FEM analysis of dielectric loaded waveguides with additive hierarchical singular vector elements

For problems with smooth surfaces or other regular features, high order hierarchical bases successfully improve accuracy and efficiency. However, for geometries with edges or corners where unbounded fields or other singular types of behavior occur, special bases that incorporate the singular field behavior are better at improving the solution accuracy. Recently, the authors (together with other co-authors) proposed additive basis sets that offer improved generality for high order expansions. These additive bases retain the entire original polynomial set and augment it with additional singular basis functions that define the so-called Meixner subset. Additive bases are more flexible than other type of bases (e.g., those employing substitutive basis functions) and can model appropriate field behavior even if the expected singularity is not excited by the source, or if the cells are electrically large.