The method of fundamental solutions has been mainly applied to wave scattering problems in bounded domains and to our knowledge there have not been works addressing density results for general shapes, or addressing the calculation of the complex resonance frequencies that occur in exterior problems. We prove density and convergence of the fundamental solutions approximation in the context of wave scattering problems, with and without a priori knowledge of the frequency, which is of particular importance to detect resonance frequencies for trapping domains. We also present several numerical results that illustrate the good performance of the method in the calculation of complex resonance frequencies for trapping and non trapping domains in 2D and 3D.

基本解的方法主要应用于有界域中的波散射问题，据我们所知，还没有解决一般形状的密度结果或解决外部问题中出现的复杂共振频率的计算的工作。我们证明了波散射问题中基本解近似的密度和收敛性，无论是否有频率的先验知识，这对于检测捕获域的共振频率特别重要。我们还提供了几个数值结果，说明该方法在计算 2D 和 3D 捕获域和非捕获域的复共振频率方面具有良好的性能。