Adaptive finite element analysis of 2-D static and steady-state electromagnetic problems

Abstract

SUMMARYThe adaptive finite element methods developed by the authors for a class of 2-D problems in computational electromagnetics are presented. The cases covered are: magnetostatic, electrostatic, DC conduction and linear AC steady-state eddy currents, both plane and axialsymmetric. Theory is developed in the linear case only, but the resulting methods are applied on a heuristic basis also to non-linear cases and prove able to cope with them. These methods make use of an element-by-element error estimation and two different h-refinement techniques to adapt meshes made up of first or second-order triangular elements. Element-byelement error estimation has two main advantages: it is well suited to cope with the intricate geometries of electromagnetic devices and, at the same time, very cheap from a computational viewpoint. The local error is estimated by approximately solving a differential problem in each element. Theory on which this error estimation method is grounded is developed in full details and the underlying assumptions are pointed out. The presence in electromagnetic problems of surface currents and interfaces between different materials poses new problems in the error estimation with respect to other applications in which similar methods are used. The h-refinement technique can be selected between the bisection method and the centroid method followed by a Delaunay step. Accuracy and efficiency of the proposed method is discussed on the basis of previous work of the authors and further numerical experiments. Applications to realistic models showing good performances of the proposed methods are reported.

Analytical algorithm of inductive field for realising a smart eddy current NDT system

“…In a different arena, with the advent in computer technology, many efficient algorithms have been developed in the field of numerical electromagnetic analysis (Chan and Anastasiou, 1997; Fernandes and Girdinio, 1999; Fernando and Mesquita, 1996; Holzer, 1999; Stewart and Hughes, 1997; Zienkiewicz and Taylor, 1989). In 1971, Winslow, Chari and Silvester applied finite element method to the analysis of electromagnetic field.…”

“…In 1971, Winslow, Chari and Silvester applied finite element method to the analysis of electromagnetic field. Since then, many advances can be seen in both analysis and application algorithms of an electromagnetic field such as automatic mesh generation (Holzer, 1999), error estimation (Stewart and Hughes, 1997), adaptive analysis (Holzer, 1999; Stewart and Hughes, 1997), the computation of two and three‐dimensional inductive fields (Fernandes and Girdinio, 1999; Fernando and Mesquita, 1996). Although many progresses have been made in both inductive test technique and electromagnetic analysis, research effort to integrate an analysis module of inductive field into an eddy current NDT system to realise a hybrid technique, which is capable of automatically analysing the inductive field so as to set up the optimum parameters for the system, has not been well addressed.…”