Wan Luo

Fast Analysis of Electromagnetic Scattering From Three-Dimensional Objects Straddling the Interface of a Half Space

The electromagnetic scattering from 3-D perfectly electrically conducting (PEC) objects straddling the interface of a half-space is analyzed in this letter. The adaptive cross approximation (ACA) algorithm is adopted to enhance the computational efficiency. As the object is naturally separated into two parts by the interface of the half-space, two different mesh densities are required due to the contrast of the two background materials. Therefore, two multilevel tree structures are set up individually in the two regions. When the source and field points are in the same region, which corresponds to the primary terms and reflection terms, the implementation is similar to the free-space case. However, when considering the mutual coupling of the two regions, which corresponds to the transmitted terms, difficulties arise since the two trees are independent and the numbers of levels are, in general, different. In this case, a z-dependent grouping strategy is proposed to redefine the well-separated interactions and match the abrupt changes at the interface. Three clustering strategies are proposed and discussed carefully to account for the mutual coupling in the two different regions of the half-space. The combined field integral equation (CFIE) formulation is further applied to improve the convergence of the system. Several numerical examples are demonstrated to validate the proposed schemes.

A Hybrid Method for Analyzing Scattering from PEC Bodies Straddling a Half-Space Interface

In this letter, a novel hybrid method is proposed to efficiently analyze the electromagnetic (EM) scattering from arbitrarily shaped, perfect electrically conducting (PEC) bodies that penetrate the interface of a half-space. Due to different integrands involved in the reflection- and transmission-type Greens functions, a partition scheme is introduced where the adaptive cross approximation (ACA) and the multilevel fast multipole algorithm (MLFMA) are integrated seamlessly. In this scheme, different fast solvers are invoked automatically to achieve an optimal efficiency. The reconstruction of the Greens function via an image-based translational addition theorem is first investigated, and the empirical partitioning parameters are suggested. The performance of this hybrid method is then examined via two examples, including a benchmark target and a more realistic scenario in the near-surface scattering.

Efficient Higher-Order Analysis of Electromagnetic Scattering by Objects Above, Below, or Straddling a Half-Space

Efficient higher-order analysis of electromagnetic scattering from arbitrary three-dimensional conducting objects above, below, or even straddling a half-space is conducted in this letter. Due to the complexity of the half-space Greens function, it is desirable to reduce the degrees of freedom and especially the number of field-source interactions to a minimum level. To achieve this, a recently developed higher-order basis function based on curvilinear triangular patches is extended to half-space applications and investigated carefully from different aspects. Due to the flexibility of order selection, a uniform mesh guarantees the modeling accuracy even when the scatterer is straddling the interface of the half-space, where extremely nonuniform or multiscale mesh is always required in the traditional methods due to the distinct wavelengths of the surrounding media. Moreover, this higher-order method significantly simplifies the wideband simulation, which is important in various half-space applications.

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.

Fast Analysis of Electromagnetic Scattering From Conducting Objects Buried Under a Lossy Ground

Electromagnetic scattering from conducting objects is investigated for the applications of underground detection. The air-soil composite is modeled by a classical half space where the dyadic Greens function can be defined and formulated. The electric field integral equation (EFIE) is employed to guarantee the accuracy and robustness of the analysis for arbitrarily shaped scatterers. The internal resonance of EFIE is first studied under typical working conditions (frequencies, soil water contents, etc.). It is shown that this spurious resonance is much alleviated due to loss of the soil. Next, the unbounded and ill-posed spectrum of the EFIE operator is remedied by a novel localized half-space Calderón preconditioner by further exploring the lossy nature of the background. Such preconditioning is extremely useful for objects containing multiscale features. Finally, the half-space multilevel fast multipole algorithm based on real-image approximation is adopted to accelerate the computation for electrically large scatterers. Several examples in the applications of subsurface sensing are demonstrated to validate the efficiency and accuracy of this method.

Efficient analysis of EM scattering from 3D complex conducting objects buried under ground

Electromagnetic scattering by three-dimensional complex perfect electrically conducting (PEC) objects buried under ground is investigated in this paper. The air-soil composite is approximated by a half-space model, where the half-space Greens function is adopted in the formulation of the electric field integral equation (EFIE). The simulation efficiency is improved from the following two aspects: a novel half-space Calderón preconditioner is developed to improve the spectrum of the EFIE operator, and thus the convergence rate of the matrix system; a half-space multilevel fast multitpole algorithm (MLFMA) based on real-image approximation is further adopted to accelerate each matrix-vector product and reduce the memory requirement. Numerical results are presented to demonstrate the effectiveness of this method for the applications of underground detection.

A higher-order method for electromagnetic simulation of conducting objects near/across the interface of a half space

A set of higher-order basis functions based on curvilinear triangular patches is presented to analyze the electromagnetic scattering from arbitrarily shaped, perfect electric conducting objects in a half space. With this technique, the number of unknowns as well as the number of field-source interactions are significantly reduced compared with traditional low-order discretization scheme. Due to the hierarchical property of this method, a uniform mesh can be used for objects that may occupy both background layers with distinct contrast in wavelength. Moreover, For wide-band half-space applications, only one set of coarse mesh generated at the lowest frequency end is needed. Numerical results show that this higher-order method significantly reduces memory requirements and saves much labor in geometrical modeling for general half-space problems.

Analysis of EM Scattering from multiscale conducting structures in a half space

Efficient analysis of electromagnetic scattering from three-dimensional, perfect electrically conducting, multiscale structures in a half space is conducted in this paper. The half-space dyadic Greens function is adopted as the kernel of the electric field integral equation so that the unknowns are only associated with the surface of the scatterers. A recently developed Calderon preconditioner is adopted to significantly improve the ill-conditioning of the matrix due to the multiscale nature of the structures. The kernel-independent multilevel adaptive cross approximation is further implemented to accelerate the computation and reduce the memory requirement. Numerical examples are presented to demonstrate the effectiveness of this method for analyzing multiscale structures situated in a half space.

Numerical analysis of electromagnetic scattering from complex conducting objects on the ground

The electromagnetic scattering from complex conducting objects on the ground is numerically analyzed in this paper. The air-ground environment is modeled as a half space, where the half-space Greens function is invoked in the electric field integral equation. The half-space multilevel fast multitpole algorithm is employed to accelerate the computation and reduce the memory requirement. To improve the condition of the system, the recently developed Calderon preconditioner is extended to the half-space case. Numerical examples will be presented to validate our method.

The adaptive cross approximation algorithm for general half-space scattering problems

The general half-space scattering problems (i.e., the scatterers are straddling the interface of a half-space) are analyzed using the algebraic adaptive cross approximation (ACA) algorithm. As the object is naturally separated into two parts by the interface, two different mesh densities are required due to the contrast of the two background materials. Therefore, two multilevel tree structures are set up individually in the two regions. For the same-side interactions, the grouping strategy is the same as that for free-space problems; while for the different-side couplings, we present a z-dependent grouping scheme. The numerical example is demonstrated to validate the proposed method.