Abstract
This paper discusses the efficient extraction of eigenfrequencies in two-dimensional acoustic cavities using higher order finite elements, called “Coons-patch macroelements”. The acoustic pressure is approximated within the entire domain using the bivariate transfinite (Coons-Gordon) interpolation formula. Basically, the proposed macroelements constitute a generalization of the well-known Serendipity and Lagrangian type elements. The paper investigates the performance of the proposed methodology in several examples and definitely correlates the necessity of using internal nodes or domain decomposition with the percentage of open boundaries over the entire boundary as well as their relative position. It was found that for simple shapes, the entire acoustic cavity can be considered as a single quadrilateral patch, i.e. as one Coons-patch macroelement, while for complex shapes the cavity should be divided into a small number of subregions.
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