Application of Dirichlet-to-Neumann Map to Calculation of Band Gaps for Scalar Waves in Two-Dimensional Phononic Crystals
Application of Dirichlet-to-Neumann Map to Calculation of Band Gaps for Scalar Waves in Two-Dimensional Phononic Crystals
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DOI：
10.3813/aaa.918408
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发表时间：
2011-03
影响因子：
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通讯作者：
Fenglian Li;Yuesheng Wang
中科院分区：
文献类型：
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作者：
Fenglian Li;Yuesheng Wang
本文旨在应用Dirichlet-to-Neumann （DtN）映射计算二维声子晶体中标量波的带隙，该晶体由嵌入在正方形或三角形晶格中的圆柱体组成。对固体/固体和流体/流体系统进行了详细的计算，重点是与平面波展开法的比较。数值结果表明了DtN方法的一些优点。它的计算成本非常低，可以获得高精度的结果，特别是对于更高频率的计算或声学失配较大的系统。DtN方法的另一个特点是它可以在任意频率区间产生频带结构，而该频率区间不一定从零开始。
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.