Analysis of Radial Complex Scaling Methods: Scalar Resonance Problems

نویسندگان

چکیده

We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. introduce a new abstract framework to analyze the convergence of domain truncations and discretizations. Our theory requires rather minimal assumptions on scaling profile includes affine, smooth, unbounded profiles. report swift technique more technical one approximations through simultaneous truncation discretization. established results include rates eigenvalues eigenfunctions. The introduced is based following ideas: interpret as Galerkin approximation, apply holomorphic Fredholm operator eigenvalue approximation linear problem, employ notion weak T-coercivity T-compatible approximations, construct suitable T-operator multiplication operator, smooth its symbol, discrete commutator technique.

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ژورنال

عنوان ژورنال: SIAM Journal on Numerical Analysis

سال: 2021

ISSN: ['0036-1429', '1095-7170']

DOI: https://doi.org/10.1137/20m1354234