the unphysical reflections at subdomain interfaces can be further suppressed. It is shown that the condition of the new JMCFIE-DDM system is much improved in this new implementation. Accuracy and efficiency of the proposed method are demonstrated through several numerical experiments.

The nested complex source beam method with singular value decomposition

This work present a new aggregation procedure to improve the efficiency of the Nested Complex Source Beam (NCSB) method. The procedure is based on the application of the singular value decomposition (SVD) to the complex source beams (CSBs) aggregation matrices. The matrices, which represent the CSBs relationship between two adjacent levels, are decomposed into new combinations of the original CSBs. By choosing the most relevant singular values and singular vectors, a much more compact representation is obtained to accurately calculate the CSBs interactions. The numerical example is demonstrated to validate the proposed procedure.

Efficient Higher-Order Analysis of Electromagnetic Scattering of Objects in Half-Space by Domain Decomposition Method with a Hybrid Solver

Integral equation domain decomposition method (IE-DDM) with an efficient higher-order method for the analysis of electromagnetic scattering from arbitrary three-dimensional conducting objects in a half-space is conducted in this paper. The original objects are decomposed into several closed subdomains. Due to the flexibility of DDM, it allows different basis functions and fast solvers to be used in different subdomains based on the property of each subdomain. Here, the higher-order vector basis functions defined on curvilinear triangular patches are used in each subdomain with the flexibility of order selection, which significantly reduces the number of unknowns. Then a novel hybrid solver is introduced where the adaptive cross approximation (ACA) and the half-space multilevel fast multipole algorithm (HS-MLFMA) are integrated seamlessly in the framework of IE-DDM. The hybrid solver enhances the capability of IE-DDM and realizes efficient solution for objects above, below, or even straddling the interface of a half-space. Numerical results are presented to validate the efficiency and accuracy of this method.

IE-DDM with a novel multiple-grid p-FFT for analyzing multiscale structures in half space

We present an integral equation domain decomposition method accelerated by a novel multiple-grid precorrected fast Fourier transform (MG-p-FFT) for the efficient analysis of multiscale structures in a half space. Based on the philosophy of DDM, the original computational domain is partitioned into several non-overlapping sub-domains. By employing non-conformal discretizations to each domain boundaries, combined field integral equation with half-space dyadic Green’s function is proposed for each individual sub-domain. Subsequently, the MG-p-FFT with auxiliary Cartesian grids with different size, order, location, and spacing, is adopted in each sub-domain independently to account for the self-interactions. Here, the proposed MG-p-FFT scheme outperforms the existing single-grid p-FFT scheme for multiscale problems by reducing the computational time and memory consumption. The proposed method can also be viewed as an effective preconditioning scheme for multiscale problems in a half space. The validity and advantages of the proposed method are illustrated by several representative numerical examples.

P-FFT Accelerated EFIE with a Novel Diagonal Perturbed ILUT Preconditioner for Electromagnetic Scattering by Conducting Objects in Half Space

A highly efficient and robust scheme is proposed for analyzing electromagnetic scattering from electrically large arbitrary shaped conductors in a half space. This scheme is based on the electric field integral equation (EFIE) with a half-space Green’s function. The precorrected fast Fourier transform (p-FFT) is first extended to a half space for general three-dimensional scattering problems. A novel enhanced dual threshold incomplete LU factorization (ILUT) is then constructed as an effective preconditioner to improve the convergence of the half-space EFIE. Inspired by the idea of the improved electric field integral operator (IEFIO), the geometrical-optics current/principle value term of the magnetic field integral equation is used as a physical perturbation to stabilize the traditional ILUT perconditioning matrix. The high accuracy of EFIE is maintained, yet good calculating efficiency comparable to the combined field integral equation (CFIE) can be achieved. Furthermore, this approach can be applied to arbitrary geometrical structures including open surfaces and requires no extra types of Sommerfeld integrals needed in the half-space CFIE. Numerical examples are presented to demonstrate the high performance of the proposed solver among several other approaches in typical half-space problems.

IE-DDM-FFT for EM scattering by objects in half-space structures

In this paper, an extension of the integral equation based on domain decomposition method (IE-DDM) is presented for dynamic electromagnetic scattering problems above a lossy half space. In the framework of the IE-DDM, the proposed method divides the composite object into several homogeneous sub-domains. Each sub-domain is properly described by a closed surface, and robin transmission condition is introduced to weakly enforce the continuity of tangential field across the touching-face between adjacent sub-domains. Multiple-grid precorrected fast Fourier transform (MG-pFFT) is adopted in each sub-domain independently to account for the self-interactions. Numerical experiments validate the accuracy and efficiency of this method.

EFIE with a novel perturbed ILUT preconditioner for electromagnetic scattering by conducting objects in half space

In this paper, a highly efficient and robust scheme is proposed to analyzing electromagnetic (EM) scattering of arbitrary shaped perfect electrically conducting (PEC) objects in half space. The electric field integral equation (EFIE) with the half-space Greens function is chosen as the basis of this method due to its great versatility and accuracy. A perturbed dual threshold incomplete LU factorization (ILUT) preconditioner based on the near-field interactions in the improved EFIE (IEFIE) operator is proposed as an effective preconditioner. It will be further shown that such preconditioner enhances the stability of the traditional ILUT preconditioner based on EFIE, which may occasionally encounter problems of instability for real-life problems. Numerical examples are presented to demonstrate the high efficiency and robustness of this method over other existing alternative solutions.

A 3-D precorrected FFT algorithm for electrically large objects in planarly layered media

A three-dimensional (3D) pre-corrected fast Fourier transform (pFFT) is presented for the fast analysis of electromagnetic (EM) scattering from electrically large perfect electrically conducting structures embedded inside a planarly layered medium. The mixed-potential integral equation (MPIE) is used to formulate the problem and the method of moments (MOM) with Rao-Wilton-Glisson (RWG) basis function is employed to solve the integral equation. In order to avoid direct numerical computation of Sommerfeld integrals (SIs), the two-level discrete complex image method (DCIM) is employed to expedite the matrix filling process. In the iterative stage, the pFFT method is further adopted to accelerate the matrix-vector product, since the resulting matrix contains both cyclic convolution and correlation terms after proper splitting. Moreover, the incomplete LU preconditioner is applied to improve the convergence of the matrix equation. Numerical results are presented to show the efficiency and capability of the method.