Fast and robust method for screened Poisson lattice Green's function using asymptotic expansion and Fast Fourier Transform

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Bibliografiske detaljer
Udgivet i:	arXiv.org (Mar 5, 2024), p. n/a
Hovedforfatter:	Hou, Wei
Andre forfattere:	Colonius, Tim
Udgivet:	Cornell University Library, arXiv.org
Fag:	Algorithms Green's functions Asymptotic methods Convergence Robustness (mathematics) Solid state physics Screening Fast Fourier transformations Asymptotic series Numerical analysis Random walk Poisson equation
Online adgang:	Citation/Abstract Full text outside of ProQuest
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Beskrivelse
Resumen:	We study the lattice Green's function (LGF) of the screened Poisson equation on a two-dimensional rectangular lattice. This LGF arises in numerical analysis, random walks, solid-state physics, and other fields. Its defining characteristic is the screening term, which defines different regimes. When its coefficient is large, we can accurately approximate the LGF with an exponentially converging asymptotic expansion, and its convergence rate monotonically increases with the coefficient of the screening term. To tabulate the LGF when the coefficient is not large, we derive a one-dimensional integral representation of the LGF. We show that the trapezoidal rule can approximate this integral with exponential convergence, and we propose an efficient algorithm for its evaluation via the Fast Fourier Transform. We discuss applications including computing the LGF of the three-dimensional Poisson equation with one periodic direction and the return probability of a two-dimensional random walk with killing.
ISSN:	2331-8422
Fuente:	Engineering Database