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2007 A local corrections algorithm for solving Poisson's equation in three dimensions
Peter McCorquodale, Phillip Colella, Gregory Balls, Scott Baden
Commun. Appl. Math. Comput. Sci. 2(1): 57-81 (2007). DOI: 10.2140/camcos.2007.2.57


We present a second-order accurate algorithm for solving the free-space Poisson’s equation on a locally-refined nested grid hierarchy in three dimensions. Our approach is based on linear superposition of local convolutions of localized charge distributions, with the nonlocal coupling represented on coarser grids. The representation of the nonlocal coupling on the local solutions is based on Anderson’s Method of Local Corrections and does not require iteration between different resolutions. A distributed-memory parallel implementation of this method is observed to have a computational cost per grid point less than three times that of a standard FFT-based method on a uniform grid of the same resolution, and scales well up to 1024 processors.


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Peter McCorquodale. Phillip Colella. Gregory Balls. Scott Baden. "A local corrections algorithm for solving Poisson's equation in three dimensions." Commun. Appl. Math. Comput. Sci. 2 (1) 57 - 81, 2007.


Received: 30 October 2006; Accepted: 31 March 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1133.65106
MathSciNet: MR2327083
Digital Object Identifier: 10.2140/camcos.2007.2.57

Rights: Copyright © 2007 Mathematical Sciences Publishers


Vol.2 • No. 1 • 2007
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