New analytical expressions for the computation of physical optics (PO) integrals in the analysis of scattered or radiated fields due to large objects are presented. The PO current is expanded in terms of current modes. Each current mode is defined by an exponential term whose amplitude and exponent are smooth functions. The analytical expressions are valid to compute the PO integral of modes with the exponent (phase) defined by means of quadratic functions. These expressions permit an accurate and efficient evaluation of the integrals over electrically large surfaces. Representative results showing the performance obtained are presented

Analytical Field Calculation Involving Current Modes and Quadratic Phase Expressions

A new physical optics (PO) formulation is presented to treat radiation and scattering problems of curved bodies, including multiple reflections between the body parts. The approach uses electric and magnetic PO currents that are expanded as exponential terms. These terms are defined by spatially slow-varying amplitude and exponent functions. All the reflections of a multiple bounce contribution are computed by using PO, considering a very efficient recursive scheme to evaluate the PO integrals using quasi-analytical expressions. The complex problem of obtaining the shadowed areas in curved bodies for multiple reflections is avoided, thanks to the electric and magnetic PO currents chosen. These currents extend over the complete area of the body, including lit or shadowed parts. In the lit parts, the currents provide the reflected field, while in the shadow parts, they give a scattered field that, together with the incident field, causes a total null field in the shadows. The currents do not radiate on their back directions. This approach is useful for the analysis of bodies that can be characterized electrically by an impedance boundary condition (IBC). A combination of these currents with the angular Z-buffer (AZB) ray tracing technique makes it possible to analyze simple or complex cases efficiently.

New Physical Optics Approach for an Efficient Treatment of Multiple Bounces in Curved Bodies Defined by an Impedance Boundary Condition

To extend hybrid high-frequency shooting and bouncing rays–physical optics (SBR–PO) method to the modeling of electromagnetic (EM) scattering from an object in half-space, this paper focuses on addressing two key issues: 1) how to accurately obtain the induced electric currents on the object surface by taking into account the EM interactions between the object and half-space and 2) how to accurately calculate far-fields in half-space configuration. First, by introducing virtual interface of half-space, the proposed method avoids physically modeling the underlying ground, and only induced electric currents on the object are effectively taken into account in the SBR process. Second, the closed-form half-space Green’s function is used to calculate scattered far-fields to avoid the time-consuming evaluation of the Sommerfeld integrals. The computational errors are only from the approximation of induced electric currents with the same level of the SBR–PO method for the solution of the free-space problem, so the proposed method is more accurate than the conventional SBR–PO technique. Besides, performing the proposed method on the graphics processing unit platform to further accelerate the ray-tracing process makes the method even more powerful to solve the extra-large-scale scattering problems in the half-space.

Novel Extension of SBR–PO Method for Solving Electrically Large and Complex Electromagnetic Scattering Problem in Half-Space

A hierarchical interpolative decomposition multilevel fast multipole algorithm (ID-MLFMA) is proposed to handle multiscale, dynamic electromagnetic problems. The hierarchical scheme to conduct the ID skeletonization and to implement the matrix vector multiplication is discussed. A strategy to improve the e-ciency of ID skeletonization is developed. The hierarchical ID-MLFMA are investigated by numerical experiments on complex targets, demonstrating the capability of the hierarchical ID-MLFMA.

/pdf/hierarchical-interpolative-decomposition-multilevel-fast-ohstb505lu.pdf

Hierarchical interpolative decomposition multilevel fast multipole algorithm for dynamic electromagnetic simulations

A method and system for analyzing the RCS of an object using N Point signature prediction models is provided. N-point signature prediction models are created for each object in a scenario and stored in lookup tables. Shooting and Bounce trace back techniques are used to determine RCS signatures of multiple objects in modeled scenarios to account for blockage by and coupling phenomena of a scattered field.

Rcs signature generation for closely spaced multiple objects using n-point models

The paper presents several improvements in ray-tracing acceleration techniques to compute diffraction and doubles and triples effects in the RCS (radar cross section) as fast as possible and minimize the use of computer memory. The approach is based on the application of the angular Z-buffer (AZB) algorithm together with the SVP (space volumetric partitioning) algorithm, for electrically large and complex bodies modelled by a high number of flat and/or curved surfaces.

Improvements in ray-tracing acceleration techniques to compute diffraction effect and doubles and triples effects in the RCS prediction of complex targets

A numerically e-cient approach for the rigorous compu- tation of bi-static scattering and radiation problems is presented. The approach is based on an improvement of a previous method scheme that combines the Characteristic Basis Function Method (CBFM) and the Multilevel Fast Multipole Algorithm (MLFMA). The approach com- bines Characteristic Basis Functions (CBFS) and subdomains func- tions for reducing the CPU time in the pre-process and in the solving iterative process for simple or multiple excitations. It is intended for use in very large cases where an iterative solution process cannot be avoided, even considering the matrix size reduction achieved by the CBFM. This reduction is particularly important for solving radiation or bistatic problems in which an integral equation is solved once.

/pdf/an-efficient-hybrid-scheme-combining-the-characteristic-mbay9ewd83.pdf

An Efficient Hybrid-Scheme Combining the Characteristic Basis Function Method and the Multilevel Fast Multipole Algorithm for Solving Bistatic RCS and Radiation Problems

Efficient combination of acceleration techniques applied to high frequency methods for solving radiation and scattering problems

An efficient hybrid technique in RCS predictions of complex targets at high frequencies

A new ray-tracing method has been developed for the analysis of antennas on-board complex structures and to compute the propagation at indoor/outdoor environments considering n-bounces. The structures (satellites, ships, aircrafts, etc.) are modeled by planar and/or curved surfaces defined by perfectly electrical conductors or dielectric materials (with or without losses). The structures are defined as parametric surfaces, in particular by NURBS (Non-Uniform Rational B-Spline) surfaces. The approach is based on the Uniform Theory of Diffraction (UTD) for the field computation.

Lorena Lozano

Papers

Improvements in ray-tracing acceleration techniques to compute diffraction effect and doubles and triples effects in the RCS prediction of complex targets

An Efficient Hybrid-Scheme Combining the Characteristic Basis Function Method and the Multilevel Fast Multipole Algorithm for Solving Bistatic RCS and Radiation Problems

Efficient combination of acceleration techniques applied to high frequency methods for solving radiation and scattering problems

An efficient hybrid technique in RCS predictions of complex targets at high frequencies

Fast ray-tracing for computing n-bounces between curved surfaces