Ali E. Yilmaz

Time domain adaptive integral method for surface integral equations

An efficient marching-on-in-time (MOT) scheme is presented for solving electric, magnetic, and combined field integral equations pertinent to the analysis of transient electromagnetic scattering from perfectly conducting surfaces residing in an unbounded homogenous medium. The proposed scheme is the extension of the frequency-domain adaptive integral/pre-corrected fast-Fourier transform (FFT) method to the time domain. Fields on the scatterer that are produced by space-time sources residing on its surface are computed: 1) by locally projecting, for each time step, all sources onto a uniform auxiliary grid that encases the scatterer; 2) by computing everywhere on this grid the transient fields produced by the resulting auxiliary sources via global, multilevel/blocked, space-time FFTs; 3) by locally interpolating these fields back onto the scatterer surface. As this procedure is inaccurate when source and observer points reside close to each other; and 4) near fields are computed classically, albeit (pre-)corrected, for errors introduced through the use of global FFTs. The proposed scheme has a computational complexity and memory requirement of O(N/sub t/N/sub s/log/sup 2/N/sub s/) and O(N/sub s//sup 3/2/) when applied to quasiplanar structures, and of O(N/sub t/N/sub s//sup 3/2/log/sup 2/N/sub s/) and O(N/sub s//sup 2/) when used to analyze scattering from general surfaces. Here, N/sub s/ and N/sub t/ denote the number of spatial and temporal degrees of freedom of the surface current density. These computational cost and memory requirements are contrasted to those of classical MOT solvers, which scale as O(N/sub t/N/sub s//sup 2/) and O(N/sub s//sup 2/), respectively. A parallel implementation of the scheme on a distributed-memory computer cluster that uses the message-passing interface is described. Simulation results demonstrate the accuracy, efficiency, and the parallel performance of the implementation.

Fast and Rigorous Analysis of EMC/EMI Phenomena on Electrically Large and Complex Cable-Loaded Structures

A fast and comprehensive time-domain method for analyzing electromagnetic compatibility (EMC) and electromagnetic interference (EMI) phenomena on complex structures that involve electrically large platforms (e.g., vehicle shells) along with cable-interconnected antennas, shielding enclosures, and printed circuit boards is proposed. To efficiently simulate field interactions with such structures, three different solvers are hybridized: (1) a time-domain integral-equation (TDIE)-based field solver that computes fields on the exterior structure comprising platforms, antennas, enclosures, boards, and cable shields (external fields); (2) a modified nodal-analysis (MNA)-based circuit solver that computes currents and voltages on lumped circuits approximating cable connectors/loads; and (3) a TDIE-based transmission line solver that computes transmission line voltages and currents at cable terminations (guided fields). These three solvers are rigorously interfaced at the cable connectors/loads and along the cable shields; the resulting coupled system of equations is solved simultaneously at each time step. Computation of the external and guided fields, which constitutes the computational bottleneck of this approach, is accelerated using fast Fourier transform-based algorithms. Further acceleration is achieved by parallelizing the computation of external fields. The resulting hybrid solver permits the analysis of electrically large and geometrically intricate structures loaded with coaxial cables. The accuracy, efficiency, and versatility of the proposed solver are demonstrated by analyzing several EMC/EMI problems including interference between a log-periodic monopole array trailing an aircrafts wing and a monopole antenna mounted on its fuselage, coupling into coaxial cables connecting shielded printed circuit boards located inside a cockpit, and coupling into coaxial cables from a cell phone antenna located inside a fuselage.

A parallel FFT accelerated transient field-circuit simulator

A novel fast electromagnetic field-circuit simulator that permits the full-wave modeling of transients in nonlinear microwave circuits is proposed. This time-domain simulator is composed of two components: 1) a full-wave solver that models interactions of electromagnetic fields with conducting surfaces and finite dielectric volumes by solving time-domain surface and volume electric field integral equations, respectively, and 2) a circuit solver that models field interactions with lumped circuits, which are potentially active and nonlinear, by solving Kirchoffs equations through modified nodal analysis. These field and circuit analysis components are consistently interfaced and the resulting coupled set of nonlinear equations is evolved in time by a multidimensional Newton-Raphson scheme. The solution procedure is accelerated by allocating field- and circuit-related computations across the processors of a distributed-memory cluster, which communicate using the message-passing interface standard. Furthermore, the electromagnetic field solver, whose demand for computational resources far outpaces that of the circuit solver, is accelerated by a fast Fourier transform (FFT)-based algorithm, viz. the time-domain adaptive integral method. The resulting parallel FFT accelerated transient field-circuit simulator is applied to the analysis of various active and nonlinear microwave circuits, including power-combining arrays.

Fast analysis of transient scattering in lossy media

The solution of time-domain integral equations pertinent to scattering from perfectly conducting objects residing in unbounded lossy media is considered. The computational cost of classical marching-on-in-time (MOT) schemes for the solution of such equations scales as O(N/sub t//sup 2/N/sub s//sup 2/), where N/sub t/ and N/sub s/ are the number of temporal and spatial unknowns, respectively. A fast Fourier transform (FFT)-based algorithm that reduces the computational complexity to O(N/sub t/N/sub s//sup 2/log/sup 2/N/sub t/) is introduced. When combined with spatial FFT algorithms, the proposed scheme further reduces the complexity of MOT-based integral equation solvers, for example to O(N/sub t/N/sub s/log(N/sub t/N/sub s/)logN/sub t/) if the objects are uniformly meshed. Numerical simulations that demonstrate the accuracy and efficiency of the algorithm are presented.

Fast solution of mixed-potential time-domain integral equations for half-space environments

A fast Fourier transform-accelerated integral-equation based algorithm to efficiently analyze transient scattering from planar perfect electrically conducting objects residing above or inside a potentially lossy dielectric half-space is presented. The algorithm requires O(N/sub t/N/sub s/(logN/sub s/+log/sup 2/N/sub t/)) CPU and O(N/sub t/N/sub s/) memory resources when analyzing electromagnetic wave interactions with uniformly meshed planar structures. Here, N/sub t/ and N/sub s/ are the numbers of simulation time steps and spatial unknowns, respectively. The proposed scheme is therefore far more efficient than classical time-marching solvers, the CPU and memory requirements of which scale as O(N/sub t//sup 2/N/sub s//sup 2/) and O(N/sub t/N/sub s//sup 2/). In the proposed scheme, all pertinent time-domain half-space Green functions are (pre) computed from their frequency-domain counterparts via inverse discrete Fourier transformation. In this process, in-band aliasing is avoided through the application of a smooth and interpolatory window. Numerical results demonstrate the accuracy and efficiency of the proposed algorithm.

A hierarchical FFT algorithm (HIL-FFT) for the fast analysis of transient electromagnetic scattering phenomena

A fast algorithm for accelerating the time-marching solution of time-domain integral equations pertinent to the analysis of free-space electromagnetic scattering from perfectly conducting, platelike and uniformly meshed structures is presented. The matrix-vector multiplications required by the time-marching scheme are accelerated by use of the fast Fourier transform (FFT). This acceleration is achieved in a multilevel fashion by hierarchically grouping sparse interactions to extract denser pieces that are efficiently evaluated by the FFT. The total computational cost and storage requirements of this algorithm scale as O(N/sub t/N/sub s/log/sup 2/ N/sub s/) and O(N/sup 1.5/), respectively, as opposed to O(N/sub t/N/sub s//sup 2/) and O(N/sub s//sup 2/) for classical time-marching methods (N/sub s/ and N/sub t/ denote the total number of spatial unknowns and time steps, respectively). Simulation results demonstrate the accuracy and efficiency of the algorithm.

A Fast Fourier Transform Accelerated Marching-on-in-Time Algorithm for Electromagnetic Analysis

A fast algorithm is presented for solving a time-domain electric field integral equation (EFIE) pertinent to the analysis of scattering from uniformly meshed, perfectly conducting structures. The marching-on-in-time (MOT) scheme that results from discretizing this EFIE is accelerated by using the fast Fourier transform to perform spatial convolutions. The computational cost and storage requirements of this algorithm scale as O(NtNs 1.5) and O(Ns 1.5), respectively, as opposed to O(NtNs 2) and O(Ns 2) for classical MOT methods. Simulation results demonstrate the accuracy and efficiency of the approach and suggestions for extending the technique are proffered.

An FFT-Accelerated Time-Domain Multiconductor Transmission Line Simulator

A fast time-domain multiconductor transmission line (MTL) simulator for analyzing general MTL networks is presented. The simulator models the networks as homogeneous MTLs that are excited by external fields and driven/terminated/connected by potentially nonlinear lumped circuitry. It hybridizes an MTL solver derived from time-domain integral equations (TDIEs) in unknown wave coefficients for each MTL with a circuit solver rooted in modified nodal analysis equations in unknown node voltages and voltage-source currents for each circuit. These two solvers are rigorously interfaced at MTL and circuit terminals, and the resulting coupled system of equations is solved simultaneously for all MTL and circuit unknowns at each time step. The proposed simulator is amenable to hybridization, is fast Fourier transform (FFT)-accelerated, and is highly accurate: 1) It can easily be hybridized with TDIE-based field solvers (in a fully rigorous mathematical framework) for performing electromagnetic interference and compatibility analysis on electrically large and complex structures loaded with MTL networks; 2) It is accelerated by an FFT algorithm that calculates temporal convolutions of time-domain MTL Green functions in only O(N t log2 N t ) rather than O(N t 2) operations, where N t is the number of time steps of simulation. Moreover, the algorithm, which operates on temporal samples of MTL Green functions, is indifferent to the method used to obtain them; 3) It approximates MTL voltages, currents, and wave coefficients, using high-order temporal basis functions. Various numerical examples, including the crosstalk analysis of a (twisted) unshielded twisted-pair (UTP)-CAT5 cable and the analysis of field coupling into UTP-CAT5 and RG-58 cables located on an airplane, are presented to demonstrate the accuracy, efficiency, and versatility of the proposed simulator.

Microwave-assisted Low-temperature Growth of Thin Films in Solution

Thin films find a variety of technological applications. Assembling thin films from atoms in the liquid phase is intrinsically a non-equilibrium phenomenon, controlled by the competition between thermodynamics and kinetics. We demonstrate here that microwave energy can assist in assembling atoms into thin films directly on a substrate at significantly lower temperatures than conventional processes, potentially enabling plastic-based electronics. Both experimental and electromagnetic simulation results show microwave fields can selectively interact with a conducting layer on the substrate despite the discrepancy between the substrate size and the microwave wavelength. The microwave interaction leads to localized energy absorption, heating, and subsequent nucleation and growth of the desired films. Electromagnetic simulations show remarkable agreement with experiments and are employed to understand the physics of the microwave interaction and identify conditions to improve uniformity of the films. The films can be patterned and grown on various substrates, enabling their use in widespread applications.

A Three-Dimensional Adaptive Integral Method for Scattering From Structures Embedded in Layered Media

A 3-D extension of the adaptive integral method (AIM) is presented for fast analysis of scattering from electrically large perfect electrically conducting structures embedded inside a single layer of a planar layered medium. The proposed scheme accelerates the iterative method-of-moments (MOM) solution of the combined-field integral equation by employing a 3-D auxiliary regular grid. It uses the auxiliary grid to execute the standard four-stage AIM procedure; unlike the procedure for free space, two different sets of matrices are obtained for the AIM propagation stage by decomposing the Green functions to terms that are in convolution or correlation form in the stratification direction. These matrices are in (three level) block-Toeplitz and Hankel-(two level)-block-Toeplitz forms and can be multiplied by using 3-D FFTs. The dominant computational costs of the scheme are the evaluation of O(N) different layered-medium Green functions, which is accelerated by extracting asymptotic terms and using interpolation tables, and the matrix multiplications in the propagation stage, which require only O(NC log NC) per iteration; these should be contrasted to the O(N2) Green function evaluations and O(N2) operations per iteration required by the classical MOM. Here, NC denotes the number of nodes on the auxiliary grid, and N denotes the number of degrees of freedom of the surface current density. Numerical results validate the proposed methods complexity, demonstrate its accuracy for several large-scale structures in layered media, and compare its computational costs to those of its counterpart for free space.