基于SiPESC平台的声子晶体能带结构分析算法研究及软件实现

RESEARCH AND SOFTWARE IMPLEMENTATION OF ENERGY BAND STRUCTURE ANALYSIS ALGORITHM OF PHONONIC CRYSTALS BASED ON SiPESC PLATFORM

为了快速准确得分析声子晶体的能带结构,该文基于工程与科学计算仿真平台SiPESC,开发了一类高效三维声子晶体能带结构分析软件。软件针对能带结构分析过程中计算量庞大的Hermitian矩阵的广义特征值求解问题和边界约束节点匹配问题,提出了相关软件设计方案。针对Hermitian矩阵的广义特征值求解,在实对称矩阵子空间迭代法的基础上,发展了Hermitian矩阵子空间迭代法。针对边界约束节点匹配问题,该文将三维周期性条件划分为点、边、面约束分别处理。针对面约束,该文使用定位格匹配策略将单层的点-点匹配更改为2层的点-定位格-点加速匹配。开展了与多物理场分析软件COMSOL进行数值算例对比。使用三维局域共振声子晶体算例验证了软件在满足数值精度的前提下计算效率高于对比软件。通过大规模模型算例验证了软件具有高效的大规模计算能力。

In order to quickly and accurately analyze the energy-band structure of phononic crystal,an efficient software for analyzing the band structure of three-dimensional phononic crystal is developed based on the engineering and scientific simulation platform SiPESC.The software design is proposed the optimization design for the generalized eigenvalue of Hermitian matrix and the boundary constraint node matching the problem occurred in the band-structure analysis process.Based on the subspace iterative method for real symmetric matrix,a subspace iterative method for Hermitian matrix is developed for solving generalized eigenvalues of Hermitian matrix.Aiming at the problem of node matching with boundary constraints,the three-dimensional periodic conditions are divided into point,edge and,face constraints,and the face constraints are processed separately.The location lattice matching strategy is used to change the single-layer point-point matching into two-layer pointlocation lattice-point matching to accelerate the face matching.The software is compared with COMSOL.The numerical results show that the efficiency of the software is higher than the contrast software.The large-scale computing ability of the software is verified by a large-scale model.