Felipe Vico

Overcoming Low-Frequency Breakdown of the Magnetic Field Integral Equation

In the electromagnetics literature, significant attention has been paid to the problem of low-frequency breakdown in the electric field integral equation. By contrast, the magnetic field integral equation is well-conditioned (in simply connected domains) and can be used in the low frequency limit without modification or preconditioning. Reconstruction of the electric field, however, is subject to catastrophic cancellation unless appropriate measure are taken. In this paper, we show that solving an auxiliary (scalar) integral equation for the charge overcomes this form of low frequency breakdown, both in the near and far fields. Moreover, both the current and charge can be discretized using simple piecewise polynomial basis functions on triangulated surfaces. We also analyze an alternative formulation involving magnetic current and charge and illustrate the performance of the methods with several numerical examples.

Fast convolution with free-space Green's functions

We introduce a fast algorithm for computing volume potentials - that is, the convolution of a translation invariant, free-space Greens function with a compactly supported source distribution defined on a uniform grid. The algorithm relies on regularizing the Fourier transform of the Greens function by cutting off the interaction in physical space beyond the domain of interest. This permits the straightforward application of trapezoidal quadrature and the standard FFT, with superalgebraic convergence for smooth data. Moreover, the method can be interpreted as employing a Nystrom discretization of the corresponding integral operator, with matrix entries which can be obtained explicitly and rapidly. This is of use in the design of preconditioners or fast direct solvers for a variety of volume integral equations. The method proposed permits the computation of any derivative of the potential, at the cost of an additional FFT.

Boundary integral equation analysis on the sphere

We present a systematic analysis of the integral operators of potential theory that arise when solving the Helmholtz or Maxwell equations in the exterior (or interior) of a sphere in the frequency domain. After obtaining expressions for the signatures of layer potentials in the spherical harmonic or vector spherical harmonic basis, we turn to a consideration of various integral equations that have been proposed in the literature for problems of acoustic and electromagnetic scattering. The selection of certain parameters in “combined field” and “Calderon-preconditioned” formulations is shown to have a significant impact on condition number, extending earlier work by Kress and others.

A High-Order Locally Corrected Nyström Scheme for Charge-Current Integral Equations

A high-order Nyström scheme is developed for electromagnetic (EM) scattering problems of smooth objects. The implementation is based on different well-known charge-current formulations. This study aims to develop a novel quadrature scheme to compute different singular integrals that appear on integral equation methods in EMs. The proposed quadrature scheme is used on a locally corrected Nyström method, and applied to charge-current integral equations to obtain a fast, accurate, and a low-frequency stable method to solve EM scattering problems. The proposed method allows obtaining accuracy in the range 4-10 digits in the near electric and magnetic scattered field for certain simple geometries and a wide range of frequencies. We also do a preliminary research on nonsmooth geometries obtaining a certain degree of accuracy depending on the particular charge-current integral equation used.

Optimization of Beam-Tilted Linearly Polarized Radial-Line Slot-Array Antennas

This letter investigates the performance of beam-tilting technique when applied to improve matching of linearly polarized radial-line slot-array antennas. The application of a full-wave analysis reveals a severe deterioration of radiation patterns even for small tilt angles. An iterative optimization procedure is proposed in order to restore the radiation performance in conjunction with the desired matching enhancement. Performance and limitations of the correction procedure are discussed in terms of the beam pointing direction. One prototype is fabricated, and measurements are reported to validate the conclusions of this letter.

Moment Method Analysis of Corrugated Surfaces Using the Aperture Integral Equation

This communication describes a method of moments formulation to analyze the scattering from corrugated surfaces. The approach is based on the aperture integral equation. Such approach decouples the analysis of the impedance effect of the grooves from the external coupling among grooves and allows us to deal accurately with grooves of any shape. Advantage is taken of the geometrical properties of the problem to solve it efficiently using a conjugate gradient-FFT algorithm.

A new Fast Physical Optics method for very large PEC surfaces

A new 3D Fast Physical Optics method is presented for computing backscattered fields at high frequencies of PEC parabolic surfaces. This method can be easily extended to more complex surfaces. By virtue of Cauchy theorem a suitable surface deformation is used to convert a double highly oscillatory integral into a double slow varying integral, easily calculable by means of Gaussian quadrature.

Reduction of the impedance dependence on the Suspended-Strip Gap Waveguide

Summary form only given. Gap waveguides have been recently proposed as an alternative to classical waveguides for the high frequency microwave regime. The use of a periodic bed of nails leads to obtain a guiding structure which do not require contact between metallic walls and do not need the use of dielectrics. Consequently, better results in the manufacturing process and lower losses are obtained. Among gap waveguides, the Suspended-Strip Gap Waveguide (SSGW), shown in Fig. 1a) and 1b), seems to be an interesting option for the prototyping stage, since the same periodic structure can be used for several printed circuits.To the date, designs have been focused to maximize the stopband (SB) of the periodic structure. This implies a period comparable to the strip width. Therefore, the structure will change depending on the strip position and orientation and, hence, the impedance of the transmission line will also have this dependence. As an example, the design presented in (Carlos Gahete Arias et. al, IEEE Microwave and Wirelesss Components Letters, 23, 6, 2013) presents a SB=23GHz-49GHz, Fig. 1c), which covers the operating band (28GHz-40GHz). This structure presents a variation of 7-10 at all frequencies when the strip is horizontally shifted, Fig. 1d), what complicates noticeably the circuit design. In this work, it is proposed the use of a dense periodic structure which results more homogenous. By using optimized p, wp and hp, it is obtained a stopband only slightly lower than previous, SB=25,8GHz-44,5GHz, see Fig. 1e), but now with much lower impedance dependence on position (lower than 2), and also on frequency, Fig. 1f). Moreover, losses remain almost unchanged since the distance ha has been maintained.

Analysis of a multi-quasi-TEM-mode oversized waveguide with one hard wall using the aperture integral equation

An efficient and accurate moment method analysis of a parallel-plate waveguide with one single hard wall using the aperture integral equation (AIE) and the CG-FFT method is presented. This approach is perfectly applicable to new realizations of soft/hard surfaces apart from the classical corrugations. A realization of this waveguide with classical corrugations has been analyzed here. The results corroborate the unique property found for this waveguide: the simultaneous propagation of several independent degenerate quasi-TEM waves.

Asymptotic phase extraction as a preconditioning technique for mom

The most common preconditioners are of algebraic nature, based on sparse inverse approximations of the MoM matrix Z, like the incomplete LU decomposition (ILU). An improvement in the condition number can be also obtained directly in Z using appropriate basis functions, such as higher order basis functions, and multi-resolution techniques. The asymptotic phase integral equation method (AP-IE) is also a method to increase the range of applicability of MoM for high frequencies and smooth scatterers.