This paper presents a review of finite element open boundary techniques for the computation of static and quasistatic electromagnetic fields. The underlying assumptions and ideas behind these techniques are outlined and explained. The advantages and shortcomings of each technique are discussed. The goal of this review is to aid those working on numerical solutions of open boundary problems using the finite element method to gain perspectives on the variety of techniques presently available or being developed. This review is also intended to facilitate the communication of numerical techniques between the low-frequency field computation community and those in the high-frequency community.

A review of finite element open boundary techniques for static and quasi-static electromagnetic field problems

The flow of blood in the presence of a magnetic field gives rise to induced voltages in the major arteries of the central circulatory system. Under certain simplifying conditions, such as the assumption that the length of major arteries (e.g., the aorta) is infinite and that the vessel walls are not electrically conductive, the distribution of induced voltages and currents within these blood vessels can be calculated with reasonable precision. However, the propagation of magnetically induced voltages and currents from the aorta into neighboring tissue structures such as the sinuatrial node of the heart has not been previously determined by any experimental or theoretical technique. In the analysis presented in this paper, a solution of the complete Navier-Stokes equation was obtained by the finite element technique for blood flow through the ascending and descending aortic vessels in the presence of a uniform static magnetic field. Spatial distributions of the magnetically induced voltage and current were obtained for the aortic vessel and surrounding tissues under the assumption that the wall of the aorta is electrically conductive. Results are presented for the calculated values of magnetically induced voltages and current densities in the aorta and surrounding tissue structures, including the sinuatrial node, and for their field-strength dependence. In addition, an analysis is presented of magnetohydrodynamic interactions that lead to a small reduction of blood volume flow at high field levels above approximately 10 tesla (T). Quantitative results are presented on the offsetting effects of oppositely directed blood flows in the ascending and descending aortic segments, and a quantitative estimate is made of the effects of assuming an infinite vs. a finite length of the aortic vessel in calculating the magnetically induced voltage and current density distribution in tissue. © 1996 Wiley-Liss, Inc.

Theoretical analysis of magnetic field interactions with aortic blood flow.

This paper reviews the history and present state of finite-element methods, as applied to electromagnetic-field problems in the microwave range (including element definitions and error estimation, guided wave propagation, scattering and antenna problems). It provides a selective bibliography, current as of the first months of 1996, with annotations and evaluative comments on the works surveyed. It briefly notes the capabilities of the finite-element method, and estimates how fully they have been realized to date. Some conjectures on the future of finite-element methods are also hazarded.

Finite-element methods in microwaves: a selected bibliography

The author describes a novel boundary-element discretization scheme in the hybrid finite-element/boundary-element method, using a mixed linear and constant boundary element. A novel boundary-element vector potential formulation is presented, together with another formulation in terms of the magnetic field intensity and the magnetic scalar potential. Several practical applications of the method to electromagnetic field problems are presented. Besides the ordinary two-dimensional, axially symmetrical, and three-dimensional magnetic field problems, the two-semi-infinite-regions problem is investigated. The integration in the boundary-element method for this problem has integrating paths as far as infinity. Results of the hybrid method in which the integration path to infinity is cancelled out are also presented. >

Hybrid finite element and boundary element method applied to electromagnetic problems

The work of P. P. Silvester - mainly on the Finite-Element Method applied to problems in electrical engineering and as recorded by his writings - is reviewed, with particular reference to the innovations he introduced. A complete bibliography of Silvester's work is appended.

The Finite-Element Method, Part 2: P. P. Silvester, an Innovator in Electromagnetic Numerical Modeling

A finite element recursion technique is described for the solution of open-boundary electric and magnetic field problems. The method is to model the exterior region by an annular "super-element" in which all the nodes except those on the inside edge have been eliminated. The routine to generate the annulus and its element division automatically is detailed. This algorithm calculates the boundary coefficients representing the exterior Laplacian region from a knowledge of the interior region boundary node distribution. The method has been tested by comparing calculated solutions with results obtained from both analytical and experimental models and good agreement achieved.

C. Rajanathan

Papers

A finite element technique for solving 2-D open boundary problems