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Darwin’s model is a reduced form of Maxwell’s equations, where radiations are neglected, while inductive, resistive, and capacitive effects are still taken into account. In this article, we propose a method for the efficient modeling of electrically long, thin wires using a Darwin-based integral equation approach, thus keeping the number of DoFs and runtime low. This model provides further numerical techniques to efficiently take into account special inhomogeneities via the modification of the Green’s functions unlike in full-wave models. The benefits are discussed through the example of the automotive CISPR 25 measurement setup. [ABSTRACT FROM AUTHOR]

Integral equation (IE) methods have recently been proposed for the modeling of inductively coupled resonant wireless power transfer. These approaches usually result in a low number of degrees of freedom. However, their applicability is mostly limited to homogeneous background media. In the present contribution, integral formulations are extended to take certain foreign objects into account in the model. By using quasi-static approximations, homogeneous foreign objects of canonical shape (e.g., spheres, plates) modify the Green’s function such that it can still be analytically expressed; thus, the computational cost of the IE method remains low. The method is validated against 3-D finite-element simulation and experimental data. [ABSTRACT FROM AUTHOR]

A full-wave surface integral equation method is used for modeling coils in a wide frequency range. This is of high importance in the analysis of resonant wireless power transfer links, for example. This paper presents a nonlocal generalization of the impedance boundary condition (BC) concept by incorporating a 2-D model (using the finite element method here) of the quasi-static electromagnetic field within the wire. This yields a numerical approximation of the nonlocal impedance BC on the wire surface that holds true at any frequency. The 2-D eddy-current model has to be evaluated only twice at one frequency, which makes the scheme computationally efficient. The method accurately predicts the ohmic loss as shown by the validations against alternative methods. [ABSTRACT FROM AUTHOR]

A full-wave integral equation scheme for modeling resonant coils applied in wireless power transfer systems is presented. An A-\Phi formulation is applied with current and charge densities on the wire surface as unknowns. The method overcomes the limitation of the “thin-wire approximation” as it enables the unknowns to vary on the wire surface. Thus, proximity effects (that typically emerge when modeling dense windings) are taken into account. The numerical implementation of the formulation has smaller computation cost than, for example, finite element methods. The proposed scheme is tested against closed-form solutions and alternative simulations. [ABSTRACT FROM AUTHOR]

With resonant wireless power transfer systems in operation, objects and/or humans having divers material properties come into the vicinity of the resonant coils. To model such systems efficiently, a novel full-wave multisolver is developed where the tangentially continuous vector finite element (FE) method is coupled with a method of moments (MoM) technique. The MoM technique is based on an electric field integral equation specifically designed to model the singular behavior of the thin coil wires, while the FE method is used to model the scattered field due to material inhomogeneities. A simplified sequential solver similar to the scattered field formulation is derived from the linear system of the multisolver in order to be applied as an efficient preconditioner, thereby speeding up the solution time significantly. The impedance change due to the material inhomogeneities can be calculated directly by applying the reaction concept. This ensures that the accuracy of the impedance change does not depend on the relative magnitude of the impedance change compared with the total impedance. The performance of the multisolver is illustrated by solving a test problem with a helical coil and a dielectric sphere with moderate conductivity, and comparing the multisolver results with the full FE solutions. [ABSTRACT FROM AUTHOR]

An integral equation method is used for the modeling of electromagnetic scattering from a rotating propeller, of which the length is about half a wavelength. This provides a convenient way of calculating its backscattering spectrum that is useful, for example, when radar detection capabilities are studied. This theoretical model is used to predict the discrete nature of the scattered spectrum and the intensity of its peaks. The simulations are compared with anechoic chamber measurements for different orientations of the propeller’s axis with respect to the polarization of the incident wave. [ABSTRACT FROM AUTHOR]