Abstract
This paper proposes an efficient technique to solve the electromagnetic scattering problem, in the near zone of scatterers illuminated by external fields. The technique is based on a differential formulation of the Helmholtz equation discretized in terms of a finite element method (FEM). In order to numerically solve the problem, it is necessary to truncate the unbounded solution domain to obtain a bounded computational domain. This is usually done by defining fictitious boundaries where absorbing conditions are imposed, for example by applying the perfect matching layer (PML) approach. In this paper, these boundary conditions are expressed in an analytical form by using the Dirichlet-to-Neumann (DtN) operator. Compared to classical solutions such as PML, the proposed approach based on the DtN: (i) avoids the errors related to approximated boundary conditions; (ii) allows placing the boundary in close proximity to the scatterers, thus, reducing the solution domain to be meshed and the related computational cost; (iii) allows dealing with objects of arbitrary shapes and materials, since the shape of the boundary independent from those of the scatterers. Case-studies on problems related to the scattering from cable bundles demonstrate the accuracy and the computational advantage of the proposed technique, compared to existing ones.
Highlights
The near-field electromagnetic interaction between components has become an issue in high-frequency complex electronic systems, where it is highly likely to generate phenomena that affect the system performance, such as unwanted electromagnetic interference (EMI) or crosstalk noise.An accurate knowledge of the near-field distribution is mandatory in the design and verification of cable harnesses, integrated circuits, printed circuit boards, and Radio-Frequency (RF) systems
We focus on differential formulations solved by means of the finite element method (FEM)
The use of the Dirichlet-to-Neumann (DtN) operator has been, here, shown to be a suitable way to efficiently evaluate the near-zone electromagnetic field in a scattering problem, when such a problem is numerically solved by means of differential formulations, discretized with the finite elements method
Summary
The near-field electromagnetic interaction between components has become an issue in high-frequency complex electronic systems, where it is highly likely to generate phenomena that affect the system performance, such as unwanted electromagnetic interference (EMI) or crosstalk noise.An accurate knowledge of the near-field distribution is mandatory in the design and verification of cable harnesses, integrated circuits, printed circuit boards, and Radio-Frequency (RF) systems. The near-field analysis allows, for instance, the location of hot spots and possible noise sources, or the estimation of the currents induced on the scatterers [1]. Facing both the emission and immunity issues related to unwanted scattering has become a major challenge for high-frequency systems in vehicles, aircraft, ships, and buildings. This problem poses many challenges both in experimental characterization (e.g., [2,3]) and in numerical modeling, usually based on full-wave or hybrid models (e.g., [4,5,6,7,8]).
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