W.M. Rucker

A BEM code for 3-D eddy current calculations

A software package for solving time-harmonic 3-D eddy current problems using the boundary-element method (BEM) is described. The package solves coupled boundary integral equations for the magnetic vector potential and the electric scalar potential within the conductors, and for the magnetic vector potential in non-eddy-current regions. The authors describe the boundary integral formulation and its BEM realization. As an example, the eddy current field of a nonmagnetic conducting cube immersed in a homogeneous magnetic field with harmonic time variation is calculated. Additional numerical results are presented for a multiply connected eddy-current problem (benchmark problem No. 7 defined by the International TEAM workshops). The boundary-element solutions are compared with finite-element results and show excellent agreement. >

Boundary element analysis of 3-D magnetostatic problems using scalar potentials

A boundary element formulation for 3-D nonlinear magnetostatic field problems using the total scalar potential and its normal derivative as unknowns is described. The boundary integral equation is derived from a differential equation for the total scalar potential where a nonlinear operator term can be separated from a linear term. The nonlinear term leads to a volume integral which can be treated as a known forcing function within an iterative solution process. An additional forcing term results from the magnetic excitation coil system. It is shown that the line integral of the magnetic source field which can be defined outside of the current-carrying regions as a gradient of a scalar potential acts as an excitation term. The proposed method is applied to a test problem where an iron cube immersed in the magnetic field of a cylindrical coil is investigated. The numerical results for different saturation stages are compared with finite element method (FEM) calculations. The comparison with FEM calculations shows a good agreement only in highly saturated iron parts. >

Various BEM formulations for calculating eddy currents in terms of field variables

Several boundary element formulations using the electric and magnetic field vectors are presented for eddy current problems. The robustness and the accuracy of the numerical approach depending on the frequency and the material properties of the eddy current region are investigated. Numerical results of a conducting sphere model are compared with analytical solutions. In additional examples the treatment of structures containing geometrical singularities (ideal edges and corners) is shown and numerical results are presented. >

Accuracy improvement using a modified Gauss-quadrature for integral methods in electromagnetics

A Gaussian quadrature technique for evaluating shape-function-boundary-element kernel produce integrals over three-dimensional isoparametric boundary elements is presented. The procedure allows the integration of singular kernels of O(1/r) on curved surfaces. The integration of the normal derivative of Greens function is also possible. Integrals which exist in the sense of Cauchy principal values are dealt with using the addition-subtraction technique. The accuracy of the numerical integration scheme is compared with that of the double exponential formula and the subdivision technique. Some examples show the effectiveness of the procedure. >

The solution of 3D multiple scattering problems using the boundary element method

The electromagnetic multiple scattering from lossless and lossy three-dimensional objects of arbitrary shape is computed using the boundary element method. Three different formulations starting from a combination of the magnetic field and the electric field integral equation are investigated. The influence of the material properties and the discretization on the solution accuracy is discussed by comparing the numerical results with analytic ones for spheres using the Mie series solution. As an example, the numerical solution of the electromagnetic scattered field of a rain drop model is presented. >

Calculation of antenna near field reactions on low conducting materials using the finite element method

On account of the progress in using mobile telecommunications systems in the high frequency range, the human body is increasingly exposed to electromagnetic fields. Therefore, the numerical simulation of the power absorbed in human tissue becomes extremely important in order to avoid thermal destruction. A typical example is the strong interaction between the near field of a receiving antenna of a hand held transceiver and the sensitive organs on the head, like the eyes. A finite element formulation is given for calculating 3D electromagnetic scattering problems. The influence of a dipole excited field on low conducting materials situated very close to the antenna is discussed. The backscattering from the conducting object to the antenna can be treated as well. Along the far boundaries of the computational domain, absorbing boundary conditions of second order have been prescribed in order to avoid non-physical reflections. The formulation described is assessed by applying it to a special problem and the solution obtained is compared with a boundary element calculation.

Boundary element computations of 3D stationary and time-dependent problems using Bezier-spline elements

A method for computing stationary and time-dependent problems using C/sup 1/-continuous Bezier boundary elements is presented. The Bezier element and the approximation of the solution is discussed. The method is validated against a biomedical problem, the results are compared with the analytical solution of a spherical model of a human thorax excited by a single dipole inside the heart. Further investigations concerning the scattering of a transient electromagnetic wave from simple shaped bodies are carried out with isoparametric Bezier spline representation of geometry and solution. In the case of integral equations of second order, it can be shown that the solutions smoothness is improved due to the C/sup 1/-continuity of the scatterers shape. First order integral equations are amenable to direct application of the boundary element method with derivation of the kernel inside the integral and point collocation. >

A marching-on-in-time method for 2-D transient electromagnetic scattering from homogeneous, lossy dielectric cylinders using boundary elements

A method for determining the fields scattered by arbitrarily shaped cylindrical, lossy dielectric structures with a transient incident wave is described. The transient scattering problem is reduced to the solution of a time-domain integral equation which is solved directly in the time domain by a time-stepping method. As the scatterer is homogeneous, the solution can be obtained by means of a boundary integral formulation and the problem-independent free-space Greens function. The approximate electromagnetic impulse response for a number of cylindrical targets is calculated using this method. >