Develops and analyzes single- and double-layer potential operators for doubly-periodic harmonic functions on finitely-connected tori, proves compactness and boundary limits, constructs the null space for multiply-connected cases, and demonstrates spectral convergence for Dirichlet, Neumann, and Stek
and Marple, Gary R
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DMK extended to rectangular cuboids with arbitrary periodicity via localized octree evaluations on cubical tilings and Fourier-space root-level summation with truncated kernels for reduced periodicity.
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Layer Potential Methods for Doubly-Periodic Harmonic Functions
Develops and analyzes single- and double-layer potential operators for doubly-periodic harmonic functions on finitely-connected tori, proves compactness and boundary limits, constructs the null space for multiply-connected cases, and demonstrates spectral convergence for Dirichlet, Neumann, and Stek
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Fast summation on rectangular cuboids with arbitrary periodicity in the DMK framework
DMK extended to rectangular cuboids with arbitrary periodicity via localized octree evaluations on cubical tilings and Fourier-space root-level summation with truncated kernels for reduced periodicity.