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The subdomain perturbation (SDP) finite-element (FE) method is a very efficient numerical technique and it speeds up the analysis of magneto- and electroquasi-static problems significantly. In order to solve quasi-static Darwin models, the authors have recently developed a low-frequency stable FE A-V formulation that incorporates both capacitive and the inductive effects, thereby allowing solving for resonances. This article combines the Darwin FE formulation with the SDP strategy at the first time. It successfully validates the combined technique and demonstrates a significant run-time improvement compared to the full Darwin FE solution. The breakdown of the Darwin approximation at higher frequencies is also investigated. [ABSTRACT FROM AUTHOR]

A nonlocal generalization of the IBC (impedance boundary condition) concept is introduced in this work for modeling the coil wires in resonant WPT (wireless power transfer) links. Such NLIBCs (nonlocal IBCs) can accurately account for the skin and proximity effects in the wires for all frequencies relevant to resonant WPT systems and can be utilized in both finite-element and surface-integral-equation numerical frameworks. The NLIBCs have run-time performance close to that of the IBC because the NLIBCs take advantage of the quasi-2D nature of the electromagnetic field inside the wires. The results for a typical WPT configuration illustrate the performance. [ABSTRACT FROM AUTHOR]

The change in the two-port parameters of a wireless power transfer (WPT) chain is evaluated when an object (foreign object) with given material parameters is placed in the vicinity of the WPT transmitter and receiver. An integral formula for the change of the two-port parameters due to the presence of a foreign object has been derived by using the generalized theory of reciprocity. It is emphasized that—instead of taking the differences of the two-port parameters calculated with and without the presence of the foreign object—the presented method provides the change of the two-port parameters directly from the calculated electromagnetic field at the location of the foreign object. As a result, the relatively small parameter changes can be predicted with good accuracy. Based on the application of the Born approximation, the possibility of computing an approximation of the changes of the two-port parameters is explored. [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]

The major contribution of the paper is a theoretical proof of the equivalence between two approaches of near-field validation techniques for the numerical models of personal wireless communication devices. The current validation practice is to compare measured and computed electromagnetic field or specific absorption rate distributions. A new validation technique introduced by the authors recently compared measured and computed antenna input-impedance changes while the near field is systematically perturbed by a dielectric control object. The proof of the equivalence is based on two novel formulas derived here: a reaction impedance-change formula, and an error formula that establishes a quantitative relationship between the errors of the impedance changes and the near-field values. The equivalence of the two validation techniques is verified experimentally too by comparing measurements and computations for a planar-inverted F antenna. By performing numerical experiments for two types of printed-circuit board antennas, it is also proved here the first time that the new validation technique is feasible even if the geometric and material properties of the control object are such that the Born approximation can be introduced in the impedance-change formula. [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]

A time-harmonic full wave electromagnetic potential formulation is developed with stable broadband behavior including the static limit. The formulation ensures low-frequency stability not only when sub-domains with wavenumber proportional losses are present but also when sub-domains with ohmic losses are part of the computational domain. The low-frequency stability is achieved by introducing the induced electric charge distributions as unknowns in the sub-domains, where ohmic losses are present. To increase the numerical efficiency we utilize the so-called nodal charges that incorporate both volume and surface charge distributions into one scalar. Relevant numerical examples are presented to illustrate the zero-frequency stability of the formulation. [ABSTRACT FROM PUBLISHER]

This paper introduces a multi-solver technique to enhance the broadband performance of time-harmonic finite element solvers when solving electromagnetic problems with high-conductivity regions. The high-conductivity regions are modeled by the Trefftz-discontinuous Galerkin (TDG) formulation, whereas a tangential vector finite element (TVFE) formulation is used in the rest of the computational domain. The novel multi-solver technique couples the TVFE and TDG models by making use of Robin-type transmission conditions. The efficiency is shown by computing the broadband frequency sweep of the inductance of a two-wire transmission line; the necessary number of DoFs in the multi-solver case decreases significantly compared with the pure TVFE solution. The results of this problem also verify the new formulation and its implementation because the problem has an analytical solution. [ABSTRACT FROM AUTHOR]

The partial delamination of two metallic parts, one ferromagnetic and one non-magnetic, is inspected using nondestructive magnetic measurements. Defects of this type occur among others in the reactor of nuclear power plants, and are usually hidden. In the real-life inspection, low frequency AC current is injected into the metals, and the perturbation of the surrounding magnetic field is measured. However, numerical simulation of the defect-probe interaction is necessary too for the proper reconstruction of the parameters of hidden defects. In this paper an efficient finite element formulation is derived including both volumetric and surface type models of the delamination, and the numerical models are compared on a test problem. [ABSTRACT FROM PUBLISHER]

An adaptive parabolic-elliptic time-integration method based on a singly diagonally implicit Runge-Kutta (SDIRK) algorithm is described for the finite element (FE) solution of nonlinear electroquasistatic (EQS) problems. The method uses the nodal charges as dynamic variables in addition to the electric scalar potential, thereby achieving better stability and performance than methods based on the scalar potential only. No Newton iteration is required in a time step because the Jacobian is incorporated into the time integration formula; only one linear equation with multiple right hand sides has to be solved. The global time-integration error is controlled by limiting the local error at each time step selection. The efficiency of the formulation and time stepping algorithm is illustrated by solving a typical nonlinear benchmark problem. [ABSTRACT FROM PUBLISHER]

This paper examines the application of the total and scattered field formuIations in transfinite element analysis. The scattered field formulation is extended to include inhomogeneous magnetic materials, ports, internal, and external impedance boundary conditions. In the case of the total field formulation, the total field is used in the whole computational domain and the incident field excitation is taken into account by simultaneously utilizing both E and H fields via a Robin boundary condition. Thus, the incident field excitation is formulated as a generalized "space port" in the transfinite element method, similar to regular waveguide port excitations. In this way, infinite scatterers can be treated with high accuracy for the first time. [ABSTRACT FROM AUTHOR]

An efficient strategy is described for the solution of time-harmonic electromagnetic and elastic wave problems. The strategy is based on the framework of the discontinuous Galerkin (DG) method, thereby using approximation bases that are locally conservative. Additionally, in the Trefftz DG method each approximation function satisfies the underlying partial differential equation in each finite element. The Trefftz DG method is similar to the ultra weak variational formulation (UWVF) but the local bases are constructed differently. Electromagnetic wave, eddy current and elastic wave problems are solved in order to analyze the performance of the method. The ultrasonic testing (UT) example is a two-dimensional elastic wave model of the Inconel welding area in reactor vessels. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm using mesh incidence matrices is developed for the fast generation of source magnetic fields. The mesh incidence matrices arise by applying cohomology concepts to the discrete form of the topological laws for source magnetic fields. The algorithm admits a unique and very fast integer Gaussian elimination procedure. The same algorithm is used to generate solenoidal current density in stranded conductors. [ABSTRACT FROM AUTHOR]

A fast Newton-Raphson algorithm is developed for the finite-element solution of nonlinear boundary value problems The linearized equation systems in the nonlinear iteration steps are solved by a block-preconditioned conjugate gradient (CG) technique, in which the stopping criterion of the CG iteration is adaptively controlled by the nonlinear residual error. The Jacobian matrix is partitioned into linear and nonlinear blocks, thereby allowing the relatively rapid generation of an efficient multiplicative preconditioner for the CG iteration. The results obtained for a magnetostatic and a coupled steady conduction-static thermal problem confirm the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

Presents information on a study which described the techniques for decreasing the forward solution time in eddy current inversion loops. System matrix and signal; Description of the algorithms; Conclusions.

Focuses on an eddy current flaw reconstruction strategy based on the minimization of nonlinear least-squares error functionals for problems with arbitrary specimen, probe and defect shapes. Major problem in eddy current flaw reconstruction; Information on eddy current probe signal.

Proposes a three dimensional finite element scheme to calculate eddy current probe responses due to conducting shells in eddy current nondestructive evaluation (NDE) problems. The theory; Test results; Conclusions.

Describes the basic idea of the flaw field calculation in finite element modeling and discusses the algorithm for zero-conductivity flaws in detail. Basic concept of the scheme; Finite element scheme for zero-conductivity flaws; Defect with negligible thickness; Results of the experiment; Conclusions.

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]

The near‐field validation of computational electromagnetic models of personal wireless communication devices is becoming indispensable, especially, when assessing specific absorption rate (SAR) compliance to regulatory limits by computer simulation. A possible practice for such validation is to compare measured and simulated electromagnetic field distributions in a standard flat phantom designed for SAR compliance measurements. The authors recently presented an input impedance measurement‐based validation method. They extend their scheme with a deconvolution procedure. This enables near field validation based on the reconstructed E2 field obtained by the deconvolved measurement of the impedance change compared to the calculated E2. However, the reconstruction problem is inherently ill conditioned and requires numerical treatment. They demonstrate that the regularisation of the convolution matrix makes the reconstruction of the E2 field feasible with promising error. Through examples of a 1 GHz printed inverted F and a 1.8 GHz printed monopole antenna, they show that the mean‐square error as low as 1% between the original and the reconstructed E2 is achievable with the proposed method. [ABSTRACT FROM AUTHOR]

The utilization of Graphical Processing Units (GPUs) for the element-by-element (EbE) finite element method (FEM) is demonstrated. EbE FEM is a long known technique, by which a conjugate gradient (CG) type iterative solution scheme can be entirely decomposed into computations on the element level, i.e., without assembling the global system matrix. In our implementation NVIDIA's parallel computing solution, the Compute Unified Device Architecture (CUDA) is used to perform the required element-wise computations in parallel. Since element matrices need not be stored, the memory requirement can be kept extremely low. It is shown that this low-storage but computation-intensive technique is better suited for GPUs than those requiring the massive manipulation of large data sets. [ABSTRACT FROM PUBLISHER]

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]

A full-wave integral formulation has recently been proposed for the simulation of magnetically coupled resonant wireless power transfer (WPT) arrangements in homogeneous medium. In this paper, the formulation is extended to the case where two different types of dielectrics are separated by a planar interface. This configuration has extensive practical interest nowadays, especially for modeling biomedical WPT applications. The new formulation is based on a stationary approximation, which is valid at the typical operating frequencies. The proposed scheme requires much less computational resources compared with standard finite-element simulations. The results are validated against alternative simulations and measured data as well. [ABSTRACT FROM AUTHOR]