This paper aims at reviewing and analysing the method of reflections, which is an iterative procedure designed for solving linear boundary value problems set in multiply connected domains. Being based on a decomposition of the domain boundary, this method is particularly well-suited to numerical solvers relying on boundary integral representation. For both the sequential and parallel forms of the method appearing in the literature, we interpret the procedure in terms of projection operators. Using a Hilbert space setting and orthogonality, we prove the unconditional convergence of the sequential form and propose a modification of the parallel one that makes it unconditionally converging. Several examples of boundary value problems that enter such a framework are given, an alternative proof of convergence is provided in a case which does not. A few numerical tests conclude the study.

本文旨在回顾和分析反射方法，它是一种迭代过程，旨在解决多连通域中设置的线性边值问题。由于基于域边界的分解，该方法特别适用于依赖边界积分表示的数值求解器。对于文献中出现的方法的顺序和并行形式，我们根据投影算子解释该过程。使用希尔伯特空间设置和正交性，我们证明了序列形式的无条件收敛，并提出了并行形式的修改，使其无条件收敛。给出了进入这种框架的边值问题的几个例子，在没有的情况下提供了收敛的替代证明。