Wavelets and electromagnetics

Wavelets are an exciting new topic in applied mathematics and signal processing. This paper will provide a brief review of wavelets which are also known as families of functions with an emphasis on interpretation rather than rigor. We will derive an indirect use of wavelets for the solution of integral equations based techniques adapted from image processing. Examples for resistive strips will be given illustrating the effect of these techniques as well as their promise in reducing dramatically the requirement in order to solve an integral equation for large bodies. We also will present a direct implementation of wavelets to solve an integral equation. Both methods suggest future research topics and may hold promise for a variety of uses in computational electromagnetics

User manual for EXCALIBUR: A FE-BI numerical laboratory for cavity-backed antennas in a circular cylinder, version 1.2

The Finite Element-Boundary Integral (FE-BI) technique was used to analyze the scattering and radiation properties of cavity-backed patch antennas recessed in a metallic groundplane. A program, CAVITY3D, was written and found to yield accurate results for large arrays without the usual high memory and computational demand associated with competing formulations. Recently, the FE-BI approach was extended to cavity-backed antennas recessed in an infinite, metallic circular cylinder. EXCALIBUR is a computer program written in the Radiation Laboratory of the University of Michigan which implements this formulation. This user manual gives a brief introduction to EXCALIBUR and some hints as to its proper use. As with all computational electromagnetics programs (especially finite element programs), skilled use and best performance are only obtained through experience. However, several important aspects of the program such as portability, geometry generation, interpretation of results, and custom modification are addressed

A collection of edge-based elements

Edge-based elements have proved useful in solving electromagnetic problems since they are nondivergent. Previous authors have presented several two and three dimensional elements. Herein, we present four types of elements which are suitable for modeling several types of three dimensional geometries. Distorted brick and triangular prism elements are given in cartesian coordinates as well as the specialized cylindrical shell and pie-shaped prism elements which are suitable for problems best described in polar cylindrical coordinates

A finite element-boundary integral method for conformal antenna arrays on a circular cylinder

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This is due to the lack of rigorous mathematical models for conformal antenna arrays, and as a result the design of conformal arrays is primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. Herewith we shall extend this formulation for conformal arrays on large metallic cylinders. In this we develop the mathematical formulation. In particular we discuss the finite element equations, the shape elements, and the boundary integral evaluation, and it is shown how this formulation can be applied with minimal computation and memory requirements. The implementation shall be discussed in a later report

A finite element-boundary integral method for conformal antenna arrays on a circular cylinder

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This was due to the lack of rigorous mathematical models for conformal antenna arrays. As a result, the design of conformal arrays was primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We are extending this formulation to conformal arrays on large metallic cylinders. In doing so, we will develop a mathematical formulation. In particular, we discuss the finite element equations, the shape elements, and the boundary integral evaluation. It is shown how this formulation can be applied with minimal computation and memory requirements

Scattering by cavity-backed antennas on a circular cylinder

Conformal arrays are popular antennas for aircraft, spacecraft, and land vehicle platforms due to their inherent low weight and drag properties. However, to date there has been a dearth of rigorous analytical or numerical solutions to aid the designer. In fact, it has been common practice to use limited measurements and planar approximations in designing such non-planar antennas. The finite element-boundary integral method is extended to scattering by cavity-backed structures in an infinite, metallic cylinder. In particular, the formulation specifics such as weight functions, dyadic Green's function, implementation details and particular difficulties inherent to cylindrical structures are discussed. Special care is taken to ensure that the resulting computer program has low memory demand and minimal computational requirements. Scattering results are presented and validated as much as possible

Radiation by cavity-backed antennas on a circular cylinder

Conformal antenna arrays are popular antennas for aircraft, spacecraft and land vehicle platforms due to their inherent low weight, cost and drag properties. However, to date there has been a dearth of rigorous analytical or numerical solutions to aid the designer. In fact, it has been common practice to use limited measurements and planar approximations in designing such non-planar antennas. The finite element-boundary integral method is extended to radiation by cavity-backed structures in an infinite, metallic cylinder. The formulation is used to investigate the effect of cavity size on the radiation pattern for typical circumferentially and axially polarized patch antennas. Curvature effect on the gain, pattern shape, and input impedance is also studied. Finally, the accuracy of the FE-BI approach for a microstrip patch array is demonstrated

Electromagnetic characterization of conformal antennas

The ultimate objective of this project is to develop a new technique which permits an accurate simulation of microstrip patch antennas or arrays with various feed, superstrate and/or substrate configurations residing in a recessed cavity whose aperture is planar, cylindrical or otherwise conformed to the substructure. The technique combines the finite element and boundary integral methods to formulate a system suitable for solution via the conjugate gradient method in conjunction with the fast Fourier transform. The final code is intended to compute both scattering and radiation patterns of the structure with an affordable memory demand. With upgraded capabilities, the four included papers examined the radar cross section (RCS), input impedance, gain, and resonant frequency of several rectangular configurations using different loading and substrate/superstrate configurations

A Charge Conserving Exponential Predictor Corrector FEMPIC Formulation for Relativistic Particle Simulations

The state of art of charge-conserving electromagnetic finite element particle-in-cell has grown by leaps and bounds in the past few years. These advances have primarily been achieved for leap-frog time stepping schemes for Maxwell solvers, in large part, due to the method strictly following the proper space for representing fields, charges, and measuring currents. Unfortunately, leap-frog based solvers (and their other incarnations) are only conditionally stable. Recent advances have made Electromagnetic Finite Element Particle-in-Cell (EM-FEMPIC) methods built around unconditionally stable time stepping schemes were shown to conserve charge. Together with the use of a quasi-Helmholtz decomposition, these methods were both unconditionally stable and satisfied Gauss' Laws to machine precision. However, this architecture was developed for systems with explicit particle integrators where fields and velocities were off by a time step. While completely self-consistent methods exist in the literature, they follow the classic rubric: collect a system of first order differential equations (Maxwell and Newton equations) and use an integrator to solve the combined system. These methods suffer from the same side-effect as earlier--they are conditionally stable. Here we propose a different approach; we pair an unconditionally stable Maxwell solver to an exponential predictor-corrector method for Newton's equations. As we will show via numerical experiments, the proposed method conserves energy within a PIC scheme, has an unconditionally stable EM solve, solves Newton's equations to much higher accuracy than a traditional Boris solver and conserves charge to machine precision. We further demonstrate benefits compared to other polynomial methods to solve Newton's equations, like the well known Boris push.Comment: 12 pages, 15 figure

An ultrawideband (UWB) switched-antenna-array radar imaging system

phased array radar system is developed that requires only one exciter and digital receiver that is time-division-multiplexed (TDM) across 8 receive elements and 13 transmit elements, synthesizing a fully populated 2.24 m long (λ/2 element-to-element spacing) linear phased array. A 2.24 m linear phased array with a 3 GHz center frequency would require 44 antenna elements but this system requires only 21 elements and time to acquire bi-static pulses across a subset of element combinations. This radar system beamforms in the near field, where the target scene of interest is located 3-70 m down range. It utilizes digital beamforming, computed using the range migration synthetic aperture radar (SAR) algorithm. The phased array antenna is fed by transmit and receive fan-out switch matrices that are connected to a UWB LFM pulse compressed radar operating in stretch mode. The peak transmit power is 1 mW and the transmitted LFM pulses are long in time duration (2.5-10 ms), requiring the radar to transmit and receive simultaneously. It will be shown through simulation and measurement that the bi-static antenna pairs are nearly equivalent to 44 elements spaced λ/2 across a linear array. This result is due to the fact that the phase center position errors relative to a uniform λ/2 element spacing are negligible. This radar is capable of imaging free-space target scenes made up of objects as small as 15.24 cm tall rods and 3.2 cm tall metal nails at a 0.5 Hz rate. Applications for this radar system include short-range near-real-time imaging of unknown targets through a lossy dielectric slab and radar cross section (RCS) measurements. I