Solution Of Electric Field Integral Equation Research Articles

Dual-Surface Electric Field Integral Equation Solution of Large Complex Problems

The integral equation analysis of large perfect electric conductor bodies is commonly formulated in terms of combined field integral equations (CFIE) that avoid spurious internal resonances. The dual-surface electric field integral equation (DSEFIE) is a less employed alternative approach; we discuss here how to cure its shortcomings and enhance its advantages over the CFIE for large bodies of nontrivial geometrical complexity. We study the convergence and accuracy of the DSEFIE also with respect to the current state of the art in the testing of the magnetic field integral equation. Examples of applications to large and realistic composite structures show the effectiveness of the proposed approach.

Accurate and efficient numerical integration of weakly singular integrals in galerkin EFIE solutions

A Galerkin descretization of the electric field integral equation for perfectly conducting surfaces using Rao-Wilton-Glisson (1982) basis functions requires the numerical evaluation of integrals with singular kernels over triangular regions. These singularities have been traditionally handled by utilizing a singularity extraction procedure to produce a regular integral and an analytic function to replace the original singular integral. A new approach is presented here in which the four-dimensional (4-D) weakly singular integrals unique to the Galerkin Rao-Wilton-Glisson electric field integral equation solution for perfectly conducting surfaces are transformed into integrals with regular integrands. The transformations allow some of the integrations to be performed analytically, in some cases reducing the original 4-D integral into a 1-D numerical integration. The accuracy and convergence properties of the new method are demonstrated by evaluating the scalar potential function over a unit triangle.

An electromagnetic model of lightning return stroke channel using electric field integral equation in time domain

We use an electromagnetic approach based on antenna theory (AT) to evaluate the lightning return stroke current as a function of time and height. The lightning channel is modeled as a lossy, straight, and vertical monopole antenna above a perfectly conducting ground, which is excited by a source voltage at the base of the channel. This voltage source is a function of the current assumed at the ground level and the input impedance of the monopole antenna. An electric field integral equation (EFIE) is employed to describe the electromagnetic behavior of the antenna. The numerical solution of EFIE by the method of moments in time domain provides the time-space distribution of the current along the lightning channel. This AT model with specified current at the channel base requires only two adjustable parameters, namely the return-stroke propagation speed and the channel resistance per unit length. To demonstrate the accuracy of the proposed model, we compare it to the most commonly used models in terms of the temporal and spatial distributions of channel current and predicted electromagnetic fields. We also present results to show the effectiveness of the model in the analysis of lightning-related problems dealing with complex structures. In this regard, the lightning induced overvoltages on the neighboring overhead lines and the lightning strikes to tall structures are investigated.

Iterative near-zone preconditioning of iterative method of moments electric field integral equation solutions

A preconditioning operator for the iterative solution of the electric field integral equation as applied to metallic scattering objects is iteratively computed employing the generalized minimal residual algorithm (GMRES). Using the strongest method of moments matrix elements only (typically in the near zone), iteration of the sparse preconditioner converges very quickly. In contrast to direct factorization of the near-zone matrix, no matrix fill-ins need to be handled. Excellent convergence of the preconditioned system using GMRES again is demonstrated by scattering computations for a rectangular metallic plate and a metallic cube.