A new Method of Internal Auxiliary Source–Sinks (MIASS) is developed for the numerical solution of the two-dimensional interior Dirichlet acoustic problem for the Helmholtz equation. We give two versions of MIASS, one for a closed auxiliary curve (MIASS-C) and another for an open auxiliary curve (MIASS-O). The mathematical and numerical foundations of both versions are provided. In particular, we show that the integral operator that pertains to the associated integral equation has a dense range. We then demonstrate completeness and linear independence of the discrete system of source-sinks. Indicative numerical results are given and numerical implementation aspects are discussed.

针对Helmholtz方程的二维内部Dirichlet声学问题的数值解，开发了一种新的内部辅助源－汇方法（MIASS）。我们提供两种版本的MIASS，一种用于封闭的辅助曲线（MIASS-C），另一种用于开放的辅助曲线（MIASS-O）。提供了两个版本的数学和数值基础。特别是，我们表明属于相关积分方程的积分算子具有密集的范围。然后，我们演示了源-接收器离散系统的完整性和线性独立性。给出了指示性数值结果并讨论了数值实现方面。