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An interface‐enriched generalized finite element analysis for electromagnetic problems with non‐conformal discretizations
Author(s) -
Zhang Kedi,
Najafi Ahmad Raeisi,
Jin JianMing,
Geubelle Philippe H.
Publication year - 2015
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.2073
Subject(s) - polygon mesh , finite element method , conformal map , discontinuity (linguistics) , basis function , interface (matter) , mathematics , basis (linear algebra) , electromagnetic field , convergence (economics) , extended finite element method , computer science , mixed finite element method , mathematical analysis , geometry , physics , parallel computing , economics , thermodynamics , economic growth , bubble , quantum mechanics , maximum bubble pressure method
Summary An interface‐enriched generalized finite element method is presented for analyzing electromagnetic problems involving highly inhomogeneous materials. To avoid creating conformal meshes within a complex computational domain and preparing multiple meshes during optimization, enriched vector basis functions are introduced over the finite elements that intersect the material interfaces to capture the normal derivative discontinuity of the tangential field component. These enrichment functions are directly constructed from a linear combination of the vector basis functions of the sub‐elements. Several numerical examples are presented to verify the method with analytical solutions and demonstrate its h‐refinement convergence rate. The proposed interface‐enriched generalized finite element method is shown to achieve the same level of accuracy as the standard finite element method based on conformal meshes. Two examples, involving multiple microvascular channels and circular inclusions of different radii, are analyzed to illustrate the capability of the proposed approach in handling complicated inhomogeneous geometries. Copyright © 2015 John Wiley & Sons, Ltd.