O. Biro

Global optimization methods for computational electromagnetics

Both higher-order (pseudo)deterministic and zeroth-order probabilistic optimization methods have been analyzed and tested for solving the global optimization problems arising in computational electromagnetics. Previously recommended, but seemingly independent schemes (evolution strategies, simulated annealing, Monte Carlo iteration) have been unified into a robust general method: the global evolution strategy (GES). Regularization techniques, the stability of solutions, and nonlinear phenomena are shown to be topics closely related to global optimization and inverse problems. The speed of convergence is evaluated for different optimization methods. A real-world application (from nuclear magnetic resonance and magnetic resonance imaging) demonstrates the favorable behavior of GES in the context of the finite element method. >

Finite element scheme for 3D cavities without spurious modes

A numerically efficient finite-element formulation is presented for the analysis of inhomogeneously loaded three-dimensional cavities of arbitrary shape. The electromagnetic field is described either by the three components of a magnetic vector potential and by an electric scalar potential, or by the three components of an electric vector potential and by a magnetic scalar potential. The uniqueness of the potentials is ensured by the incorporation of the Coulomb gauge and by proper boundary conditions. Owing to the correct description of the electromagnetic field, no spurious modes appear. The Galerkin equations are formulated for the finite element method leading to a generalized eigenvalue problem with symmetric, sparse matrices. This is solved by means of the bisection method with the sparsity of the matrices fully utilized. Several 3-D cavity problems are solved to illustrate the method. >

Parameter estimation for PMLs used with 3D finite element codes

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 electromagnetic field of a linear dipole antenna in the vicinity of lossy objects.

Finite element analysis of multiport filters using perfectly matched layers

A 3D edge finite element analysis is presented to calculate the resonance frequencies and quality factors of inhomogeneously loaded cavity resonators (filters) terminated by waveguides (ports). The matching of the ports is modeled by perfectly matched layers (PML). The selection of the PML parameters is discussed. A complex nonlinear eigenvalue problem is obtained which is solved by a special solver with the sparsity of the matrices fully utilized. An approximation is applied to reconstruct the frequency response of the scattering parameters from the field calculated at the resonance frequencies.

A virtual electromagnetic laboratory for the classroom and the WWW

A virtual laboratory for the classroom as well as for distance education on World Wide Web is presented making use of the various FEM software packages for the numerical calculation of electromagnetic field problems developed at IGTE. For creating interactive educational examples, the HTML-format specification was chosen. The interaction between the HTML document and the FEM software is performed by the widespread Tool Command Language (TCL).

Use of an optimization algorithm in designing medium-voltage switchgear insulation elements

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

A proof of the perfect matching property of PMLs in static 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 also illustrates the feasibility of PMLs for magnetostatic fields.

Numerical simulation and design of a fluxset sensor by finite element method

A 3D model of a fluxset sensor serving to measure the 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.