B-Spline Entire-Domain Higher Order Finite Elements for 3-D Electromagnetic Modeling

A novel entire-domain finite element technique based on curvilinear hexahedral geometrical modeling using B-splines in conjunction with higher order hierarchical polynomial curl-conforming vector basis functions for field expansions is proposed for electromagnetic analysis of microwave devices. The effectiveness of the technique is evaluated in analysis of microwave cavities and it is compared with alternative reference solutions and with HFSS. Examples demonstrate large single-element (entire-domain) models with
$p$
-refined field distributions and better accuracy in curvature modeling than with the Lagrange interpolation. Extraordinary flexibility of the B-spline hexahedral elements, combined with higher order field expansions, allows accurate modeling of complex structures with sharp edges using a single finite element.