h-p adaptive numerical integration techniques for finite element analysis in magnetics

Advanced numerical integration methods for finite element magnetics are investigated. Standard h-type, p-type and h-p adaptive finite element solver methodologies are extended to develop analogous adaptive integration procedures. The schemes are analyzed and compared in terms of efficiency and reliability. For practical implementations, it is established that only combined h-p approaches can be guaranteed to yield reliable results, which are converged to within a pre-specified tolerance, at a reasonable computational cost. A relatively simple h-p adaptive integration method is proposed for practical magnetics applications in which accuracy and reliability are essential. In addition, the similarities and subtle differences between corresponding adaptive solver and adaptive integration approaches are identified and discussed.