Discretization In Method Of Moments Research Articles

Locally Corrected Nyström to Moment Method Conversion for Volume Integral Equations

In this paper, a technique to convert a locally corrected Nystrom discretization into a moment method discretization is detailed. The method is general and does not rely directly on any specific relationship between the basis functions used to compute the local corrections and the basis and test functions used in the moment method. The technique is applied to a quasi-magnetostatic volume integral equation for both interpolatory and algebraically constrained moment method bases. Numerical results for a variety of problems in terms of error convergence, system condition number, and degrees-of-freedom are provided.

Divergence-Conforming Constrained Basis Functions for Hexahedral Volume Elements

This communication presents an algebraic method for constructing arbitrary-order, divergence-conforming basis functions on hexahedral volume elements. The appropriate constraints within and on the boundaries of elements are provided. In particular, the handling of faces where quantities are discontinuous is discussed. The resulting bases are numerically characterized in terms of error convergence and system conditioning for a moment method discretization of the electric field volume integral equation for dielectric scatterers. Results show the accuracy of the proposed method as well as the low system matrix condition number that can be maintained as the basis order and mesh discretization are increased.

A Mixed Potential MLFMA for Higher Order Moment Methods With Application to the Generalized Method of Moments

The application of the multilevel fast multipole algorithm (MLFMA) to higher order moment method discretizations is a continuing open problem. Herein, we present a point-based mixed potential variant of the MLFMA algorithm that exhibits an MLFMA tree of arbitrary height with no restriction related to basis function support size, efficient nearfield precomputation, and that maintains favorable scaling for any mixture of low- and high-order bases. The flexibility of the algorithm is also leveraged to accelerate the precomputation of algebraic preconditioners. We demonstrate the method through application to the generalized method of moments (GMM), a recently introduced moment method discretization capable of combining both low- and high-order bases and geometries in the same simulation; however, the method may be used to accelerate other higher order moment methods as well.

Rapid RWG Moment Method Solution of EFIE for Multiscale Problems via Hierarchical Center of Radiation Approximation in Barnes–Hut Algorithm

The Barnes-Hut algorithm utilizing hierarchical center-of-radiation approximation is applied for acceleration of quasi-static interactions in RWG Moment Method discretization of the electric field integral equation. As the method uses imbalanced oct-tree in hierarchical partitioning of the model, it maintains efficiency in memory and CPU usage when geometry of about a wavelength in size presents multiscale features. Because the center-of-radiation position in each box of hierarchically partitioned space is dependent on the direction to the observation point, the field evaluation in the Barnes-Hut algorithm is done via an interpolation scheme. Augmentation of the Barnes-Hut algorithm with local interpolation schemes is demonstrated. Impact on the error control mechanisms via angular interpolation and source clustering distance on the efficiency of the algorithm is studied.

Divergence-conforming discretization of second-kind integral equations for the RCS computation in the Rayleigh frequency region

[1] The divergence-conforming discretization in method of moments of the magnetic field integral equation (MFIE) shows huge inaccuracies in the computed radar cross section (RCS) at the very low or extremely low frequency regime. We justify theoretically that the presence of this error in the computed RCS can be mitigated to some extent for some sharp-edged objects, where this discrepancy is most evident, through the adoption of uniformly triangular or quadrangular meshings. Moreover, we present two discretizations in method of moments of second-kind integral equations that are free from these huge RCS inaccuracies: (1) a modified implementation of the conventional Rao-Wilton-Glisson (RWG) discretization of the MFIE that provides in two steps the static and dynamic current components so that the nonsolenoidal static contribution can be discarded in the far-field computation; and (2) the loop-star discretization in method of moments of the novel electric-magnetic field integral equation (EMFIE) which provides inherently a null static nonsolenoidal current contribution whereby a static-dynamic decomposition of the current is not required.

Modal properties of surface and leaky waves propagating at arbitrary angles along a metal strip grating on a grounded slab

A full-wave analysis is presented of the dispersion properties of modes supported by a grounded dielectric slab periodically loaded with metal strips, which represents a canonical configuration employed in planar microwave antennas and arrays and in the realization of artificially hard and soft surfaces. Propagation of surface and leaky modes at arbitrary angles is considered here, without any restrictive assumption on the values of the involved physical and geometrical parameters. Spectral properties of modes are studied, by deriving generalized conditions for establishing the proper or improper nature of the spatial harmonics in the Floquet representation of the fields. The proposed approach, based on a full-wave moment-method discretization of the relevant electric-field integral equation in the spectral domain, is validated through comparisons with the available data in the literature. Novel results are presented which illustrate the continuous evolution of modes as a function of the propagation angle along the grating, both in surface and leaky propagation regimes.

Surface currents induced on a dielectric half‐space by a Gaussian beam: An extended validation for point matching method of moment codes

An approximate analytical solution for electric surface currents induced on a planar dielectric half‐space by a normally incident Gaussian beam is presented. This solution provides a useful tool for testing discretization methods in point matching moment method codes for penetrable rough surface scattering which use a Gaussian beam “tapered” incident field to avoid edge effects. For one example case illustrated, the surface current solution obtained can be shown to satisfy standard impedance boundary condition integral equations at the beam center to within 0.01% accuracy, and a separation of individual term contributions to the entire integral equation enables a detailed check of moment method discretization procedures to be performed.

Transient excitation of a straight thin-wire segment: a new look at an old problem

The transient excitation of a straight thin-wire segment is analyzed with the aid of a one-dimensional integral equation for the current along the wire. An almost exact derivation of that equation, in which only the radial current on the end faces is approximated, is given. The integral equation obtained turns out to be identical to the reduced version of Pocklington's equation. On the basis of this derivation, existing and new numerical solution techniques are critically reviewed. Pocklington's equation and Hallen's equivalent form are solved directly by marching on in time as well as indirectly via a transformation to the frequency domain. For Pocklington's equation, a conventional moment-method discretization leads to a Toeplitz matrix that is inverted with Levinson's algorithm. For Hallen's equation, the Toeplitz structure is disturbed, and the frequency-domain constituents are determined with the aid of the conjugate-gradient-FFT method. Illustrative numerical results are presented and discussed. >

Physical and mathematical structure determine convergence rate of iterative techniques

The use of various iterative techniques used to solve the moment-method equation is discussed. The conjugate gradient method has previously been used to solve moment-method problems. Since the moment-method matrix (theoretically) has a positive definite Hermitian part, the generalized conjugate residual (GCR) method can also be used. Sample calculations show that the GCR has superior convergence, especially when the moment-method discretization preserves the abovementioned matrix property. >