D. J. Ludick

Characteristic mode analysis of arbitrary electromagnetic structures using FEKO

This paper considers the characteristic mode analysis (CMA) of arbitrary electromagnetic structures using the comprehensive 3D electromagnetic field solver, FEKO [1]. The theory of characteristic modes, as presented in [2], is used to derive the real orthogonal current modes. These modes are obtained by solving a generalised symmetric eigenvalue problem defined by the real and imaginary parts of the Method-of-Moments (MoM) impedance matrix. The research presented in this article discusses the techniques used in FEKO to solve this generalised eigenproblem. Furthermore, paralleli-sation using both distributed and shared memory programming models, as well as GPU computation is considered within the FEKO framework to accelerate the CMA.

A hybrid tracking algorithm for characteristic mode analysis

Characteristic mode analysis (CMA) is a useful design tool that enables antenna designers to follow a systematic approach for extracting the radiating properties of a structure. These properties are quantified with CMA in the form of eigenvalues and eigenvectors, i.e., the solutions of a generalised eigenvalue equation that is formulated from the Method-of-Moments (MoM) impedance matrix. One particular challenge to CMA, however, is the manner in which quantities such as eigenvalues are plotted as a function of frequency. At each discrete frequency sample, the eigenvalues are sorted according to modal significance, i.e., based on the efficiency with which they radiate. At higher frequencies, the ordering of modes may differ from that obtained at lower frequencies. A tracking algorithm will be introduced that keeps the ordering of modes as consistent as possible over frequency. The method presented is an extension of that done in [1], where a linear correlation is applied to the characteristic currents between adjacent frequency increments to obtain a ranking vector. This new hybrid technique is based on extrapolating the eigenvalue and characteristic angle curves and then applying linear correlation between the characteristic currents where needed to verify a successful mapping.

Numerical analysis of finite antenna arrays using the Domain Green's Function Method

This paper considers the efficient numerical analysis of arbitrary finite antenna array structures using the Domain Greens Function Method (DGFM). The DGFM is implemented in the comprehensive 3D electromagnetic field solver, FEKO [1], and uses the Method-of-Moments (MoM) formulation. The technique is based on that initially presented in [2] and is a perturbation approach where mutual coupling between antenna array elements is accounted for during the formulation of the Greens function for each element. The DGFM takes into account the edge effects attributed to the finite size of the array, complex excitations with non-linear phase shift and is not limited to periodic array configurations.

Investigating efficient parallelization techniques for the characteristic basis function method (CBFM)

Two message-passing parallelization schemes for the Method of Moment (MoM) based Characteristic Basis Function Method (CBFM) are presented. The CBFM algorithm is implemented in the high-level scripting languages, Python and Octave and is parallelized using the Message Passing Interface (MPI) standard. The MPI implementations used for the parallelization, i.e. MPI for Python and MPI Toolbox for Octave and Matlab, are compared in terms of bandwidth, latency, speed-up and efficiency. The results are obtained from simulations conducted on an IBM e1350 Linux Cluster.

Aspects of and Insights Into the Rigorous Validation, Verification, and Testing Processes for a Commercial Electromagnetic Field Solver Package

This paper focuses on rigorous validation, verification, and testing methodologies applied to a commercial electromagnetic software package to ensure that as accurate as possible results are given dependent on the accuracy of the solution method, for instance, whether a full-wave or approximate numerical method is used. In this paper, the general availability of reliable benchmark results such as analytical solutions, measurements, results from other codes and other numerical methods, and general benchmarking activities will be presented. The cross-validation aspects, once the benchmark results are available, will be discussed with respect to amongst other sequential runs compared with parallel multcore/cluster runs or, with and without, GPU acceleration. Internal consistency checks (which are a required but not necessary condition when assessing the accuracy) such as power budget, mesh size convergence, or boundary condition error estimates are also covered. Special emphasis is put on the validation of the actual computational model that is used as input to simulations. This is necessary, for example, because incomplete representation of real geometry might ignore small details that are needed for the specific quantity that is analyzed. Also, uncertainties with regards to material parameters or transition impedances could lead to discrepancies between the computed results and reality that are not to be attributed to the electromagnetic solution as such, but rather the model generation.

Applying the CBFM-enhanced domain Green's function method to the analysis of large disjoint subarray antennas

This paper considers the efficient numerical analysis of large, finite antenna arrays comprising of disjoint subarrays by using the Domain Greens Function Method (DGFM) [1] in conjunction with the Characteristic Basis Function Method (CBFM) [2]. In the CBFM-enhanced DGFM we consider large arrays consisting of multiple disjoint subarrays and impose the infinite array type assumption, i.e. that the currents on subarrays are identical except for a complex-valued scaling factor. Scan impedance matrices are then constructed for each of the subarrays from the block-partitioned CBFM reduced impedance matrix which account for the mutual coupling in the array environment. Runtime and memory usage scale efficiently for the CBFM-enhanced DGFM as we limit the computational complexity to that required to analyse a single subarray. The paper discusses the hybridisation of the DGFM with the CBFM, and illustrates the results of applying the proposed solution technique to an example consisting of a large finite array of disjoint subarrays.

Applying characteristic mode analysis to finite antenna array design

This paper considers the characteristic mode analysis (CMA) of finite antenna arrays, specifically for the design of the array element. The approach incorporates the Domain Greens Function Method (DGFM), i.e. a method-of-moments (MoM) based approach, to extract an active impedance matrix for each array element. The impedance matrices model the array environment for each antenna element and serve as input to an eigenvalue solver for the CMA. From here the eigencurrents and eigenvalues can be obtained that provide insight into the radiating properties of the elements in an active array environment.

DGFM-enhanced theory of characteristic modes for finite antenna array analysis

This work considers a method for including mutual coupling in the characteristic mode analysis (CMA) formulation of finite antenna array elements. The approach applies the domain Greens function method, i.e., a domain decomposition approach based on the method of moments, to extract an active impedance matrix for each array element. These impedance matrices model the active array environment for each antenna element and serve as input to an eigenvalue solver for the CMA. From here the eigencurrents and eigenvalues can be obtained that provide insight into the radiating properties of the elements in an active array environment.

Applying the NGF-enhanced Domain Green's Function Method to the analysis of antenna arrays and ground planes of finite sizes

In this work, antenna arrays will be analysed in the presence of ground planes that are both of finite extent. A hybrid approach between a partitioned MoM scheme called the Numerical Greens Function (NGF) and the Domain Greens Function Method (DGFM) is presented, viz., the NGF-enhanced DGFM. The method allows for computationally efficient simulations, in that various array configurations can be investigated without solving again the part of the problem associated with the ground plane.

Method of moments accelerations and extensions in FEKO

This paper introduces several extensions and accelerations to the Method of Moments (MoM) formulation in the computer code FEKO, which all aim in solving large problems faster or using less memory.