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Aortic dissection is caused by a tear on the aortic wall that allows blood to flow through the wall layers. Usually, this tear involves the intimal and partly the medial layer of the aortic wall. As a result, a new false lumen develops besides the original aorta, denoted then as the true lumen. The local hemodynamic conditions such as flow disturbances, recirculations and low wall shear stress may cause thrombus formation and growth in the false lumen. Since the false lumen status is a significant predictor for late‐dissection‐related deaths, it is of great importance in the medical management of patients with aortic dissection. The hemodynamic changes in the aorta also alter the electrical conductivity of blood. Since the blood is much more conductive than other tissues in the body, such changes can be identified with non‐invasive methods such as impedance cardiography. Therefore, in this study, the capability of impedance cardiography in monitoring thrombosis in the false lumen is studied by multiphysics simulations to assist clinicians in the medical management of patients under treatment. To tackle this problem, a 3D computational fluid dynamics simulation has been set up to model thrombosis in the false lumen and its impact on the blood flow‐induced conductivity changes. The electrical conductivity changes of blood have been assigned as material properties of the blood‐filled aorta in a 3D finite element electric simulation model to investigate the impact of conductivity changes on the measured impedance from the body's surface. The results show remarkable changes in the electrical conductivity distribution in the measurement region due to thrombosis in the false lumen, which significantly impacts the morphology of the impedance cardiogram. Thus, frequent monitoring of impedance cardiography signals may allow tracking the thrombus formation and growth in the false lumen. [ABSTRACT FROM AUTHOR]

This paper presents application of multiobjective optimization methods on a capacitive divider finite element model. Modeling is based on the differential evolution algorithm (DE), including the concept of the Pareto nondominance. Through calculations, this concept allows differential evolution algorithm variation in order to achieve uniformly distributed results on the Pareto front, including the lowest population size as possible. Selection step, as a part of the differential evolution method, is properly modified to improve the convergence of the algorithm. The entire research leads to a hybrid algorithm development. Index Terms--Epoxy resin insulators, optimization methods, Pareto distributions, voltage dividers.

A discontinuous Galerkin finite element approach is presented to solve eddy-current problems in the time domain based on a magnetic vector potential formulation. The mass matrix in the eddy-current region is block-diagonal allowing explicit time stepping without having to solve a large algebraic system here. Traditional finite elements, leading to well conditioned system matrices, are used in the eddy-current free domain. The time steps are different in the two regions. The method is illustrated by a simple two-dimensional example. Index Terms--Discontinuous Galerkin method, eddy currents, finite element methods, time domain analysis.

A method is presented for the optimal choice of the fixed-point reluctivity in nonlinear eddy current problems solved for steady-state in the frequency and the time domain. The optimal selection is shown to ensure a minimal contraction number for the fixed-point method. The proposed technique is compared to earlier approaches using a 2-D example. Index Terms--Convergence of numerical methods, eddy currents, Fourier transforms, numerical analysis.

A procedure based on the finite element method (FEM) is presented to determine the strongly distorted wave-forms of the magnetizing currents having given direct current (dc) components in each phase of a three-phase power transformer. The three phase voltages forming a symmetric sinusoidal system are assumed to be known. The relationships between the flux linkages of the three windings and the three values of the magnetizing current are determined using FEM and assuming static conditions. Suitable techniques are employed to establish the dependence of the dc components of the three magnetizing currents upon the three bias fluxes. The flux bias values yielding the given dc components are hence obtained by an iterative method yielding the wave-forms of the magnetizing currents having the prescribed dc values. The method is illustrated by a numerical example. Index Terms--Finite element methods, geomagnetism, power transformer losses.

A procedure based on the finite-element method (FEM) is presented to determine the eddy currents and losses in large axisymmetric filter air coils built with a special type of turns. To reduce the eddy current losses, the turns consist of several single insulated copper wires which are twisted similarly to a cable to form a conductor. Therefore, axisymmetry in the cable is destroyed. Since the wires are not stranded perfectly within the cable (they are stranded within layers only), there is a non-uniform current distribution between the different layers. To take this into account and still retain axisymmetry, an FEM procedure using a one component vector potential combined with circuit considerations has been used where the single wires of the cable are located in a special manner to simulate their stranding within their respective layers. The numerical results are validated by measurements showing excellent agreement. Index Terms--Air coils, eddy current losses, finite-element methods (FEMs), stranded conductors.

The fixed-point method together with the Fourier decomposition of time dependent quantities can be used to determine the steady state solution of sinusoidaily driven electrodynamic problems in the presence of nonlinear materials. The advantage of this method is to obtain the steady state immediately without having to calculate transient processes. However, the convergence rate of the method is heavily influenced by the so called fixed-point permeability. An appropriate choice of this parameter can speed up the convergence whereas an unsuitable value leads the method to divergence. The aim of this paper is to present a strategy to choose the value for the fixed-point permeability in order to enhance the convergence rate. The result is illustrated by two 2-D examples. Index Terms--Eddy currents, frequency domain analysis, nonlinearities, numerical analysis.

This paper describes the impact of selected insulation elements and the surrounding material, on the magnitude and distribution of electrical potential in a switch device. The procedure is based on finite element method numerical analysis and stochastic optimization algorithm of differential evolution (DE). The optimal selection of mutually independent insulation materials has an impact on the control of potential and, consequently, on dielectric strengths, both inside the bushing and in other switchgear elements. Two different methods are used for an extension of the multiobjective optimization of the problem. The entire modeling procedure also includes optimization of the bushing's geometrical shape. Index Terms--Finite element methods, gas insulated switchgear, insulators, optimization methods.

The transfinite-element time-domain method using the A, V-formulation for analyzing printed circuit boards is presented in this paper. To solve the resulting system of equations, a multigrid algorithm is implemented. The standard prolongation operator has to be altered to fit the transfinite elements and a new method for constructing the hierarchy of grids is presented. Numerical examples will show the properties of this method. Index Terms--Edge elements, microwaves, multigrid, solution of algebraic systems of equations.

In order to compute the scattering parameters of printed circuit board structures, the transfinite element method (TFEM) in conjunction with the A, v-potential formulation with edge elements has been implemented. The obtained matrix equation is sparse and symmetric and is solved by the complex conjugate gradient method with incomplete Cholesky factorization. Two simple problems demonstrate the validity of this method. Index Terms--Perfectly matched layer (PML), scattering parameter, transfinite element method (TFEM).

A method is presented which determines the steady-state solution of nonlinear eddy current problems. The unknown potentials are represented by Fourier-series and the nonlinear behavior of the material is split into a linear and a nonlinear term using a fixed-point technique. This approach leads to decoupled linear equations for each harmonic component. To take the nonlinearity into account, several fixed-point iterations have to be made. The method avoids calculating transient processes which normally have to be stepped through if using time-stepping methods. The present method is illustrated by two 2-D examples. Index Terms--Eddy currents, nonlinear equations, nonlinear magnetics, periodic functions.

A simple method is presented to generate impressed current vector potential functions with limited support whose curl yields a given net current. They are advantageously used in finite-element eddy current analysis employing a current vector potential represented by edge basis functions. A current vector potential describing a static current field with the given net current in the eddy current domain is first constructed. This source field is nonzero in the entire problem domain. Thereupon, it is restricted to a minimal simply connected region. The method is illustrated by a numerical example. Index Terms--Eddy currents, finite-element methods, numerical analysis, source fields.

Modern design of medium-voltage switchgear insulation elements is based upon the use of optimization methods. This paper presents an algorithm for the design of such elements using numerical calculations on the basis of the finite elements method in connection with evolution optimization methods. The use of differential evolution and evolution strategy algorithms is presented in the case of modeling a medium-voltage post insulator, the secondary function of which is voltage indication. A comparison between these two algorithms is also presented. The task of both optimization algorithms is to find an adequate capacitance of the voltage divider and the optimal distribution of electric field strength. All other requirements and constraints that have to be taken into consideration in the design of insulation elements are also included in the algorithm. Index Terms--Finite-element method (FEM), high-voltage techniques, optimization methods, switchgear.

A finite element method is presented to compute the electromagnetic field and hence the temperature rise in complex three-dimensional structures such as power transformers. The temperature dependence of both the heat transfer coefficients and the electric conductivity is taken into account establishing a strong coupling between the thermal and electromagnetic equations. Index Terms--Electromagnetic coupling, finite element methods (FEM), power transformer thermal factors.

A time-domain method is presented yielding the periodic steady-state solution of nonlinear eddy current problems without having to step through the transient process. A novel technique is introduced which, under periodic conditions, in the linear ease, decouples the finite element equation systems written for different time steps. Thereupon, a fixed point method is used to iteratively solve the nonlinear equations. The resulting procedure retains the decoupling property valid in the linear case, therefore, it suffices to step through one period only. The efficiency of the method is illustrated by two two-dimensional examples. Index Terms--Eddy currents, nonlinear equations, periodic functions, time-domain analysis.

The paper presents a numerical analysis of a permanent-magnet brushless motor. The goal of the research was to estimate and reduce the torque ripple of a motor under research. The rotor movement was also taken into account in order to consider all the prime causes for torque ripple production. Therefore, two different types of analysis were carried out. The first approach was based on a transient analysis of a two-dimensional (2-D) planar finite-element model coupled to a voltage-fed electric circuit. The second approach was based on a static analysis of 2-D and three-dimensional models where stator current waveforms were calculated separately by a circuit model. Both analyses enable a comprehensive study of the electric machine's performance under arbitrary load conditions considering the effects of the time-varying electrical variables as well as those due to rotor movement. An analysis was done of differently constructed varieties of motor model and different source voltage waveforms. Numerical results were verified by measurements in the laboratory. Index Terms--Brushless machines, finite-element methods, permanent magnets, torque.

A complex multigrid algorithm for the calculation of time-harmonic three-dimensional eddy currents is presented. The finite-element method with edge elements is used for the discretization of the problems. Different multigrid smoothers are compared for two formulations of the time-harmonic eddy-current problem. It turns out that, using the right combination of smoother and eddy-current formulation, the computation times can be substantially reduced. Index Terms--Convergence of solutions, edge elements, solution of algebraic systems of equations, time-harmonic eddy-currents.

In the last decade, edge finite-elements (FEs) have prevailed over nodal ones to approximate vector potentials especially in computing eddy current problems. Various tetrahedral edge FEs have been developed to treat three dimensional problems. The computational effort to solve the resulting equation system by the incomplete Cholesky conjugate gradient (ICCG) technique using Whitney elements and symmetric tetrahedral nodal and edge FEs of second order have been compared for different potential formulations. Index Terms--Convergence of numerical methods, eddy currents, edge elements, finite-element (FE) method, potential formulations.

A finite element method is presented to compute three-dimensional eddy current distributions in nonlinear laminated iron cores. In a first step, the core is assumed to have an anisotropic conductivity of zero value in the direction perpendicular to the laminations. In a second step, the eddy currents within the sheets are computed by solving the nonlinear field problem individually in each layer. The boundary conditions for these essentially two-dimensional analyses are taken from the three dimensional field distribution determined in the first step. Numerical examples prove the validity of the method. Index Terms--Eddy currents, finite element calculations.

Finite-element formulations using a current vector and a magnetic scalar potential are presented for low-frequency electromagnetic problems involving voltage driven coils. Windings both with and without skin effect are treated. The voltage constraint is directly incorporated into the finite-element equation system. Numerical examples are also presented. Index Terms--Eddy currents, finite-element calculations, voltage drive.

A time-domain method is presented to treat transient quasistatic electric problems if the permittivity depends on frequency. The inverse Fourier transform of the complex permittivity spectrum is used in a time-stepping procedure. The method is numerically realized using finite-element techniques. The approach is validated by assuming a frequency dependence having an analytical inverse transform. Thus, the frequency dependence of the permittivity of a real electroceramic material is determined from measurement results by curve fitting. An example using this curve illustrates the effect of the frequency dependence of permittivity on the time-domain solution. Index Terms--Finite-element calculations, frequency-dependent permittivity, time-dependent electric fields, transient analysis.

In the computation of eddy current fields with edge elements it is known that the numerical stability can be rather inferior for the A *-formulation, in comparison to that of the A, v-formulation. In this paper, the differences of the two formulations with regard to the convergence of an iterative solver will be pointed out. The result is a suggestion about a new preconditioner for the conjugate gradient method. Index Terms--Convergence of solutions, edge elements, solution of algebraic systems of equations, transient eddy currents.

A numerical method for calculation of the power losses of nonlinear laminated ferromagnetic cores is presented. The calculation is made in two subsequent steps. In the first step, the approximate magnetic field distribution in the material is determined assuming a nonlaminated bulk nonlinear ferromagnetic material with anisotropic conductivity. In the second step, the nonlinear ferromagnetic material of the laminated core is replaced to linear material with spatially inhomogeneous permeability. The actual permeability distributions of the lamination are determined based on the magnetic field obtained from the first calculation and the nonlinear B-H curve of the material. In this paper, the outlined method is verified through calculations and measurements made on simple benchmark arrangements. Different methods for assigning the inhomogeneous permeability are also investigated. Index Terms--Cell method, eddy currents, finite element methods, lamination stack.

In this paper, an electromagnetic field analysis tool for education in electrical engineering courses which is also accessible from the Web is described. The tool is based on the finite-element model (FEM). However, the main aim here is not to convey the methods of computational electromagnetics, but to give a deeper insight into electromagnetic phenomena. Three examples are shown, an eddy current problem in an axisymmetric ferrite core with air gap and the other two illustrate quasi-static electric transient behavior of the electric field considering imperfect dielectric media. Index Terms--Computational electromagnetics, computer-aided analysis, electric engineering education.

Edge basis functions associated with loops forming fundamental sets on finite element facets rather than with single edges are introduced. It is shown that using these to approximate vector potentials results in less linearly interdependent equations than with usual edge basis functions. Furthermore, the conditioning of the matrix in the Galerkin equations system obtained is demonstrated to be substantially better than when using a tree--cotree gauge. Index Terms--Edge elements, finite element calculations, static magnetic fields.

An improved proof of the perfect matching property of fictitious anisotropic layers (PMLs) with the product of the relative permittivities in two directions equal to 1 is presented for the static case. An example involving a three-dimensional magnetic problem illustrates the feasibility of PMLs for magnetostatic fields, too. Index terms - Finite element methods, magnetostatic analysis, open boundaries, perfectly matched layers.

A 3D model of a fluxset sensor serving to measure magnetic fields arising in Eddy Current Nondestructive Testing applications is analyzed by the finite element method. The voltage induced in the pick-up coil is obtained by computing the flux of the core of the sensor for several values of the exciting current at various external fields. It is shown that the time shift of the ensuing voltage impulse depends linearly on the external field in a wide range. The behavior of the sensor is furthermore simulated in a real nondestructive testing arrangement consisting of an exciting coil located above a conducting plate with a crack. Index terms - Eddy current testing, finite element methods, detectors, fluxset sensor.

Perfectly Matched Layers (PMLs) are used to truncate the mesh in a 3D edge finite element code. A new interpretation of the PMLs helps to solve the problem of joining PMLs of different directions and to estimate the proper setting of the PML parameters. The finite element code uses an A,V description to obtain a better convergence rate of the iterative solver. The program is used to model the electro-magnetic field of a linear dipole antenna in the vicinity of lossy objects. Index terms - Propagation, finite element methods, mesh truncation, perfectly matched layers