On magnetic leaf-wise intersections

In this article we introduce the notion of a magnetic leaf-wise intersection point which is a generalization of the leaf-wise intersection point with magnetic effects. We also prove the existence of magnetic leaf-wise intersection points under certain topological assumptions.Comment: 43 page

Accuracy and efficiency considerations in the solution of extremely large electromagnetics problems

This study considers fast and accurate solutions of extremely large electromagnetics problems. Surface formulations of large-scale objects lead to dense matrix equations involving millions of unknowns. Thanks to recent developments in parallel algorithms and high-performance computers, these problems can easily be solved with unprecedented levels of accuracy and detail. For example, using a parallel implementation of the multilevel fast multipole algorithm (MLFMA), we are able to solve electromagnetics problems discretized with hundreds of millions of unknowns. Unfortunately, as the problem size grows, it becomes difficult to assess the accuracy and efficiency of the solutions, especially when comparing different implementations. This paper presents our efforts to solve extremely large electromagnetics problems with an emphasis on accuracy and efficiency. We present a list of benchmark problems, which can be used to compare different implementations for large-scale problems. © 2011 IEEE

Design and simulation of circular arrays of trapezoidal-tooth log-periodic antennas via genetic optimization

Circular arrays of log-periodic (LP) antennas are designed and their operational properties are investigated in a sophisticated simulation environment that is based on the recent advances in computational electromagnetics. Due to the complicated structures of the trapezoidal-tooth array elements and the overall array configuration, their analytical treatments are prohibitively difficult. Therefore, the simulation results presented in this paper are essential for their analysis and design. We present the design of a three-element LP array showing broadband characteristics. The directive gain is stabilized in the operation band using optimization by genetic algorithms. We demonstrate that the optimization procedure can also be used to provide beam-steering ability to LP arrays

Interpolation techniques to improve the accuracy of the plane wave excitations in the finite difference time domain method

The importance of matching the phase velocity of the incident plane wave to the numerical phase velocity imposed by the numerical dispersion of the three-dimensional (3-D) finite difference time domain (FDTD) grid is demonstrated. In separate-field formulation of the FDTD method, a plane wave may be introduced to the 3-D computational domain either by evaluating closed-form incident-field expressions or by interpolating from a 1-D incident-field array (IFA), which is a 1-D FDTD grid simulating the propagation of the plane wave. The relative accuracies and efficiencies of these two excitation schemes are compared, and it has been shown that higher-order interpolation techniques can be used to improve the accuracy of the IFA scheme, which is already quite efficient

Solid-angle factor in the magnetic-field integral equation

The magnetic-field integral equation (MFIE) contains a geometry-dependent solid-angle factor due to the limit value of the magnetic field at the source region. Determination of the solid-angle factor becomes bewildering, especially at the points of geometric discontinuities caused by the simultaneous discretization of the MFIE and the geometry. In this paper, we clarify the ambiguity by scrutinizing the magnetic-field radiation integrals of the MFIE formulation. We prove that the solid-angle factor can be implicitly determined if the singular source-region magnetic-field expressions are correctly treated, thus eliminating the need for guessing or explicitly inserting solid-angle values in the formulation. © 2005 Wiley Periodicals, Inc

Hierarchical parallelisation strategy for multilevel fast multipole algorithm in computational electromagnetics

A hierarchical parallelisation of the multilevel fast multipole algorithm (MLFMA) for the efficient solution of large-scale problems in computational electromagnetics is presented. The tree structure of MLFMA is distributed among the processors by partitioning both the clusters and the samples of the fields appropriately for each level. The parallelisation efficiency is significantly improved compared to previous approaches, where only the clusters or only the fields are partitioned in a level. © The Institution of Engineering and Technology 2008

An efficient parallel implementation of the multilevel fast multipole algorithm for rigorous solutions of large-scale scattering problems

We present the solution of large-scale scattering problems discretized with hundreds of millions of unknowns. The multilevel fast multipole algorithm (MLFMA) is parallelized using the hierarchical partitioning strategy on distributed-memory architectures. Optimizations and load-balancing algorithms are extensively used to improve parallel MLFMA solutions. The resulting implementation is successfully employed on modest parallel computers to solve scattering problems involving metallic objects larger than 1000λ and discretized with more than 300 million unknowns. © 2010 IEEE

Contamination of the accuracy of the combined-field integral equation with the discretization error of the magnetic-field integral equation

We investigate the accuracy of the combined-field integral equation (CFIE) discretized with the Rao-Wilton-Glisson (RWG) basis functions for the solution of scattering and radiation problems involving three-dimensional conducting objects. Such a low-order discretization with the RWG functions renders the two components of CFIE, i.e., the electric-field integral equation (EFIE) and the magnetic-field integral equation (MFIE), incompatible, mainly because of the excessive discretization error of MFIE. Solutions obtained with CFIE are contaminated with the MFIE inaccuracy, and CFIE is also incompatible with EFIE and MFIE. We show that, in an iterative solution, the minimization of the residual error for CFIE involves a breakpoint, where a further reduction of the residual error does not improve the solution in terms of compatibility with EFIE, which provides a more accurate reference solution. This breakpoint corresponds to the last useful iteration, where the accuracy of CFIE is saturated and a further reduction of the residual error is practically unnecessary. © 2009 IEEE

Combined-field solution of composite geometries involving open and closed conducting surfaces

Combined-field integral equation (CFIE) is modified and generalized to formulate the electromagnetic problems of composite geometries involving both open and closed conducting surfaces. These problems are customarily formulated with the electric-field integral equation (EFIE) due to the presence of the open surfaces. With the new definition and application of the CFIE, iterative solutions of these problems are now achieved with significantly improved efficiency compared to the EFIE solution, without sacrificing the accuracy. © 2005 ACES