Hierarchical functions for multiscale problems

Recently, the authors have developed a number of new hierarchical and singular basis functions for field representation in two- and three-dimensional cells. Scalar and vector basis functions of both interpolatory and hierarchical kind together with some singular functions of the additive kind are discussed in detail, with several results, in a recent SciTech-IET book (R.D. Graglia and A.F. Peterson: Higher-order Techniques in Computational Electromagnetics), as well as in several other publications (for example, Graglia et al., IEEE TAP, vol. 61, pp. 3674–3692, Jul. 2013; IEEE TAP, vol. 62, pp 3632–3644, Jul. 2014; IEEE AWPL, vol. 13, pp 1701–1704, 2014, and in the special issue on “Finite Elements for Microwave Engineering,” Electromagnetics, vol. 34, pp. 171–198, 2014).