Method Of Moments Code Research Articles

Efficient Parallelization of Electromagnetic Field Computations on a Beowulf Cluster

In this paper, efficient high performance computation of electromagnetic field problems using a Beowulf cluster and MatLab® is presented. A cluster with one master node, eight identical computing nodes, and a Gigabit Ethernet (GbE) switch is firstly built. An open source Rocks toolkit solution is used to simplify the process of deploying high-performance parallel computing clusters. Then, three computational electromagnetic applications are developed and implemented on the cluster using parallel MatLab. In the first application, is calculated the input impedance of a multilayer multiconductor circular microstrip antenna that is excited with coaxial probe and operating in a wide frequency band. Parallelization is then performed over the frequency vector permitting a speedup ratio of 23. In the second application, is presented a systematic method for generating and computing symbolic expressions of 3D tetrahedral FEM basis functions of higher orders up to 10. The final application is dedicated to the parallelization of the spatial moment method code for 2D array of bowtie antenna. The simulation results have shown that the array size can be increased considerably leading to a linear system with a size up to 100 times greater than the one under study.

Optimization Methods for the Design of Sensitive Surface ESR Resonators

Electron spin resonance (ESR) is a powerful spectroscopic technique that has many applications in a wide variety of scientific fields, including chemistry, biology, materials science, and physics. One significant drawback of conventional ESR, however, is its relatively low sensitivity compared to other spectroscopic techniques. Arguably, the most dominant element affecting ESR sensitivity is the microwave resonator used to pick up the ESR signal of the spins. Traditionally, ESR mostly employs a limited set of resonator configurations (e.g., rectangular cavity, dielectric, or loop-gap resonator) that are suboptimal with respect to a wide range of samples. In principle, a smart resonator design can be used to optimize spin sensitivity for a given sample’s properties. In this work, we make use of an efficient Genetic Algorithm (GA) approach to numerically solve, analyze, and optimize a unique class of surface microresonators. The GA is based on a method of moments code, customized directly to render the complexity of a particular resonator’s geometries in our search. The main purposes of the algorithm are to routinely generate more sensitive microresonators, optimized for a predefined sample’s dimensions, and to study the functional relations between the devices’ resonance frequency, quality, and filling factors and their topology, in order to reach a rational optimal design. Preliminary results associated with new, unique, and sensitive surface microresonators are shown and analyzed. Such resonators are cheap and easy to produce on a mass scale with an arbitrary surface geometry.

Current recovery for the RWG‐based method of moments

Derivative recovery through local smoothing, is a well-known approach to obtain an estimate of a solution field's derivative, to one polynomial order higher than its direct representation. In the finite element method context, this is often referred to as ‘gradient recovery’. The method of moments (MoM) is routinely used to solve electromagnetic field integral equations in terms of the electric surface current density, which is often represented by mixed first-order, Rao–Wilton–Glisson (RWG) basis functions upon a mesh of triangle elements. A procedure for recovering a mixed second-order, approximate solution from an RWG-based MoM solution is presented. Recovery of the solution itself rather than its derivative, is made possible by exploiting specific properties of the mixed-order, surface divergence-conforming function spaces. The procedure is not strictly local, however, only sparse, positive-definite global linear systems must be solved. The procedure is independent of the integral operator. Computational complexity is lower than that of existing residual-based MoM error estimators. Results are shown with the recovered solution being a better approximation than the original solution. The procedure is useful for post-processing and for local or global a posteriori error estimation. It can be incorporated into any RWG-based MoM code.

A computational method for modeling arbitrary junctions employing different surface integral equation formulations for three-dimensional scattering and radiation problems

This paper presents a new method, based on the well-known method of moments (MoM), for the numerical electromagnetic analysis of scattering and radiation from metallic or dielectric structures, or both structure types in the same simulation, that are in contact with other metallic or dielectric structures. The proposed method for solving the MoM junction problem consists of two separate algorithms, one of which comprises a generalization for bodies in contact of the surface integral equation (SIE) formulations. Unlike some other published SIE generalizations in the field of computational electromagnetics, this generalization does not require duplicating unknowns on the dielectric separation surfaces, except duplications for a very small fraction of unknowns corresponding to junction edges, which introduces a negligible computational cost. Additionally, this generalization is applicable to any ordinary single-scatterer SIE formulations employed as baseline. The other algorithm deals with enforcing boundary conditions and Kirchhoff’s Law, relating the surface current flow across a junction edge. Two important features inherent to this latter algorithm consist of a mathematically compact description in matrix form, and importantly, from a software engineering point of view, an easy implementation in existing MoM codes which makes the debugging process more comprehensible. A practical example involving a real grounded monopole antenna for airplane-satellite communication is analyzed for validation purposes by comparing with precise measurements covering different electrical sizes.

MATLAB-Based 3-D MoM and FDTD Codes for the RCS Analysis of Realistic Objects [Testing Ourselves

Three-dimensional (3-D) MATLAB-based codes are developed for radar cross-section (RCS) modeling and simulation (MODSIM) using method of moments (MoM) and finite-difference time-domain (FDTD) approaches. Any object can realistically and comparatively be investigated.

Efficient Electromagnetic Scattering Computation Using the Random Auxiliary Sources Method for Multiple Composite 3-D Arbitrary Objects

The electromagnetic (EM) scattering problem from three-dimensional (3-D) arbitrary composite objects is proposed using the random auxiliary sources (RAS) method. Based on direct application of the boundary conditions with the uniqueness theorem and the use of random equivalent problems concept, more degrees-of-freedom to the sources’ positions are added resulting in significantly efficient solutions with lower memory requirements. The technique does not require any singularity treatment due to placing the equivalent sources away from the boundaries. While boundary conditions are not enforced exactly, an iterative framework is introduced that can achieve an acceptable level of error in their satisfaction for an arbitrary, randomly generated set of equivalent sources. The presented technique promises a significant reduction in the execution time and memory requirements compared to the surface-equivalent-based method of moments (MoM). The solution stability, repeatability, and numerical noise susceptibility are investigated thoroughly through this work. Also, a novel edge correction scheme has been implemented to extend the capabilities of this procedure to structures with sharp edges. The results of the presented technique are compared to series solutions for conducting spheres and a commercially available MoM code for arbitrarily shaped objects and combinations of different materials.

Nested Equivalent Source Approximation for the Modeling of Multiscale Structures

We introduce a method to compress the impedance matrix of the method of moments (MoM) for the modeling of high-fidelity multiscale structures at low- to moderate-frequencies. We start from a method recently proposed to compress static (scalar) problems, proved to have O(N) computational complexity. We represent far coupling between groups through equivalent source distributions on properly defined, automatically generated equivalence surfaces. The equivalent sources are obtained via an inverse-source process that enforces equivalence of radiated fields on testing surfaces within a prescribed accuracy, and are intrinsically multiscale. This results in an O(N) complexity scaling of matrix-vector products, but reduces multiplicative constants (i.e., reduces time and memory requirements) for all structures. It affords an improved representation of couplings in multiscale structures, resulting in a fast convergence of iterative solvers. Our approach is Green's function independent and easy to be implemented in existing MoM codes; the present version is based on the electric field integral equation (EFIE). Numerical results prove the effectiveness of the proposed algorithm for complex multiscale structures.

Optimization of a Dual-Band Helical Antenna for TTC Applications at S Band

A compact dual-band equatorial helical antenna for TTC (telemetry, tracking, and control) applications in satellites is presented. The network feeding system of the antenna was also designed, analyzed, and measured to achieve circular polarization. A Moment Method code was used to evaluate the performance of both the helical antenna and the feed-circuit network. The whole system was optimized to fulfill rather strict specifications, while maintaining quite small size and weight. A prototype of the helical antenna was fabricated and measured. The design process of the geometrical model, and comparisons between the predicted and measured values, are presented. The results led to the conclusion that it is a very suitable antenna for operating at S band.

Efficient Higher Order Full-Wave Numerical Analysis of 3-D Cloaking Structures

Highly efficient and versatile computational electromagnetic analysis of 3-D transformation-based metamaterial cloaking structures based on a hybridization of a higher order finite element method for discretization of the cloaking region and a higher order method of moments for numerical termination of the computational domain is proposed and demonstrated. The technique allows for an effective modeling of the continuously inhomogeneous anisotropic cloaking region, for cloaks based on both linear and nonlinear coordinate transformations, using a very small number of large curved finite elements with continuous spatial variations of permittivity and permeability tensors and high-order p-refined field approximations throughout their volumes, with a very small total number of unknowns. In analysis, there is no need for a discretization of the permittivity and permeability profiles of the cloak, namely for piecewise homogeneous (layered) approximate models, with material tensors replaced by appropriate piecewise constant approximations. Numerical results show a very significant reduction (three to five orders of magnitude for the simplest possible 6-element model and five to seven orders of magnitude for an h-refined 24-element model) in the scattering cross section of a perfectly conducting sphere with a metamaterial cloak, in a broad range of wavelengths. Given the introduced explicit approximations in modeling of the spherical geometry and continuous material tensor profiles (both by fourth-order Lagrange interpolating functions), and inherent numerical approximations involved in the finite element and moment method techniques and codes, the cloaking effects are shown to be predicted rather accurately by the full-wave numerical analysis method.

A New Method for the Analysis of Perturbed-Wall Waveguide Mode Converters

An improved method for the analysis of the fields within a section of nonuniform cylindrical waveguide is presented. The technique uses the method of successive approximations to obtain consistent solutions to the Stratton-Chu equations and the cylindrical harmonic representations of the fields that satisfy the Maxwell equations and the boundary conditions of the nonuniform waveguide. As opposed to some recently reported methods, this new method is not restricted to oversized waveguide structures and can directly evaluate the fields within a tapered section of waveguide. The method is validated by evaluating the fields within two different mode converters for gyrotron launchers. The accuracy is seen to be competitive with the commercial method of moments code, Surf3d, and requires a fraction of the computational resources.

Multilevel Adaptive Cross Approximation (MLACA)

The Multilevel Adaptive Cross Approximation (MLACA) is proposed as a fast method to accelerate the matrix-vector products in the iterative solution of the linear system that results from the discretization of electromagnetic Integral Equations (IE) with the Method of Moments (MoM). The single level ACA, already described in the literature, is extended with a multilevel recursive algorithm in order to improve the asymptotical complexity of both the computational cost and the memory requirements. The main qualities of ACA are maintained: it is purely algebraic and independent of the integral equation kernel Green's function as long as it produces pseudo-rank-deficient matrix blocks. The algorithm is presented in such a way that it can be easily implemented on top of an existing MoM code with most commonly used Green's functions.

A Multi-Resolution Moment Method for Wire-Surface Objects

We present a multi-resolution (MR) basis for the method of moments (MoM) analysis of the electric field integral equation (EFIE) for fully arbitrary 3-D conductors composed of wires connected to surfaces. Representation of the unknown current with the MR basis results in a physics-based preconditioner, especially for geometrically complex and/or finely meshed structures, and/or low frequency problems. The proposed MR basis is constructed as a linear combination of the basis functions usually employed in the MoM-based codes, namely the piecewise linear (PWL) functions for wires modelled via line segments, the Rao-Wilton-Glisson (RWG) functions for surfaces modelled with triangles, and junction basis functions for modelling their connections. The key challenge and the novelty of the present work is the construction of multi-resolution basis functions defined on arbitrary cells formed by triangles and line segments modelling surfaces, wires and junctions that coherently include all three types of conventional basis functions. Application of the MR basis results in a basis change, algorithmically equivalent to a purely multiplicative algebraic preconditioner of the EFIE, that can be easily interfaced with pre-existing MoM codes.

DESIGN OPTIMIZATION OF A BOW-TIE ANTENNA FOR 2.45 GHz RFID READERS USING A HYBRID BSO-NM ALGORITHM

Recently the Bacterial foraging optimization algorithm (BFA) has attracted a lot of attention as a high-performance optimizer. This paper presents a hybrid approach involving Bacterial Swarm Optimization (BSO) and Nelder-Mead (NM) algorithm. The proposed algorithm is used to design a bow-tie antenna for 2.45GHz Radio Frequency Identiflcation (RFID) readers. The antenna is analyzed completely using Method of Moments (MoM), then the MoM code is coupled with the BSO-NM algorithm to optimize the antenna. The simulated antenna and the optimization algorithm programs were implemented using MATLAB version 7.4. To verify the validity of numerical simulations, the results are compared with those obtained using Feko Software Suite 5.3.

Wideband Yagi-Uda Antenna Design Using Adaptive Differential Evolution Algorithm

A series of control parameter researches of differential evolution algorithm (DE) and adaptive DE (ADE) for a wideband six-element Yagi-Uda antenna optimization is presented. A method of moments code (NEC) was used to evaluate each of the antenna designs generated by ADE and DE. The optimized Yagi-Uda antenna is fabricated and measured to validate the efficiency and the flexibility of the parameter analysis. The simulated and measured impedance bandwidth of VSWR < 1.5 achieves 14.0%, which trebles the bandwidth of the Yagi-Uda antenna with a driven dipole element. The measured maximum antenna gain across the operating frequency band reaches 12.75 dB. Measured results of the fabricated antenna prototype is in good agreement with simulated results. Numerical and measured results confirm that the proposed ADE method is superior to or at least competitive with the conventional DE in terms of convergence speed and solution quality.

Parallel MoM Using Higher-Order Basis Functions and PLAPACK In-Core and Out-of-Core Solvers for Challenging EM Simulations

Typically, the problem size that can be solved by the Method of Moments (MoM) is limited by the amount of RAM installed in the computer. To reduce the number of unknowns for MoM, higher-order polynomial functions have been introduced as the basis functions. To extend the capability of the MoM code, this paper presents a new development: the use of a new parallel out-of-core solver called PLAPACK. The PLAPACK library package offers benefits that are not available in the more commonly used ScaLAPACK libraries. Numerical results on a typical computer platform for two different challenging electromagnetic problems show that the PLAPACK out-of-core solver introduced here is a very efficient way to deal with large matrix equations. The implementation of these advancements creates a powerful tool for the efficient computational electromagnetic solution of large and complex real-world problems.

The Computer Simulation of Radiation Pattern for Cylindrical Conformal Microstrip Antenna

FEKO is a 3D simulation tool for the analysis of electromagnetic fields. The simulation using FEKO is based on the well-known method of moments (MoM) for the Maxwell equations. FEKO can solve the problem of any structural type with a very comprehensive MoM code or tailored code. First, a radiation pattern for conformal microstrip antenna on the surface of cylinder is calculated using FEKO. In addition, the impact of conformal carrier on the radiations of microstrip antennas in different positions is simulated by FEKO. The simulation results accord with the true characteristics of conformal microstrip antennas.

Optimised design of multi-band cellular base station antenna array for GSM and UMTS deployment

A tri-band dual polarised printed patch array is designed for GSM and UMTS cellular deployment using an efficient moment method code driven by a marginal distribution optimisation algorithm. Novel techniques are introduced to expedite analysis while maintaining adequate accuracy, and two methods are used to aggregate elements into an array for pattern synthesis: unequal spacing and phasing. Optimisation criteria such as cross-polar isolation, return loss and radiation pattern characteristics are successfully achieved in simulation, and a measured prototype element supports the antenna concept.

Optimization Technique Using Differential Evolution for Yagi-Uda Antennas

Differential Evolution (DE) can solve multi-objective optimization problem in an extremely efficient manner. Based on thin wire modeling, method of moments code is developed for evaluating the antenna designs. DE is employed to optimize the geometric parameters of Yagi-Uda antennas. The length and spacing of Yagi-Uda antennas are optimized variables. The results clearly show that the DE is a robust and useful optimization tool for designing antennas.

Strong Singularity Reduction for Curved Patches for the Integral Equations of Electromagnetics

A method for weakening strong singularity contributions to the integral equations of electromagnetics is demonstrated. The remaining weakly singular integral derived after the reduction can be computed by any suitable method. Numerical results demonstrate that the singularity reduction method converges and that the new integration method can be used in high-order moment method or Nystrm codes without any adverse effect on their accuracy.

Improved Formulation for Investigation of Proximity-Coupled Microstrip Antenna in Homogeneous Dielectric Half Space

Analytical evaluation of asymptotic part of the Green's function, in product with piece-wise sinusoidal, entire domain, and travelling wave mode basis functions, is presented. The Sommerfeld type double integral in spectral domain is solved and reduced into a single integral in spatial domain with very short integration range. The derived results lead to develop a computational efficiency improved code, which has been found 27 times faster than the earlier validated common method of moments code.