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

Dorschner, Benedikt and Yu, Ke and Mengaldo, Gianmarco and Colonius, Tim (2020) A fast multi-resolution lattice Green's function method for elliptic difference equations. Journal of Computational Physics, 407 . Art. No. 109270. ISSN 0021-9991.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Mengaldo, Gianmarco0000-0002-0157-5477
Colonius, Tim0000-0003-0326-3909
Additional Information:© 2020 Elsevier Inc. Received 29 May 2019, Revised 15 November 2019, Accepted 13 January 2020, Available online 14 January 2020. This work was supported by the Swiss National Science Foundation Grant No. P2EZP2_178436 (B.D.) and the ONR Grant No. N00014-16-1-2734. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)P2EZP2_178436
Office of Naval Research (ONR)N00014-16-1-2734
Subject Keywords:Elliptic difference equation; Poisson problem; Lattice Green's function; Fast multipole method; Mesh refinement
Record Number:CaltechAUTHORS:20191223-155123107
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Official Citation:Benedikt Dorschner, Ke Yu, Gianmarco Mengaldo, Tim Colonius, A fast multi-resolution lattice Green's function method for elliptic difference equations, Journal of Computational Physics, Volume 407, 2020, 109270, ISSN 0021-9991, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100425
Deposited By: Tony Diaz
Deposited On:23 Dec 2019 23:58
Last Modified:28 Jan 2020 18:10

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