AI & ML
Scattering Resonances of Plane-Embedded Cavities: A Finite Element DtN Approach
arXiv cs.NA0 views
arXiv:2611.14258v1 Announce Type: new Abstract: While scattering resonances of plane-embedded cavities have wide-ranging engineering applications, numerical results for such configurations remain virtually unexplored. We present an effective finite element approach for computing these resonances. The unbounded domain is truncated using a Dirichlet-to-Neumann(DtN) boundary operator, recasting the problem as the eigenvalue problem of a holomorphic Fredholm operator function. Discretization is carried out using Lagrange finite elements with a truncated DtN expansion, and convergence is rigorously proven using Karma's approximation theory. The resulting non-linear matrix eigenvalue system is computed using a multi-step parallel spectral indicator method. Numerical experiments confirm the theoretical predictions and provide benchmark solutions for future investigations.
Source：https://arxiv.org/abs/2611.14258PreviousA posteriori error estimates for higher-order BDF methods for parabolic partial differential equationsNextAsymptotic Robustness of HDG Schemes for the Convection-Diffusion Equation
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