论文标题
径向复杂缩放方法的分析：标量共振问题
Analysis of radial complex scaling methods: scalar resonance problems
论文作者
论文摘要
我们考虑径向复合体缩放/完美匹配的层方法，用于同质外部域中的标量共振问题。我们引入了一个新的抽象框架，以分析域截断和离散化的收敛性。我们的理论需要对缩放轮廓的假设相当小，并且包括affin，平滑且无限的概况。我们报告了一项快速的技术，可以通过同时截断和离散化来分析域截断的收敛性和更具技术性的技术。我们适应后一种技术，以涵盖不需要域截断的所谓精确方法。我们既定的结果包括特征值和本征函数的收敛速率。 The introduced framework is based on the ideas to interpret the domain truncation as Galerkin approximation, to apply theory on holomorphic Fredholm operator eigenvalue approximation theory to a linear eigenvalue problem, to employ the notion of weak T-coercivity and T-compatible approximations, to construct a suitable T-operator as multiplicatin operator, to smooth its symbol and to apply the discrete commutator技术。
We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations. Our theory requires rather minimal assumptions on the scaling profile and includes affin, smooth and also unbounded profiles. We report a swift technique to analyze the convergence of domain truncations and a more technical one for approximations through simultaneaous truncation and discretization. We adapt the latter technique to cover also so-called exact methods which do not require a domain truncation. Our established results include convergence rates of eigenvalues and eigenfunctions. The introduced framework is based on the ideas to interpret the domain truncation as Galerkin approximation, to apply theory on holomorphic Fredholm operator eigenvalue approximation theory to a linear eigenvalue problem, to employ the notion of weak T-coercivity and T-compatible approximations, to construct a suitable T-operator as multiplicatin operator, to smooth its symbol and to apply the discrete commutator technique.
