Scattering resonances have important applications in many areas of science and engineering. They are the replacement of discrete spectral data for problems on non-compact domains. In this paper, we consider the computation of scattering resonances defined on the exterior to a compact sound hard obstacle. The resonances are the eigenvalues of a holomorphic Fredholm operator function. We truncate the unbounded domain and impose the Dirichlet-to-Neumann (DtN) mapping. The problem is then discretized using the linear Lagrange element. Convergence of the resonances is proved using the abstract approximation theory for holomorphic Fredholm operator functions. The discretization leads to nonlinear algebraic eigenvalue problems, which are solved by the recently developed parallel spectral indicator methods. Numerical examples are presented for validation.

翻译：散射共振在科学与工程众多领域具有重要应用，它们是非紧致域问题中离散谱数据的替代方案。本文考虑紧致声硬障碍体外域定义的散射共振计算问题，此类共振是解析弗雷德霍姆算子函数的特征值。通过截断无界域并引入狄利克雷-诺伊曼（DtN）映射，采用线性拉格朗日单元对问题进行离散化。借助解析弗雷德霍姆算子函数的抽象逼近理论，证明了共振的收敛性。离散化过程生成非线性代数特征值问题，通过近期发展的并行谱指示方法求解。最后给出数值算例进行验证。