Abstract
This paper is aimed at applying Dirichlet-to-Neumann (DtN) map to calculate the band gaps of scalar waves in a two-dimensional phononic crystal which is composed of circular cylinders embedded in a host medium in either square or triangular lattice. Detailed computation is performed for both solid/solid and fluid/fluid systems with emphasis on comparison to the plane wave expansion method. The numerical results show some merits of the DtN method. Its computing cost to obtain the results of high accuracy is very low, especially for higher frequency computation or for systems with large acoustic mismatch. Another feature of the DtN method is that it can yield band structures at an arbitrary frequency interval which does not necessarily start from zero.
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