Magnetic field computation using Delaunay triangulation and complementary finite element methods

Abstract

A two-dimensional finite element analysis package is described which automatically generates optimal finite element meshes for magnetic field problems. The system combines the concept of Delaunay triangulation with variational principles to provide a grid which adapts to the characteristics of the solution. In this procedure, two different approximate solutions to the magnetic field are derived, the difference between the two approximate solutions providing an element by element measure of the accuracy of the solution. By refining those elements having the largest errors and recomputing the solution iteractively, finite element meshes having a uniforrn error density are obtained. The system is menu oriented and utilizes multiple command and display windows to create and edit the object description interactively. Matrix solution is by means of a rapid pre-conditioned conjugate gradient algorithm, and a wide variety of post-processing operations are supported. Application of the mesh generator to a variety of problems in magnetic field design shows it to be one of the most powerful and easy to use systems yet devised.