Maximally Orthogonalized Higher Order Basis Functions in Large-Domain Finite Element Modeling in Electromagnetics

• Published in: IEEE transactions on antennas and propagation Vol. 68; no. 8; pp. 6455 - 6460
• Main Authors: Savic, Slobodan V., Ilic, Milan M., Kolundzija, Branko M.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Antennas; Basis functions; Condition number; differential equations; Domains; Electric fields; Finite element analysis; Finite element method; finite element method (FEM); higher order basis functions; higher order modeling; Integral equations; Iterative methods; Mathematical analysis; Mathematical model; Method of moments; numerical analysis; orthogonal functions; Polynomials; Silicon; Solvers
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2020.2970038

Curl-conforming max-ortho basis functions (MOBFs) are coupled with higher order large-domain curved finite elements (FEs). The performance of the functions is compared with that of the classical and near-ortho basis functions. Through numerical experiments, it is shown that max-ortho FEs yield highly orthogonal mass matrices, for practically arbitrarily high orders of polynomial field approximations. This facilitates the usage of iterative solvers and it significantly increases their efficiency. Accurate and fast computation of MOBFs, of arbitrarily high orders, is enabled by the proposed two-term recurrent formula.