A Localized Collocation Solver Based on T-Complete Functions for Anti-Plane Transverse Elastic Wave Propagation Analysis in 2D Phononic Crystals

• Main Authors: Zhuo-Jia Fu, Lu-Feng Li, De-Shun Yin, Li-Li Yuan
• Format: Article
• Language: English
• Published: MDPI AG 2021-12-01
• Series: Mathematical and Computational Applications
• Subjects: collocation; T-complete function; phononic crystals; band structures; transmission spectra
• Online Access: https://www.mdpi.com/2297-8747/26/1/2

In this paper, we introduce a novel localized collocation solver for two-dimensional (2D) phononic crystal analysis. In the proposed collocation solver, the displacement at each node is expressed as a linear combination of T-complete functions in each stencil support and the sparse linear system is obtained by satisfying the considered governing equation at interior nodes and boundary conditions at boundary nodes. As compared with finite element method (FEM) results and the analytical solutions, the efficiency and accuracy of the proposed localized collocation solver are verified under a benchmark example. Then, the proposed method is applied to 2D phononic crystals with various lattice forms and scatterer shapes, where the related band structures, transmission spectra, and displacement amplitude distributions are calculated as compared with the FEM.