Coons-patch macroelements in two-dimensional eigenvalue and scalar wave propagation problems

Recently, a global functional set has been proposed for the construction of large finite elements, here called “Coons-patch macroelements”, with degrees of freedom at the boundaries only. The background of the method is “Coons interpolation formula”; a mathematical formula capable of describing CAD surfaces initially applied to automobile applications. So far, these macroelements were found to be accurate in potential and plane elasticity problems. Based on these encouraging results, this paper continues the investigation on the universality which Coons interpolation formula offers in the development of a class of macroelements including members of the well-known serendipity family. In this context, it is shown in a systematic way that it is not necessary to use Lagrange polynomials to interpolate the potential along each side of the macroelement but one may choose piecewise-linear and/or cubic B-splines interpolants. Moreover, the paper investigates the performance of Coons-patch macroelements in eigenvalue and scalar wave propagation problems by implementing standard time-integration schemes.