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Higher order hierarchical curved hexahedral vector finite elements for electromagnetic modeling

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2 Author(s)
Ilic, M.M. ; Dept. of Electr. & Comput. Eng., Univ. of Massachusetts Dartmouth, MA, USA ; Notaros, B.M.

A novel higher order finite-element technique based on generalized curvilinear hexahedra with hierarchical curl-conforming polynomial vector basis functions is proposed for microwave modeling. The finite elements are implemented for geometrical orders from 1 to 4 and field-approximation orders from 1 to 10 in the same Galerkin-type finite-element method and applied to eigenvalue analysis of arbitrary electromagnetic cavities. Individual curved hexahedra in the model can be as large as approximately 2λ×2λ×2λ, which is 20 times the traditional low-order modeling discretization limit of λ/10 in each dimension. The examples show excellent flexibility and efficiency of the higher order (more precisely, low-to-high order) method at modeling of both field variation and geometrical curvature, and its excellent properties in the context of p-refinement of solutions, for models with both flat and curved surfaces. The reduction in the number of unknowns is by an order of magnitude when compared to low-order solutions.

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Microwave Theory and Techniques, IEEE Transactions on  (Volume:51 ,  Issue: 3 )