Gerrit Mur

Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations

When time-domain electromagnetic-field equations are solved using finite-difference techniques in unbounded space, there must be a method limiting the domain in which the field is computed. This is achieved by truncating the mesh and using absorbing boundary conditions at its artificial boundaries to simulate the unbounded surroundings. This paper presents highly absorbing boundary conditions for electromagnetic-field equations that can be used for both two-and three-dimensional configurations. Numerical results are given that clearly exhibit the accuracy and limits of applicability of highly absorbing boundary conditions. A simplified, but equally accurate, absorbing condition is derived for two- dimensional time-domain electromagnetic-field problems.

A finite-element method for computing three-dimensional electromagnetic fields in inhomogeneous media

A finite-element method is presented that is particularly suited for the computer modeling of three-dimensional electromagnetic fields in inhomogeneous media. It employs a new type of linear vectorial expansion functions. Across an interface where the constitutive coefficients are discontinuous, they have the following properties: (1) the continuity of the tangential components of the electric and the magnetic field strengths is exactly preserved, (2) the normal component of the electric and the magnetic field strengths are allowed to jump and (3) the electric and the magnetic fluxes are continuous within the pertaining degree of approximation. The system of equations from which the expansion coefficients are obtained is generated by applying a Galerkin-type weighted-residual method. Numerical experiments are described that illustrate the efficiency of our elements, and the computational costs of the method.

Computation of the Input Impedances of a Catheter for Cardiac Volumetry

Electrical impedances between the electrodes of a catheter in a spheroidal model of the left ventricle are calculated analytically. The fields in the configuration are computed using eigen function expansions of the Laplace equation. For certain realistic combinations of specific conductances of the blood and the myocardium, numerical results are given. These results show the dependence of the impedances on the volume of the ventricle while keeping the length of the major axis of the ventricle constant. Also, the accuracy of the model and the dependence of the total conductance of the ventricle on its shape, and on the conductivity of the tissues surrounding it, are discussed. The theoretical results are compared against the experimental values of conductances, measured post mortem in a canine heart, for different volumes.

The finite-element modeling of three-dimensional electromagnetic fields using edge and nodal elements

An efficient and accurate finite-element method is presented for computing transient as well as time-harmonic electromagnetic fields in three-dimensional configurations containing arbitrarily inhomogeneous media that may be anisotropic. To obtain accurate results with an optimum computational efficiency, both consistently linear edge and consistently linear nodal elements are used for approximating the spatial distribution of the field. Compared with earlier work, the formulation is generalized by adding a method for explicitly modeling the normal continuity along interfaces that are free of surface charge. In addition, the conditions for efficiently solving time-harmonic problems using a code designed for solving transient problems are discussed. A general and simple method for implementing arbitrary inhomogeneous absorbing boundary conditions for modeling arbitrary incident fields is introduced. >

Total-field absorbing boundary conditions for the time-domain electromagnetic field equations

A method is described for generating absorbing boundary conditions (ABCs) that can be applied to the total fields rather than the usual scattered fields. As compared with the traditional use of ABCs for total-field formulations, this method has the advantages that it does not require the introduction of a mathematical connection surface between the total-field region and the scattered-field region; the total field is computed in the entire domain of computation. The incident field is accounted for by augmenting the ABC used. The resulting code is much simpler than one using ABCs for scattered fields together with a connection surface and the numerical results are much more easily interpreted since they consist of total fields only.

The finite-element modeling of three-dimensional time-domain electromagnetic fields in strongly inhomogeneous media

An efficient and accurate finite-element method is presented for computing transient electromagnetic fields in three-dimensional configurations containing arbitrarily inhomogeneous media that may be anisotropic. To obtain accurate results with an optimum computational efficiency, both edge and Cartesian elements are used for approximating the spatial distribution of the field. The efficiency and the storage requirements of the method are further optimized by choosing an irreducible implicit formulation, by solving the resulting system of algebraic equations in terms of the time-dependent expansion coefficients iteratively, and by using an incomplete LU-decomposition for preconditioning. A method is described for imposing the divergence condition in a weighted sense. The theory discussed was implemented in the FEMAXT code. >

Compatibility relations and the finite-element formulation of electromagnetic field problems

When computing an electromagnetic field using the finite element method it is possible that, although Maxwells equations are discretized accurately, highly inaccurate computational results are obtained. In those cases it can easily be shown that (some of) the electromagnetic compatibility relations (field properties that follow from Maxwells equations) are not satisfied. The divergence condition on the fluxes, for instance, follows directly from the field equations but not necessarily from their discretized counterparts. This necessitates inclusion of the compatibility relations in the finite-element formulation of the field problem. A survey is given of all electromagnetic compatibility relations. >

Finite formulation and domain-integrated field relations in electromagnetics - a synthesis

Complementary formulations of the integral type have established themselves as the most adequate approach to computational electromagnetics. This paper proposes a computational strategy that benefits from the advantages offered by the finite formulation of the electromagnetic (EM) field, employing integral field quantities and dual meshes, and by the domain-integrated field relations approach to EM field computation.

The fallacy of edge elements

The present paper critically investigates the use of edge elements for computing electromagnetic fields. The application of edge elements in methods based on the use of vector potentials as well as in methods that compute electric and/or magnetic fields directly will be covered. In particular the popular idea that edge elements eliminate spurious solutions will be refuted. This erroneous idea is replaced by the insight that spurious solutions can be eliminated only by a proper finite-element formulation. A reference is made to alternative approaches, one of them introducing a new type of element, the so-called generalised Cartesian element, that combines the advantages of the classical Cartesians (nodal) elements with the ability of edge elements to allow the representation of discontinuities.

Optimum choice of finite elements for computing three-dimensional electromagnetic fields in inhomogeneous media

A finite-element method is presented that has been specially designed for the computer modeling of three-dimensional time-harmonic electromagnetic fields in arbitrarily inhomogeneous media. For this purpose, two types of elements have been constructed. In the domain of computation the corresponding program decides locally what type of element to use for obtaining the best results as regards both computational efficiency and accuracy. Numerical results are presented that demonstrate the method to be efficient as well as accurate. >