High-Order Divergence-Conforming Constrained Bases for Triangular Cells

作者：Young John C^*; Adams Robert J

来源：IEEE Transactions on Antennas and Propagation, 2017, 65(9): 4717-4727.

DOI：10.1109/TAP.2017.2722826

• Constrained bases
• Koornwinder-Dubiner polynomials
• singular value decomposition (SVD)
• triangle cells

This paper presents an algebraic technique for generating arbitrary-order divergence-conforming bases for curvilinear triangular cells. The bases are constructed by enforcing appropriate constraints on a linear combination of general functions and then extracting the desired bases using singular value decompositions. Koornwinder-Dubiner polynomials are chosen as the general function set. Basic constraints are presented to obtain divergence-conforming bases, and additional constraints are presented to further enforce the bases to be Nedelec. Results from a variety of problems are given to show that the bases exhibit high-order convergence and also produce systems that are relatively well conditioned compared to other basis sets.

• 出版日期2017-9