Application of the boundary elements method to 3-D radiation problems (original) (raw)
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2010
Boundary element methods (BEMs) are an increasingly popular approach to the modeling of electromagnetic scattering both by perfect conductors and dielectric objects. Several mathematical, numerical, and computational techniques pullulated from the research into BEMs, enhancing its efficiency. The Fast Multipole Method (FMM) and its descendants accelerate the matrix-vector product that constitutes the BEM's computational bottleneck. In particular, dedicated FMMs have been conceived for the computation of the electromagnetic scattering at complex metallic and/or dielectric objects in free space and in layered background media. Calderón preconditioning of the BEM's system matrix lowers the number of matrix-vector products required to reach an accurate solution, and thus the time to reach it. Parallelization distributes the remaining workload over a battery of affordable computational nodes, diminishing the wall-clock computation time. In honor of our former colleague and mentor, Prof. F. Olyslager, an overview of some dedicated BEMs for large and complex EM problems developed within the Electromagnetics Group at Ghent University is presented. Recent results that ramified from Prof. Olyslager's scientific endeavors are included in the survey.
IEEE Antennas and Propagation Society International Symposium. Transmitting Waves of Progress to the Next Millennium. 2000 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.00CH37118), 2000
An original boundary integral equation approach is developed for an efficient and accurate electromagnetic analysis of arbitrarily-shaped three-dimensional conducting and dielectric structures, typically involved in scattering and antenna problems. A suitable analytical pre-processing on the field integral representation allows a straightforward implementation of the Nystrom method, which is based on a direct discretization of the surface integrals by means of two-dimensional quadrature formulas: this novel approach is alternative to the more common moment-method solutions and presents various attractive computational advantages. Numerical results have been derived for canonical 3D shapes to validate the proposed implementation.
Nodal and Edge Boundary Element Methods Applied to Electromagnetic Scattering Problems
2003
In this paper both nodal and edge boundary element methods for three-dimensional electromagnetic scattering problems are analyzed. The boundary integral equation is discretized by the traditional nodal element formulation and the vector edge element formulation. The Galerkin procedure is used to perform vector element formulation. Moreover, Whitney elements of second degree are employed to build vector edge base functions. The scattering of a perfect electric conducting body is computed by both methods and comparison among them are shown for different cases. The results for the discussed formulation have been shown that edge boundary element works better than nodal one.
Engineering Analysis with Boundary Elements, 2015
The paper deals with an analysis of various EMC problems related to radiation and scattering from wires using a vertical straight wire model based on the corresponding Pocklington integro-differential equation. The rigorous solution of the Pocklington type equation is undertaken via the Galerkin-Bubnov Indirect Boundary Element Method (GB-IBEM). Many illustrative computational examples presented throughout the paper are related to dipole antenna above a lossy half-space, metal rods penetrating the ground, lightning channel and vertical grounding electrode. Obtained numerical results are somewhere compared to NEC or analytical results, respectively.
Microwave and Optical Technology Letters, 2008
In this work, we present an alternate set of basis functions, each defined over a pair of planar triangular patches, for the method of moments solution of electromagnetic scattering and radiation problems associated with arbitrarily shaped, closed, conducting surfaces. The present basis functions are point-wise orthogonal to the pulse basis functions previously defined. The prime motivation to develop the present set of basis functions is to utilize them for the electromagnetic solution of dielectric bodies using a surface integral equation formulation which involves both electric and magnetic currents. However, in the present work, only the conducting body solution is presented and compared with other data.
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 2020
In the framework solving electromagnetic scattering problems with a Leontovich impedance boundary condition (LIBC), the numerical resolution requires the evaluation of singular integrals appearing in the discretization of the variational formulation. Our main interest is to pricisely evaluate these integrals. Thus, we propose an analytic method to approximate it. The performance of this method will be evaluated by calculating the radar cross section (RCS). Then, we compare RCS to the Mie series solution for the unit sphere in various configurations.
A Boundary Element Procedure for 3D Electromagnetic Transmission Problems with Large Conductivity
Mathematics, 2022
We consider the scattering of time-periodic electromagnetic fields by metallic obstacles, or the eddy current problem. In this interface problem, different sets of Maxwell equations must be solved both in the obstacle and outside it, while the tangential components of both electric and magnetic fields are continuous across the interface. We describe an asymptotic procedure, applied for large conductivity, which reflects the skin effect in metals. The key to our method is a special integral equation procedure for the exterior boundary value problems corresponding to perfect conductors. The asymptotic procedure leads to a great reduction in complexity for the numerical solution, since it involves solving only the exterior boundary value problems. Furthermore, we introduce a FEM/BEM coupling procedure for the transmission problem and consider the implementation of Galerkin’s elements for the perfect conductor problem, and present numerical experiments.