The impedance boundary condition applied to the finite element method using the magnetic vector potential as state variable: a rigorous solution for high frequency axisymmetric problems (original) (raw)
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The Finite Element Method Applied to the Magnetostatic and Magnetodynamic Problems
Finite Element Methods and Their Applications [Working Title], 2020
Modelling of realistic electromagnetic problems is presented by partial differential equations (FDEs) that link the magnetic and electric fields and their sources. Thus, the direct application of the analytic method to realistic electromagnetic problems is challenging, especially when modeling structures with complex geometry and/or magnetic parts. In order to overcome this drawback, there are a lot of numerical techniques available (e.g. the finite element method or the finite difference method) for the resolution of these PDEs. Amongst these methods, the finite element method has become the most common technique for magnetostatic and magnetodynamic problems.
IEEE Transactions on Magnetics, 2005
Magnetic field computations using the finite-element (FE) method usually involve large air domains surrounding the conductors to satisfy boundary conditions at infinity. Elimination of these air domains saves computations and simplifies model generation-especially in large problems involving complex geometries like railguns and pulsed power generators, where fields in the air regions are calculated using fields at the air-conductor interface. The air domain can be avoided using the hybrid finite-element/boundary-element (FE/BE) method. A two-dimensional (2-D) hybrid FE/BE algorithm with the fundamental solution of Poisson's equation as the weighting function is investigated here for applications to electromagnetic launch problems. Two examples with analytical solutions are used: a rectangular conductor carrying uniform current, and a quadrupole coil configuration. Solutions obtained using the hybrid algorithm match analytical solutions favorably in all regions, including geometric corners. The effects of the number of integration nodes in quadrature formulas and coupling schemes between the FE and BE formulations through the normal fluxes at the boundaries are also presented. These 2-D analyses serve as forerunners for three-dimensional investigations. Index Terms-Boundary elements, computational electromagnetics, finite elements, hybrid FE/BE, matrix equations. I. INTRODUCTION S OLUTIONS of electromagnetic (EM) field problems require the prescription of zero potentials and fields at infinity. The infinite domain surrounding conducting sources is customarily approximated in finite-element (FE) analyses by the prescription of a boundary located far from the conductors (usually five to ten times the major dimension of the conducting region). Besides causing error due to truncation of the boundary, the FE method also requires meshing and computations in the surrounding air region. In three-dimensional (3-D) analyses, the computation of fields in the surrounding air region could become a significant portion of the overall Manuscript received December 19, 2003. The research reported in this work was performed in connection with Contract DAAD17-01-D-0001 with the U.S. Army Research Laboratory. The views and conclusions contained in this document are those of the authors and should not be interpreted as presenting the official policies or position, either expressed or implied, of the U.S. Army Research Laboratory or the U.S. Government unless so designated by other authorized documents. Citation of manufacturers' or trade names does not constitute an official endorsement or approval of the use thereof.
IEEE Transactions on Magnetics, 2000
The study concerns a flat large construction steel plate of varying thickness magnetized with a C-core magnet. Modeling of the timeand space-field distribution inside the plate is carried out. The novelty of the approach consists in carrying out a transient solution when a driving saw-tooth voltage is used. Also new is a refined magnetoacoustic emission (MAE) signal modeling, numerically deduced for various frequencies, and compared with experimental data. The distributions of fields are indirectly compared with stray field measurements and a close agreement is found.
IEEE Transactions on Magnetics, 2000
The authors propose a novel time-domain extension of the well-known frequency-domain surface-impedance method in computational magnetodynamics. Herein, the 1-D eddy-current problem in a massive conducting region (semi-infinite slab) is considered via a number of exponentially decreasing trigonometric basis functions that cover the relevant skin-depth (or frequency) range of the application at hand. The method is elaborated for the 3-D magnetic-vector-potential formulation and is applied to a simple 2-D test case. Results are shown to converge well to those obtained with an accurate brute-force finite-element (FE) model.
Modelisation of 2D and axisymmetric magnetodynamic domain by the finite elements method
IEEE Transactions on Magnetics, 1988
A finite element analysis for calculating the magnetic field under different supply conditions of voltages or currents, by using the vector potential A in 2D and axisynunetric cases is described. The formulation takes into account coils as well as massive conductors. Finally, in the sinusoidal hypothesis, the formula tion allows to characterize the finite element domain like a complex impedance matrix that make easy a coupling with exterior circuit equations.
The Finite Element Method in Magnetics
The polarization method and the fixed point technique however, the parameter of the linear term must be selected in a special way. The last chapter is the collection of seven problems solved by the finite element method. The problems have been solved by using the user friendly graphical user interface and functions of COMSOL Multiphysics, which is a commercial finite element software. The authors want to express their grateful acknowledgement to Prof. Oszkár Bíró, Prof. Imre Sebestyén, Prof. Maurizio Repetto, Prof. Carlo Ragusa for their assistance during developing the nonlinear finite element procedures, to dr. Péter Kis and dr. János Füzi for their help in developing the scalar hysteresis measurements. The authors would like to express their thanks to Prof. György Fodor, Prof. Oszkár Bíró and Prof. Imre Sebestyén for the reading of the parts of the research and for the helpful and fruitful suggestions. The authors thank to Prof. Oszkár Bíró, dr. Péter Kis, dr. István Standeisky for reading of this book and making reviews. Their advices helped us to prepare this book better. We would like to express our special thanks to Prof. Oszkár Bíró for giving advices, many helps during studying the finite element method as well as the colleagues of the Group of Electromagnetic Theory,
Calculation of Magnetic Fields with Finite Elements
The discretization of transient and static magnetic field problems with the Whitney Finite Element Method results in differential-algebraic systems of equations of index 1 and nonlinear systems of equations. Hence, a series of nonlinear equations have to be solved. This involves e.g. the solution of the linear(-ized) equations in each time step where the solution process of the iterative preconditioned conjugate gradient method reuses and recycles spectral information of previous linear systems. Additionally, in order to resolve induced eddy current layers sufficiently and regions of ferromagnetic saturation that may appear or vanish depending on the external current excitation a combination of an error controlled spatial adaptivity and an error controlled implicit Runge-Kutta scheme is used to reduce the number of unknowns for the algebraic problems effectively and to avoid unnecessary fine grid resolutions both in space and time. Numerical results are presented for 2D and 3D nonlinear magneto-dynamic problems.
A Brief History of Finite Element Method and Its Applications to Computational Electromagnetics
The Applied Computational Electromagnetics Society Journal (ACES)
The development of the finite element method is traced, from its deepest roots, reaching back to the birth of calculus of variations in the 17th century, to its earliest steps, in parallel with the advent of computers, up to its applications in electromagnetics and its flourishing as one of the most versatile numerical methods in the field. A survey on papers published on finite elements, and on ACES Journal in particular, is also included.
A Technique for Improving the Accuracy of Finite Element Solutions for Magnetotelluric Data
Geophysical Journal International, 1976
This paper develops a finite element method which gives accurate numerical approximations to magnetotelluric data over two-dimensional conductivity structures. The method employs a simple finite element technique to find the field component parallel to the strike of the structure and a new numerical differentiation scheme to find the field component perpendicular to strike. Examples show that the new numerical differentiation scheme is a significant improvement over the standard finite element procedure when meshes of poor quality are used. Algorithms for incorporating the differentiation scheme into the finite element matrix equation and for computing partial derivatives of magnetotelluric data with respect to mesh parameters are derived in order to simplify the computation needed to do the inverse problem.