Higher Order Large-Domain Hierarchical FEM Technique for Electromagnetic Modeling Using Legendre Basis Functions on Generalized Hexahedra

A novel higher-order large-domain hierarchical finite-element technique using curl-conforming vector basis functions constructed from standard Legendre polynomials on generalized curvilinear hexahedral elements is proposed for electromagnetic modeling. The technique combines the inherent modeling flexibility of hierarchical elements with excellent orthogonality and conditioning properties of Legendre curl-conforming basis functions, comparable to those of interpolatory techniques. The numerical examples show the reduction of the condition number of several orders of magnitude for high field-approximation orders (e.g., 14 orders of magnitude for entire-domain models) when compared to the technique using field expansions based on simple power functions and the same geometrical elements.