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Adaptive finite element analysis of 2‐D static and steady‐state electromagnetic problems
Author(s) -
Fernandes P.,
Girdinio P.
Publication year - 1999
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19990520)45:2<215::aid-nme590>3.0.co;2-o
Subject(s) - finite element method , basis (linear algebra) , computer science , electromagnetics , basis function , eddy current , computational electromagnetics , mathematics , algorithm , adaptive mesh refinement , mathematical optimization , electromagnetic field , mathematical analysis , geometry , computational science , physics , electronic engineering , engineering , quantum mechanics , thermodynamics
The 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‐by‐ element 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. Copyright © 1999 John wiley & Sons, Ltd.