An open boundary technique for axisymmetric and three dimensional magnetic and electric field problems

Abstract

A technique is described which allows the effect of open boundaries in axisymmetric and three-dimensional problems to be accounted for in a standard finite element package without the need for any software modification. It is based on the conventional Kelvin transformation coupled with a modification to the material properties of the exterior region. While the technique could be built into a finite element solver and would produce very accurate results at a lower computational cost than many existing methods because of the maintenance of matrix sparsity. Its major advantage is that it can be applied directly in many existing finite element packages without the need for any software modifications and can provide more accurate solutions than can be obtained by using the same number of elements to move the boundaries far away from the region of interest. A second advantage is that the exterior field is available from the solution via a very simple transformation. In addition, it is possible to place objects in the exterior region and allow for their effects on the interior solution. An application example (a solenoidal coil) is given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>