基于多层次模型的波函数法在凹域问题应用研究

波函数法（Wave Based Method，WBM）是近年来发展的基于间接 Trefftz 理论的结构—声辐射中频问题的一种重要方法。 WBM 函数收敛的充要条件是分析域为凸域。为提高使用 WBM 理论的应用范围和应用效率，根据多层次模型，提出了补域概念用于解决凹域问题。最后，以一个周边简支矩形薄板为例进行验证数值，计算结果表明了方法准确性和有效性。     

Wave Number Method for Three-Dimensional Steady-State Acoustic Problems

Based on the indirect Trefftz approach, a wave number method (WNM) is proposed to deal with three-dimensional steady-state acoustic problems. In the WNM, the dynamic pressure response variable is approximated by a set of wave functions, which exactly satisfy the Helmholtz equation. The set of wave functions comprise the exact solutions of the homogeneous part of the governing equations and some particular solution functions. The unknown coefficients of the wave functions can be obtained by enforcing the pressure approximation to satisfy the boundary conditions. Compared with the boundary element method (BEM), the WNM have a smaller system matrix, and is applicable to the radiation problems since the wave functions are independent of the domain size. A 3D acoustic cavity is exemplified to show the properties of the method. The results show that the wave number method is more efficient than the BEM, and it is fairly accurate.