Inverse Problems: Finite Elements in Hop-Stepping to Speed Up

Abstract

As opposed to the direct problem, the inverse problem of synthesizing a device from required performance criteria, is industrially more relevant. However, the need to differentiate object functions slows down the process so much that it is the chief impediment to the method's early acceptance in routine industrial use. Finite element methodology has helped this along by providing easy means of computing the derivative of the potential in magneto- and electro-statics. But much of the information computed is not used in the solution of inverse problems. This paper presents a scheme by which this unused information is put to good use in performing two iterations of design synthesis at once—the hop stepping approach.