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In this paper, a marching-on in degree solution to the problem of time domain electric field integer equation is presented where the higher order basis functions are employed for the spatial expansion. The marching-on in degree method can obtain a solution that is late-time stable, which is marching-on in time method cannot. Numerical result is presented to show the accuracy of the MOD method with...
The aim of this paper is the study of some asymptotic properties and invariances of the electric field integral equation (EFIE) when applied to large and smooth structures. It is theoretical in nature, and thus no numerical results are included in this communication.
A detailed analysis of the electric field integral equation (EFIE) at low frequencies is presented which is based on the Sobolev space mapping properties of the EFIE. The theory shows that in the low-frequency regime an EFIE with a logarithmic condition number growth can be obtained. This, provided that both the solenoidal and non-solenoidal parts of the EFIE are properly regularized. The regularization...
A self-loop basis functions is presented, a new set of solenoidal basis functions, which, together with the loop-star basis functions, define a rearrangement of the LL-discretization in method of moments of the EFIE that results in a stable impedance matrix at very low frequencies.
In this work we have extended the applicability of the GMM to a wide range of arbitrary geometries. The basis functions show excellent approximation qualities for the current, its curl and its divergence. In addition, the use of the surface Helmholtz decomposition results in a well conditioned system of equations over a wide range of frequencies. Future work is directed at fully utilizing these two...
This work presents a fast solver that always annihilates the divergence of solenoidal functions, independent of the precision of the compressed impedance matrix elements. The solver is obtained by compressing a loop-tree transformed impedance matrix by using a properly tailored fast solver. Then the impedance matrix in the usual (and undecomposed) RWG basis is reconstructed by a linear-in-complexity...
The electric field integral equation (EFIE) has been widely used in the moment method (MoM) solution of electromagnetic problems. However, due to the spectrum property of the EFIE operator, the resulting MoM impedance matrix has eigenvalues clustered around the origin and at the infinity as the mesh density increases, leading to a dramatic increase of the matrix condition number. When the object is...
The literature abounds with integral equation techniques for analyzing scattering from homogeneous penetrable objects. Dual source techniques, which are by far the most popular, solve a coupled pair of electric, magnetic, or mixed/combined field integral equations for electric and magnetic surface currents. Single source techniques on the other hand, solve one electric, magnetic, or combined field...
The electric field integral equations (EFIE) solved by method of moments (MOM) is widely used in scattering, antenna, and microwave circuit problems. However, it is well known that EFIE will break down when applied to electrically small structures or low frequency problems. A loop-star decomposition for the RWG discretization overcomes this problem and provides a valid solution from zero to microwave...
In this paper, MLFMA is implemented in the IEFIE to compute scattering from complex conducting structure coated by thin dielectric material. Numerical results demonstrate the efficiency and validity of the present method.
This paper remarks IDR(s) method as an alternative solver for GMRES(m) method. A preconditioned IDR(s) algorithm is presented. Performance evaluations are done for the computation of the dense linear system of equations of order 105 followed by BEM analysis of EM multiple scattering. IDR(s) method with the optimal parameters (5 < s < 10) converges faster than GMRES(mmax) method, using small...
The scattering of time-harmonic electromagnetic waves by perfect electrical conductors (PECs) can be modelled by several boundary integral equations, the magnetic and electric field integral equations (MFIE and EFIE) being the most prominent ones. These equations can be discretized by expanding current distributions in terms of Rao-Wilton-Glisson (RWG) functions defined on a triangular mesh approximating...
In the solution of the electric field integral equation (EFIE), discretized by the moment method (MoM) with the classical Rao-Wilton-Glisson basis, the resulting linear system has a high conditioning, in the case of low frequency problems, and fine meshes. Moreover the condition number increases with the number of unknowns, but if the dimension of all the mesh cells is close to the Nyquist limit the...
Recently, several papers have proposed using the Calderon identities to develop an analytic preconditioner for the electric field integral equation (EFIE). We extend these results by first giving simple, physical explanations for Calderon preconditioning and the special basis functions used to implement the method. Also, it is shown that the preconditioner can be easily integrated with the fast multipole...
Calderon preconditioning is very succesful in stabilising the EFIE and the use of BC functions makes the formalism valid on open surfaces. Through applying a broadband fast multipole method, the complexity can be reduced from O (N2) to O(N log N), allowing the simulation of very large structures. In the high frequency case a localised version of the preconditioner must be used to avoid excessive scattering...
Scattering of time-harmonic electromagnetic waves by perfect electrical conductors (PECs) can be modelled by electric field integral equations (EFIEs). If the If the scatterer is wire-like, the EFIE often is constructed using the thin wirescatterer is wire-like, the EFIE often is constructed using the thin wire approximation. The systems of linear equations resulting upon discretization of the EFIE...
The effectiveness of the proposed CMP-based regularization is demonstrated via the characterization of a hemispherical dielectric resonator antenna with an air gap. The resonator is excited by a feed probe. The need for fine discretization around the feed is justified by the need for properly modeling the curvature of the feed probe and the distribution of fields around it. The article demonstrates...
Method of moments (MoM)-based electric field integral equation (EFIE) solvers are widely used for analyzing time-harmonic electromagnetic scattering from perfect electrically conducting (PEC) surfaces. In the last decade, MoM-based EFIE solvers using high-order basis functions have been shown to be more accurate as well as CPU and memory efficient than their zeroth-order predecessors leveraging Rao-Wilton-Glisson...
The main issue addressed in the present paper is the proper handling of the different entities modeling surfaces (triangular facets), wires (line segments), and their interconnections (junctions), in order to construct MR bases 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...
Combined field integral equation (CFIE) solvers are widely used for analyzing electromagnetic interactions with perfect electrically conducting (PEC) closed surfaces because, unlike electric field equation (EFIE) solvers, they do not suffer from internal resonance problems. However, they are unbounded as their EFIE components contain a hypersingular term. This renders the matrix systems resulting...
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