Iterative Solutions of Hybrid Integral Equations for Coexisting Open and Closed Surfaces

We consider electromagnetics problems involving composite geometries with coexisting open and closed conductors. Hybrid integral equations are presented to improve the efficiency of the solutions, compared to the conventional electric-field integral equation. We investigate the convergence characteristics of iterative solutions of large composite problems with the multilevel fast multipole algorithm. Following a thorough study of how the convergence characteristics depends on the problem geometry, formulation, and iterative solvers, we provide concrete guidelines for efficient solutions

Preconditioned MLFMA Solution of Multiple Dielectric-Metallic Composite Objects with the Electric and Magnetic Current Combined-Field Integral Equation (JMCFIE)

We consider fast and accurate solutions of scattering problems involving multiple dielectric and composite dielectric-metallic structures with three-dimensional arbitrary shapes. Problems are formulated rigorously with the electric and magnetic current combined-field integral equation (JMCFIE), which produces well-conditioned matrix equations. Equivalent electric and magnetic surface currents are discretized by using the Rao-Wilton-Glisson (RWG) functions defined on planar triangles. Matrix equations obtained with JMCFIE are solved iteratively by employing a Krylov subspace algorithm, where the required matrix- vector multiplications are performed efficiently with the multilevel fast multipole algorithm (MLFMA). We also present a four-partition block-diagonal preconditioner (4PBDP), which provides efficient solutions of JMCFIE by reducing the number of iterations significantly. The resulting implementation based on JMCFIE, MLFMA, and 4PBDP is tested on large electromagnetics problems

Hierarchical Parallelization of the Multilevel Fast Multipole Algorithm (MLFMA)

Due to its O(NlogN) complexity, the multilevel fast multipole algorithm (MLFMA) is one of the most prized algorithms of computational electromagnetics and certain other disciplines. Various implementations of this algorithm have been used for rigorous solutions of large-scale scattering, radiation, and miscellaneous other electromagnetics problems involving 3-D objects with arbitrary geometries. Parallelization of MLFMA is crucial for solving real-life problems discretized with hundreds of millions of unknowns. This paper presents the hierarchical partitioning strategy, which provides a very efficient parallelization of MLFMA on distributed-memory architectures. We discuss the advantages of the hierarchical strategy over previous approaches and demonstrate the improved efficiency on scattering problems discretized with millions of unknowns

Subsurface-scattering calculations via the 3D FDTD method employing PML ABC for layered media

A three-dimensional finite-difference time-domain method that employs pure scattered-field formulation and perfectly matched layers (PML) as the absorbing boundary condition is developed for solving subsurface-scattering. A subsurface radar is modeled and the fields scattered from various buried objects with different parameters such as the size, depth, and number are observed and distinguished. The `derivative' signal, which can easily be obtained in practical systems, is useful in identifying the buried objects

Fast multipole method in layered media: 2-D electromagnetic scattering problems

In this study, the Fast Multipole Method (FMM) is extended to layered-media problems. As an example, the solution of the scalar Helmholtz equation for the electromagnetic scattering from a two-dimensional planar array of horizontal strips on a layered substrate is demonstrated

Three-dimensional FDTD modeling of a GPR

The power and flexibility of the Finite-Difference Time-Domain (FDTD) method are combined with the accuracy of the perfectly-matched layer (PML) absorbing boundary conditions to simulate realistic ground-penetrating radar (GPR) scenarios. Three-dimensional geometries containing modes of radar units, buried objects and surrounding environments are simulated. Simulation results are analyzed in detail

Fast noniterative steepest descent path algorithm for planar and quasi-planar patch geometries

The fast noniterative steepest descent path (SDP) algorithm for planar and quasi-planar patch geometries are discussed. The comparison of scattered fields as computed by the method of moments (MOM) and fast direct algorithm (FDA)/SDP are described. The solution times of FDA/SDP, MOM, and recursive aggregate-T-matrix algorithm (RATMA) are obtained by solving the scattering problems of increasingly larger planar arrays of patches without taking advantage of the periodicities and the symmetries of these arrays

Fast direct (noniterative) solvers for integral-equation formulations of scattering problems

A family of direct (noniterative) solvers with reduced computational complexity is proposed for solving problems involving resonant or near-resonant structures. Based on the recursive interaction matrix algorithm, the solvers exploit the aggregation concept of the recursive aggregate T-matrix algorithm to accelerate the solution. Direct algorithms are developed to compute the scattered field and the current coefficient, and invert the impedance matrix. Computational complexities of these algorithms are expressed in terms of the number of harmonics P required to express the scattered field of a larger scatterer made up of N scatterers. The exact P-N relation is determined by the geometry

Fast direct solution algorithm for electromagnetic scattering from 3D planar and quasi-planar geometries

A non-iterative method and its application to planar geometries in homogeneous media is presented. The method is extendable to the cases of quasi-planar structures and/or layered-media problems. The fast direct algorithm (FDA)/steepest descent path (SDP) takes advantage of the fact that the induced currents on planar and quasi-planar geometries interact with each other within a very limited solid angle. Thus, all the degrees of freedom required to solve a `truly 3D' geometry are not required for a planar or quasi-planar geometry, and this situation can be exploited to develop efficient solution algorithms

Efficient methods for electromagnetic characterization of 2-D geometries in stratified media

Applied to 2D planar multilayer geometries, the method of moments (MoM) transforms integral equations into matrix equations whose entries become double integrals over finite domains in the spatial domain MoM, and single integrals over infinite domain in the spectral domain MoM. To efficiently evaluate these integrals, three algorithms are considered to evaluate the MoM matrix entries. These are: the spatial domain MoM in conjunction with the closed form Green's function; the spectral domain MoM using the generalized pencil of functions (GPOF) algorithm; and the FFT algorithm. All the approaches demonstrate good accuracy; however, in terms of numerical efficiency, the GPOF-based algorithm in the spectral domain MoM performs the best