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Sponsored AI Networking Cookbook: Practical recipes for AI-assisted network automation and development AI Networking Cookbook: Practical recipes for AI-assisted network automation and development

Author

Shelvean Kapita

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Preprint Sep 2026

Efficient $C^1$ Bernstein Quasi-Trefftz Discretization for Heterogeneous High-Frequency Helmholtz Problems

We develop an efficient $C^1$ Bernstein quasi-Trefftz discretization for heterogeneous high-frequency Helmholtz problems on unstructured triangular meshes. The method first imposes strong $C^1$ continuity through Bernstein--B\'ezier smoothness relations on local macro-patches and then reduces the resulting conforming p...

Shelvean Kapita · 0 citations
Preprint Sep 2026

Adaptive local representations for Helmholtz Trefftz discontinuous Galerkin methods

We study the selection and stable realization of local approximation spaces in Trefftz discontinuous Galerkin discretizations of the Helmholtz equation. A scaled Cauchy-trace inner product places plane waves and Fourier-Bessel functions in a common geometry: Fourier-Bessel modes are orthogonal with explicit weights, wh...

Shelvean Kapita · 0 citations
Preprint Aug 2026

Direction-Adaptive Plane-Wave Discontinuous Galerkin Methods for the Helmholtz Equation

We consider plane-wave discontinuous Galerkin (PWDG) approximations of the Helmholtz equation with adaptive local propagation directions. The directions are chosen by minimizing a weighted residual on the mesh skeleton. We study two formulations: in Part A the PWDG system is solved for the coefficients at fixed directi...

Shelvean Kapita · 1 citation

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