Radar Scattering Analysis of Multi-Scale Complex Targets by Fast VSBR-MoM Method in Urban Scenes

A new efficient hybrid technique is presented, which combines the method of moments (MoM) and the shooting and bouncing ray (SBR) for analyzing scattering of complex large structures. By applying the SBR method for the whole structures, a corrected incident field including not only the direct incident field but also the multi-bounce field from the SBR region contributes to the integral equation in the MoM region. For the SBR region, it also considers the interaction from MoM region and then a physical optics (PO) type integration is performed to calculate the scattered field. For complex electrically large electromagnetic problems, the proposed technique is more efficient and simpler to implement in a general-purpose computer code. Numerical results are presented to show the efficiency and accuracy of the method.

An efficient hybrid analysis which hybridizes surface-wire integral equations (SWIE) with physical optics (PO) approximation is presented for wire antennas attached to an electrically large aircraft platform. In the analysis, the whole surface of the platform and antennas is divided into three regions, namely, the method of moments (MoM) region, the PO region and a region referred to as the joint PO-MoM (POM) region in this paper. The MoM region, generally, the smallest one among the three regions, includes wires, wire-surface junctions and a small part of the platform surface surrounding the junctions. A large part of the remaining platform surface forms the PO region with the rest being the POM region which is situated between the MoM and PO regions. The POM region is treated as a MoM region on the one hand so that the total MoM region is sufficiently large to well characterize the platform-attached antennas, whereas it is also regarded as a PO region on the other hand so that its interaction with the PO region needs not to be precisely considered so as to drastically reduce computational requirements.

Eddy current nondestructive evaluation (NDE) of airframe structures involves the detection of electromagnetic field irregularities due to non-conducting inhomogeneities in an electrically conducting material. Usually, the eddy current NDE problem can be formulated by the boundary integral equations (BIE) and discretized into matrix equations by the method of moments (MoM) or the boundary element method (BEM). The fast multipole method (FMM) is a well-established and effective method for accelerating numerical solutions of the matrix equations. Accelerated by the FMM, the BIE method can now solve large-scale electromagnetic wave propagation and diffusion problems. The traditional BIE method requires O(N) operations to compute the system of equations and another O(N) operations to solve the system using direct solvers, with N being the number of unknowns; in contrast, the BIE method accelerated by the two-level FMM can potentially reduce the operations and memory requirement to O(N). Moreover, several approaches have been proposed for the field calculation in the presence of flaws in three dimensional NDE; however, seldom work has been done in applying efficient methods to seek rapid solution in eddy current NDE simulation. As elaborated in the dissertation, we introduce a fast multipole BIE method for two-dimensional diffusive scalar problem and an efficient BIE method for three-dimensional eddy current NDE. Firstly, we work with the two-dimensional Helmholtz equation with a complex wave number for non-trivial boundary geometry. We describe the FMM acceleration procedure of the BIE method and its features briefly, explaining that the FMM is not only efficient in meshing complicated geometries, accurate for solving singular fields or

ABSTRACTA generalized hybrid scheme combining finite element method (FEM) and the method of moments (MOM) is first presented to investigate scattering from a 3-D dielectric object above a 2-D dielectric rough surface. The hybrid FEM/MOM scheme is divided into the FEM region for the object based on Helmholtz’s equation and the MOM region for the rough surface based on coupled integral function, which can greatly reduce the computed region. With the rough surface getting larger, the unknowns of the rough surface get more. So MLFMA is employed to reduce computation complexity of MOM region itself and coupling interaction matrices between MOM region and FEM region. Consequently, the iterative process can be greatly accelerated. This generalized hybrid FEM/MOM is very suitable for investigating scattering from composite model of a complex material object and electrically large dielectric rough surface. Some examples verify this generalized hybrid FEM/MOM in high efficiency, low storage requirement, high precision and generality.

A regularized fast multipole method of moments for rapid calculation of three-dimensional time-harmonic electromagnetic scattering from complex targets

In this paper, an easy method is proposed to reduce the computational complexity of matrix-vector multiplication that is required in solving integral equations using method of moments. This method approximates the Green’s function using a Fourier series. It has the advantage that its formulation separates the observation point from the source point effortlessly and regardless of the Green’s function. Since the fast multipole method uses this idea, the two methods are discussed and compared theoretically and numerically by solving the electromagnetic wave scattering from perfect conductor of three-dimensional basic canonical shape (sphere). The results showed that the proposed method is accurate, and for large number of unknowns in the problem, it has a computational complexity less than the method of moments and over the conventional fast multipole method. Hence, the generality and simplicity of this method compare with the conventional fast multipole method and the efficiency compare with the method of moments, which will be achieved.

Though computational molecular dynamics is an effective tool for nano-scale phenomenon analysis, computational costs associated with its computer simulation are extremely high. There are two major computational steps associated with computer simulation of dynamics of molecular structures. They are calculation of interatomic forces and formation and solution of the equations of motion. Currently, these two computational steps are treated separately in most commonly-used methods. For example, Fast Multipole Method (FMM) and Cell Multipole Method (CMM) have been used for calculation of interatomic forces, and Cartesian Coordinate Method (CCM) and Internal Coordinate Molecular Dynamics Method (ICMD) have been created for the formation and solution of equations of motion of an atomistic molecular system. In this paper, a new procedure is presented through a proper integration between multibody molecular algorithms (MMA) and fast multipole methods to improve computational efficiency for computer simulation of the dynamical behaviors of multibody molecular structures in polymers and biopolymers. For the computational costs associated with interatomic forces, a fast multipole method is used to calculate the interatomic forces due to the potentials. For the computational costs associated with formation and solution of equations of motion, a multibody molecular algorithm developed by the author in his previous work will be utilized to integrate with fast multipole methods. The algorithm significantly improves computational efficiency when comparing with its counterpart procedures. The fast multipole method begins by scaling all atoms into a box with coordinate ranges to ensure numerical stability of subsequent operations. The parent box is then divided into half in the direction of each Cartesian axis and each child box is then subdivided to form a computational family tree. The flow of calculations is carried out along the tree structure with five passes. The fast multipole method has been improved and modified to achieve better effectiveness and higher efficiency since it was created. The multibody molecular algorithm starts with numbering subsets, forming bond graph, and developing three computing passes along the tree structure of an atomistic molecular system. Computing data flows in the fast multipole method and the multibody molecular algorithm will properly line up with the parent-child recursive relationship along the configuration of the tree structure due to linear recursive natures of both fast multipole method and multibody molecular algorithm. Then the time spent on the recursive simulation passes in the fast multipole method for computing forces may overlap with the time spent on the three recursive computational passes in the multibody molecular algorithm for forming and solving equations of motion.

Numerical computations of electromagnetic radiation and scattering problems for arbitrarily shaped and electrically large objects in the same environment are preferably performed by combining the method of moments (MoM) with the uniform geometrical theory of diffraction (UTD). Composite metallic/dielectric objects with arbitrary shape are handled efficiently with the finite element boundary integral (FEBI) method. For large scale problems, the MoM solution is accelerated by the multilevel level fast multipole method (MLFMM). On the other hand, electrically large objects with relatively simple shape are treated sufficiently with ray-based high-frequency methods, like geometrical optics (GO) and UTD. However, until now MoM-UTD hybrid approaches have been restricted to conventional MoM formulations with only the electric field integral equation (EFIE), resulting in limited modeling capabilities. The same restrictions also exist in the hybrid FEBI-UTD method. The paper presents MLFMM-UTD hybridization for the combined field integral equation (CFIE), in order to extend further the applicability of the FEBI-UTD method. The resulting modeling technique is referred to as the FEBI-MLFMM-UTD method. The MLFMM-UTD hybridization is performed in the translation procedure on the various MLFMM levels, by taking into account additional contributions received at the testing groups due to UTD objects. Due to different ray directions for outgoing and incoming waves, appropriate interpolation and anterpolation procedures must be applied to consider the UTD contributions.

The fast multipole method (FMM) is developed to analyse electromagnetic scattering using higher-order hierarchical Legendre basis functions, which have been proposed recently and make the impedance matrix, from method of moments, a low condition number. In this method, the point-to-point based-on-sample quadrature is used because the basis functions are defined on large surface patches of scatterers. The numerical implementations of matrix–vector multiply by FMM are particularly presented. These numerical results show that the proposed second- or third-order FMM (high-order FMM) is accurate and efficient.

Abstract: In this paper, a half space adaptive fast multipole boundary facemethod (FMBFM) is presented for solving the three-dimensional half space ex-terior acoustic problems. In the presented method, the Burton-Miller equationbased on the conventional boundary integral equation (CBIE) and its hyper-singularboundary integral equation (HBIE) is used to deal with the fictitious eigenfrequen-cies problem. The half space Green’s function is employed, thus the tree structurein the fast multipole method can be used only for the real domain. The higher orderelements and an adaptive tree structure are used to improve the efficiency of theFMBFM. This half space adaptive FMBFM for half space acoustic problems is anextension of the adaptive FMBFM for full space acoustic problems developed bythe authors. Numerical examples for half space acoustic problems in this paperdemonstrate the efficiency and validity of this method.Keywords: fast multipole boundary face method, Burton-Miller equation, acous-tic problems, half space, modified hyper-singular boundary integral equation1 IntroductionAcoustic problems in half space are a major subject in engineering. Many researchworks have been done on this aspect (Seybert et al., 1988; Secgin et al., 2010; Caoet al., 2010). The half space Green’s function (Seybert et al., 1988) can be appliedby adding the source solution at the image point to the original full-space Green’sfunction for dealing with half space problems. Sound source localization and iden-tification of a refrigerator were accomplished by using the half space boundaryelement method (BEM) (Secgin et al., 2010). Using the half space Green’s func-tion, the discretization of the rigid infinite plane is removed and only the boundaries

In this paper, an efficient higher order hybrid method of moments (MoM)-physical optics (PO) modeling technique is developed for the analysis of electromagnetic scattering from electrically large conductor objects. This technique utilizes curved triangular patches for geometric modeling, and higher order (HO) basis functions for current modeling, i.e., higher order hierarchical vector (HOHV) basis functions for MoM region and phase-extracted (PE) basis function for PO region. Benefitting from the “double” higher order discretization in both MoM and PO regions, the number of unknowns can be reduced remarkably, and the accuracy and efficiency increase, in comparison to the conventional low order MoM-PO solution. A numerical example is given to demonstrate the validity and efficiency of this HO-MoM-PO.

This paper presents an e-cient and accurate hybrid approach of method of moments (MoM) and physical optics (PO) for radiation problems such as antennas mounted on a large platform. The new method employs higher-order hierarchical Legendre basis functions in the MoM region and higher-order Nystrom scheme in the PO region. The two regions are both discretized with large domains. The unknowns can be much less than those in the small-domain MoM- PO solutions, which will lead to a great reduction in computation complexity. Furthermore, with the Nystrom scheme in the PO region, the higher-order accuracy is maintained, and the calculation of the impedances can be more e-cient than that in the existing higher- order MoM-PO procedure. Numerical results show the validity of the proposed method.

Integral equation based techniques, such as the method of moments (MOM), have been widely used to analyze time harmonic surface scattering phenomena. Unfortunately, time domain counterparts of the MOM, often referred to as marching-on-in-time (MOT) schemes, have historically received scant attention. Classical MOT schemes (i) have long been conceived as intrinsically unstable, and (ii) suffer from a high computational complexity. It is well-known that the computational complexity of the MoM can be reduced by the fast multipole method. A similar time domain algorithm, namely the plane wave time domain (PWTD) algorithm, has been introduced. The PWTD algorithm is designed to be used in tandem with the conventional MOT scheme in either a two-level or a multilevel setting. This paper describes the practical implementation of the two-level scheme and demonstrates the reduction in computational complexity achieved by using the PWTD algorithm. Although the PWTD scheme is applicable to a variety of integral equations arising from the analysis of wave phenomena, this paper illustrates its application in the context of scalar wave scattering from surfaces on which Neumann boundary conditions are enforced-a problem of interest in many disciplines.

Fast multipole singular boundary method for Stokes flow problems

Standard numerical models in acoustics rely on the isentropic Helmholtz equation. Its derivation assumes adiabatic and reversible, i.e., dissipation-free, wave propagation. Sound waves in fluids are, however, subject to viscous and thermal losses. These losses originate from viscous friction and heat conduction, leading to the formation of acoustic boundary layers. Considering these effects becomes significant in setups with acoustic cavities of similar dimension as the boundary layers. Recently, boundary element methods (BEM) accounting for the viscothermal dissipation have been proposed. These methods limit the discretization to the surface of the fluid domain and require significantly fewer degrees of freedom than comparable finite element models. However, the BEM coefficient matrices are fully populated, resulting in high computational costs and storage requirements. This study develops a new BEM formulation for acoustics in viscothermal fluids that uses the fast multipole method - a low-rank approximation technique based on a hierarchical subdivision of the computational domain - to alleviate this shortcoming. It is shown that the fast viscothermal BEM improves the algorithmic complexity over the conventional formulation, reducing both the memory requirements and solution time. The results indicate good scalability of the method making it feasible for larger applications such as acoustic metamaterials.