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We are interested in boundary integral formulations adapted to the solution of low frequency inductive electromagnetics in the case where the geometry is partitioned in (potentially irregular) subdomains. In the context of electromagnetics in piecewise homogeneous media, the multi-trace formalism (MTF) provides boundary integral formulations for Maxwell's equations posed at the interfaces between...
A novel procedure is presented for the evaluation of integrals involving singular Green function and Rao-Wilton-Glisson basis functions with arbitrary mutual non-planar geometrical configuration which appear in surface integral equations representation of Maxwell equations. The proposed procedure constitutes a generalization of our previously reported result valid for planar geometries. The method...
An integral equation with non-conformal and non-overlapping domain decomposition method has aroused wide interest in the engineering community. The contribution of this paper is twofold: (I) In the framework of IE-DDM, phase-extracted (PE) basis function is employed to reduce the required number of unknowns in the large and smooth sub-domain. (II) A reverse operation self-consistent evaluation (ROSE)...
Non-physical, linearly increasing and constant current components are induced in marching on-in-time solution of time domain surface integral equations when initial conditions on time derivatives of (unknown) equivalent currents are not enforced properly. This problem can be remedied by solving the time integral of the surface integral for auxiliary currents that are defined to be the time derivatives...
In this study, a novel estimation method to determine the electromagnetic or acoustic sources located in a hemisphere using two different Green functions is developed. The inverse source problem is formulated for a scalar function which can be considered as an electromagnetic scalar potential or an acoustic pressure field. Using the explicit expressions of the Green functions obtained for two different...
A novel preconditioning for the electric field integral equation (EFIE) discretised with the Hdiv inner product is discussed. It is known that the EFIE suffers from bad accuracy in low-frequency problems. One of the remedies for this bad accuracy is the discretisation method using Hdiv inner product. The EFIE with this discretisation, however, shows slow convergence of iteration methods and, what...
We present a modified combined tangential formulation (MCTF) for stable solutions of plasmonic problems involving metallic objects that are modeled as penetrable structures. For a wide range of negative real permittivity values, corresponding to the varying characteristics of the metals at infrared and visible frequencies, MCTF provides both accurate and efficient solutions in comparison to the conventional...
Because the analysis of the time domain integral equations of electromagnetics is complicated and cannot easily take into account all sources of error in any given implementation, judgements of stability tend to rest on experience. While such an approach eliminates the worst methods immediately, subtle implementation issues may affect the stability of more promising approaches. In this work, we examine...
In this paper, a fast (and) convergent method to analyze propagation in polygonal cross-section dielectric waveguides is presented. The problem formulated as an homogeneous surface integral equation in the spectral domain is discretized by means of Galerkin method with analytically Fourier transformable expansion functions reconstructing the behavior of the fields on the wedges. Moreover, the elements...
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