The advantages and limitations of the direct boundary element method (DBEM) and the method of fundamental solutions (MFS) are compared, will illustrating examples. The salient features of the two methods are discussed. The formulations are described with the aim of illustrating the relative merits of each. The evaluation covers robustness, numerical accuracy, model development and implementation, as well as the ease of applying the impedance boundary condition (IBC). As a test problem, the case of two circular conductors carrying a total impressed current per conductor is considered. A wide range of frequencies and separating distances is examined to show the behavior of each method for skin and proximity effect problems. >

An evaluation of the direct boundary element method and the method of fundamental solutions

This work deals with the full quantitative local reconstruction of magnetization distributions from measurements of the normal component of the magnetic stray field of micro- and nanostructured magnetic films and the underlying inverse magnetostatic problem. The magneto-optical indicatorfilm technique (MOIF) is applied for magnetic imaging. Based upon the strong magneto-optical Faraday-effect in special sensor layers, this method allows a quantitative determination of the stray field z-component at a fixed height above the samples. Lithographically patterned, magnetically hard structures of well defined shape and size serve as model systems for the investigation and establishment of the relationship between the stray field and the underlying magnetization. The quantitative stray field measurements via MOIF are verified by theoretical simulations. The evaluation of the local magnetization distribution is based on transfer functions in Fourier space, taking all intrinsic measuring conditions into account. This formalism leads to a correct quantitative reconstruction of the magnetization for pattern sizes larger than the resolution limit. Constitutive upon the advanced mathematical inversion scheme, the early stages of the remagnetization process of spatially extended arrays of magnetically hard elements are studied in detail. Furthermore, this work treats the problem of calibrating a magnetic force microscope by means of quantitative MOIF measurements.

Entwicklung eines quantitativen Verfahrens zur Streufeld- und Magnetisierungsbestimmung magnetischer Strukturen

An effective optimum design method is presented. The method combines the three‐dimensional boundary element method with the (1+1) evolution strategy. The reduced scalar potential formulation with the magnetic surface charge as the unknown variable is used under the assumption that the yokes are not saturated. It is found, through the numerical example, that the global optimum shape of the magnet can be easily found within a reasonable number of generations. More elaborate design can be achieved by increasing the number of design variables.

Optimum design of voice coil motor with constant torque coefficients using evolution strategy

The application of the boundary-element method to electromagnetic problems is discussed. A number of alternatives are available as far as implementation is concerned. Some of these alternatives are examined, and their effects on accuracy and efficiency are indicated. These include the Galerkin and point-matching methods. The effects of corners and ill-posed problems are considered. >

Some technical aspects of implementing boundary element equations

The galvanic problem is frequently solved by a Fredholm integral equation of the second kind based on a single layer source formulation. At higher conductivity contrasts between the model and its surroundings the homogeneous part of the integral equation approaches an eigenvalue equation. With infinite contrast the solution of this limiting integral equation is non-unique, but in the subspace of zero total charge the solution is unique. This mathematical property of the integral equation is reflected in its numerical solution with the result that large numerical errors may appear and convergence of the solution becomes very slow. Errors are, for the most part, related to the computed excess charge generated in the numerical solution. The effect is studied by comparing the results computed from the solution of the integral equation alone with those computed from a particular solution where the requirement of zero total charge is used as a constraint. The model examples clearly show that the use of the constraint condition significantly improves the accuracy of the results.

Constraining of the zero total surface charge in galvanic modelling

In this paper, a constrained boundary integral equation is presented for the analysis of three‐dimensional magnetostatic problems. This formulation uses a simple layer of charge on the interface surface to represent the permeable object. A constraining condition that sets the total integrated surface charge to zero is used to make this formulation unique. In addition, a method of generating exact analytical solutions for use in validating the boundary element code is presented. A test comparison using this method will be shown.

Solution of three‐dimensional boundary value problems for magnetostatics by a constrained Fredholm integral equation

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Solution of three‐dimensional boundary value problems for magnetostatics by a constrained Fredholm integral equation