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A fast multi-resolution lattice Green's function method for elliptic difference equations

Guardado en:
Publicado en:arXiv.org (Nov 22, 2019), p. n/a
Autor principal: Dorschner, Benedikt
Otros Autores: Yu, Ke, Mengaldo, Gianmarco, Colonius, Tim
Publicado:
Cornell University Library, arXiv.org
Materias:
Grid refinement (mathematics)
Elliptic functions
Regularization
Green's functions
Difference equations
Mathematical analysis
Multipoles
Complexity
Fourier transforms
Domains
Fast Fourier transformations
Interpolation
Cartesian coordinates
Acceso en línea:Citation/Abstract
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Resumen:We propose a mesh refinement technique for solving elliptic difference equations on unbounded domains based on the fast lattice Green's function (FLGF) method. The FLGF method exploits the regularity of the Cartesian mesh and uses the fast multipole method in conjunction with fast Fourier transforms to yield linear complexity and decrease time-to-solution. We extend this method to a multi-resolution scheme and allow for locally refined Cartesian blocks embedded in the computational domain. Appropriately chosen interpolation and regularization operators retain consistency between the discrete Laplace operator and its inverse on the unbounded domain. Second-order accuracy and linear complexity are maintained, while significantly reducing the number of degrees of freedom and hence the computational cost.
ISSN:2331-8422
DOI:10.1016/j.jcp.2020.109270
Fuente:Engineering Database