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。

Application of wave based method analysis in concave domain problem based on multi-level modelling

The Wave Based Method (WBM) is an alternative deterministic modeling technique for time har-monic dynamic problems in the mid-frequency range, which is based on an indirect Trefftz approach. How-ever, a sufficient condition for convergence of the method is the convexity of the considered problem do-main. As a result, only problems of moderate geometrical complexity can be considered. To alleviate the geometrical limitations and extend the application range of WBM, the multi-level modelling theory is dis-cussed, and the complement graph concept which is for the efficient treatment concave domain problem is put forward. Finally, the feasibility and efficiency of the method are illustrated by means of numerical veri-fication studies in which the methodology is applied to a concave plate domain dynamic problem, it extends the ability to handle with the concave domain problem.