宽频声振耦合问题的大规模快速计算分析方法

Typical vibro-acoustic problems in many high-tech industries, including aerospace and submarine engineering, often occur in a broad frequency range. Effective and efficient modeling and analysis of such wideband vibro-acoustics are essential to the production of world-leading products with good noise and vibration performance, but are still a challenging task nowadays in both science and engineering communities. This is because, on one hand, the computational resource requirement of the large-scale wideband simulation is prohibitively huge, and on the other hand, the convergence rate of the iterative solver is always very low. In this project, a highly efficient numerical method for solving large-scale wideband vibro-acoustic problems will be established by the coupling of a newly developed kernel-independent fast directional boundary element method (BEM) for wideband acoustics and the well-established finite element method (FEM) for structure. In order to improve the convergence rate and to reduce the number of iterations, methods for transforming the BEM-FEM coupling matrix into sparse ones will be studied and developed.The state-of-the-art sparse preconditioning techniques and solvers will be investegated and employed for fast solution of the coupling equation. A simple yet efficient adaptive fast frequency sweeping method will also be develop for vibro-acoustic problems, and the method will be further used to calculated the time-domain vibro-acoustic responses based on the inverse numerical Laplace transform. The research achievements of this project will serve as powerful analysis and modelling tools for the vibro-acoustic environment prediction in many high-tech engineering.

大型复杂结构的宽频声振耦合计算分析，是大规模科学与工程计算中的一项挑战性研究，备受国际航空航天、船舶等工业领域的关注。本项目将发展大规模宽频声振耦合问题的高效数值仿真分析方法。结合国际上快速边界元法的最新进展，研究宽频声振耦合问题的快速边界元-有限元耦合求解策略；基于小波矩阵压缩和边界元快速直接解法最新成果，研究快速边界元-有限元耦合数值方法中的高效矩阵稀疏化新方法，研究大型稀疏耦合矩阵的高效预处理技术，解决目前大型复杂结构宽频声振耦合数值方法所存在的计算量和存储量巨大、求解效率低的问题。发展声振耦合频率响应函数和时域响应的快速自适应计算方法，以满足大型复杂结构声振耦合动力学特性分析的需要。本项目将为航空航天、船舶等工业领域大型复杂结构的声振耦合环境仿真预报，提供强有力的大规模计算分析工具。

大型工程结构的宽频声振耦合计算分析，是航空航天、船舶等工业领域的备受关注的问题。尤其是关于中高频问题高效计算分析方法，国际学术界和工程界进行了几十年的探索研究，却没有完全得到解决。本项目以发展快速宽频BEM-FEM声振耦合计算分析方法为目标，立足于国际工程数值计算领域的最新进展，从BEM-FEM耦合方法、大规模耦合方程数值解法、稠密矩阵压缩和预处理、结构动力学频响函数快速计算、非线性特征值解法等方面开展理论分析、算法设计和计算仿真研究。研究建立了一套高效、高精度的快速宽频BEM-FEM声振耦合计算分析方法，声场BEM和结构FEM采用二次单元离散，实现界面非协调单元上的数据交换；发展了基于Schur补的BEM-FEM耦合方程迭代解法和预处理方法，提高了耦合求解速度。改进了矩阵稀疏化（FHS）求逆方法，显著提高了FHS的稳定性和计算效率，并将其应用于宽频声学BEM矩阵预处理。针对以声学BEM、声振耦合BEM-FEM方法为代表的、系数矩阵为频率复杂非线性函数的动力学系统，提出了基于有理函数向量拟合（VF）和基于响应空间采样（RES）的两种快速扫频方法，发展了一套高效的大规模非线性特征值问题数值解法（RSRR）。典型算例和工程应用显示，本项目成果在工程复杂声场、声振耦合结构以及复杂阻尼减振结构的响应计算、扫频和模态分析等领域具有优越性。.本项目研究成果，已发表学术论文13篇，其中SCI论文8篇，包括计算力学领域国际著名期刊Computer Methods in Applied Mechanics and Engineering 2篇，International Journal for Numerical Methods in Engineering 1篇，Computational Mechanics 2篇；申报软件著作权3项；直接支持硕士论文6篇。本项目已完成项目任务书的预定研究内容，达到预期成果要求。