This paper is concerned with the numerical computation of scattering resonances of the Laplacian for Dirichlet obstacles with rough boundary. We prove that under mild geometric assumptions on the obstacle there exists an algorithm whose output is guaranteed to converge to the set of resonances of the problem. The result is formulated using the framework of Solvability Complexity Indices. The proof is constructive and provides an efficient numerical method. The algorithm is based on a combination of a Glazman decomposition, a polygonal approximation of the obstacle and a finite element method. Our result applies in particular to obstacles with fractal boundary, such as the Koch Snowflake and certain filled Julia sets. Finally, we provide numerical experiments in MATLAB for a range of interesting obstacle domains.

翻译：本文关注具有粗糙边界的Dirichlet障碍物拉普拉斯算子散射共振的数值计算问题。我们证明，在障碍物满足温和几何假设的条件下，存在一种算法，其输出保证收敛到问题的共振集合。该结果利用可解性复杂度指数框架进行表述。证明过程具有构造性，并提供了一种高效的数值方法。该算法结合了Glazman分解、障碍物多边形逼近和有限元方法。我们的结果尤其适用于具有分形边界的障碍物，例如科赫雪花和某些填充朱莉娅集。最后，我们针对一系列有趣的障碍物域提供了MATLAB数值实验。