FICTITIOUS MINIMA OF OBJECT FUNCTIONS, FINITE-ELEMENT MESHES, AND EDGE ELEMENTS IN ELECTROMAGNETIC DEVICE SYNTHESIS

The inverse solution of electromagnetic field problems is now increasingly considered a problem that can be addressed on the computer as a synthesized device output corresponding to specified performance characteristics. However, the efficiency of the process by which the solution is arrived at is also of importance and bears much on the method's acceptance. The object functions are said to have multiple minima and much research effort is expended on methods to find the global minimum. This paper points out for the first time the nature of the discontinuities in the object function as a result of mesh error. That is, they are artificial and have no physical basis. These discontinuitics, however accurate our mesh might be, persist. As such, the solution of inverse problems gets to be slow. This paper presents three approaches to minimizing this error: i. Adaptive meshes ii, Edge Elements and iii, Crunched meshes. The latter is shown to be significantly faster for optimization, although the field solutions in the iterations have accuracy depending on the fineness of the initial mesh. Adaptive approaches on the other hand significantly slow down convergence! Edge elements improve flux density based object functions by making them C1 continuous because no derivative of the potential is required, although multiple minima continue to exist; but the C1 continuity allows us to use faster algorithms employing the Hessian.