Combined Source Integral Equation Research Articles

Efficient Iterative Solution of Combined Source Integral Equation Using Characteristic Basis Function Method With Initial Guess

Efficient Iterative Solution of Combined Source Integral Equation Using Characteristic Basis Function Method With Initial Guess

An Augmented Regularized Combined Source Integral Equation for Nonconforming Meshes

We present a new version of the regularized combined source integral equation (CSIE-AR) for the solution of electromagnetic scattering problems in the presence of perfectly conducting bodies. The integral equation is of the second kind and has no spurious resonances. It is well conditioned at all frequencies for simply connected geometries. Reconstruction of the magnetic field, however, is subject to catastrophic cancelation due to the need for computing a scalar potential from magnetic currents. Here, we show that by solving an auxiliary (scalar) integral equation, we can avoid this form of low-frequency breakdown. The auxiliary scalar equation is used to solve a Neumann-type boundary value problem using data corresponding to the normal component of the magnetic field. This scalar equation is also of the second kind, nonresonant, and well conditioned at all frequencies. A principal advantage of our approach, by contrast with the hypersingular electric field integral equation, the combined field integral equation, or CSIE formulations, is that the standard loop-star and related basis function constructions are not needed, and preconditioners are not required. This permits an easy coupling to fast algorithms such as the fast multipole method. Furthermore, the formalism is compatible with nonconformal mesh discretization and works well with singular (sharp) boundaries.

Modeling of Resonating Closed Impedance Bodies With Surface Integral Equation Methods

Numerical solutions of various surface integral equation (IE) formulations in modeling resonating (lossless) closed impedance bodies are investigated. It is demonstrated that for certain values of purely imaginary surface impedances very strongly resonating field solutions can appear. Some of the considered formulations that are known to work well outside these resonances, e.g., for lossy surfaces, can lead to very poor accuracy or even diverging solutions at these resonances. Among the considered formulations only the combined source IEs, discretized with a mixed scheme, both avoid the nonphysical spurious internal resonances and work reasonably well at the physical (impedance) resonances.

A Weak-Form Combined Source Integral Equation With Explicit Inversion of the Combined-Source Condition

The combined source integral equation (CSIE) for the electric field on the surface of a perfect electrically conducting scatterer can be discretized very accurately with lowest-order Rao-Wilton-Glisson basis and testing functions if the combined-source (CS) condition is enforced in weak form. We introduce a technique to accelerate the iterative solution for this kind of CSIE. It is demonstrated that the iterative solution of the equation system can be performed very efficiently by explicitly inverting the weak-form CS condition in any evaluation of the forward operator. This reduces the number of unknowns and results in improved convergence behavior at negligible, linear cost. Numerical results demonstrate that the new CSIE outperforms the classical CFIE for high-accuracy simulations.

A Combined Source Integral Equation With Weak Form Combined Source Condition

A combined source integral equation (CSIE) is constructed on the basis of the electric field integral equation (EFIE) to solve electromagnetic radiation and scattering problems containing perfect electrically conducting bodies. It is discretized with Rao-Wilton-Glisson basis functions only, for both electric and magnetic surface current densities. The combined source condition, which ensures the uniqueness of the solution and circumvents the interior resonance problem, is implemented as a weak form side condition. Compared to the common combined field integral equation, the proposed CSIE shows superior accuracy for sharp edges as well as structures with the interior resonance problem. Furthermore, the iterative solver convergence of the CSIE is faster than for the EFIE, which shows about the same accuracy as the CSIE. Results of numerical scattering simulations are presented to demonstrate the accuracy of the presented CSIE.

Electric and magnetic combined source integral equations for electromagnetic transmission problems

Abstract Various combined source integral equation (CSIE) formulations are developed for the analysis of electromagnetic scattering by three-dimensional arbitrarily shaped homogeneous penetrable objects. The considered CSIE formulations include the classical “electric” CSIE proposed by Mautz and Harrington in 1979, and its dual “magnetic” CSIE as well as mixed “electric–magnetic” and “magnetic–electric” CSIE formulations. Novel discretization schemes by utilizing the primary (Rao–Wilton–Glisson, RWG) and the dual (Buffa–Christiansen, BC) functions are applied to convert the integral equations into matrix equations. These schemes avoid the numerical problems that would appear if the CSIE formulations were discretized with the conventional Galerkin method using the RWG functions only.

Stable Discretization of Combined Source Integral Equation for Scattering by Dielectric Objects

A stable discretization scheme is presented for the combined source integral equation (CSIE) of electromagnetic scattering from three-dimensional arbitrarily shaped homogeneous dielectric objects. The discretization scheme uses both the primary (Rao-Wilton-Glisson, RWG) and the dual (Buffa-Christiansen, BC) functions and avoids numerical problems that would appear if the equations were discretized with the RWG functions only.

On combined source solutions for bodies with impedance boundary conditions

Numerical solutions to the impedance boundary condition (IBC) combined source integral equation (CSIE) for scattering from impedance spheres are presented. The CSIE formulation is a well-posed alternative to the IBC electric and magnetic field integral equations which can be contaminated by spurious resonant modes. Compared with the IBC combined field integral equation (CFIE), CSIE solutions have the same accuracy when the combined source coupling admittance is chosen to be the same value as the combined field coupling admittance. However, the CSIE formulation is better suited than the CFIE for creating a general purpose computer code capable of handling aperture radiation problems and/or a scatterer which has a spatially varying surface impedance.