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A Local Corrections Algorithm for Solving Poisson's Equation inThree Dimensions

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We present a second-order accurate algorithm for solving thefree-space Poisson's equation on a locally-refined nested grid hierarchyin three dimensions. Our approach is based on linear superposition oflocal convolutions of localized charge distributions, with the nonlocalcoupling represented on coarser grids. There presentation of the nonlocalcoupling on the local solutions is based on Anderson's Method of LocalCorrections and does not require iteration between different resolutions.A distributed-memory parallel implementation of this method is observedto have a computational cost per grid point less than three times that ofa standard FFT-based method on a uniform grid of the same resolution, andscales well up to 1024 ... continued below

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McCorquodale, Peter; Colella, Phillip; Balls, Gregory T. & Baden,Scott B. October 30, 2006.

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We present a second-order accurate algorithm for solving thefree-space Poisson's equation on a locally-refined nested grid hierarchyin three dimensions. Our approach is based on linear superposition oflocal convolutions of localized charge distributions, with the nonlocalcoupling represented on coarser grids. There presentation of the nonlocalcoupling on the local solutions is based on Anderson's Method of LocalCorrections and does not require iteration between different resolutions.A distributed-memory parallel implementation of this method is observedto have a computational cost per grid point less than three times that ofa standard FFT-based method on a uniform grid of the same resolution, andscales well up to 1024 processors.

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  • Journal Name: Communications in Applied Mathematics and ComputationalScience; Journal Volume: 2; Related Information: Journal Publication Date: 2007

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  • Report No.: LBNL--62377
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 929486
  • Archival Resource Key: ark:/67531/metadc898637

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • October 30, 2006

Added to The UNT Digital Library

  • Sept. 27, 2016, 1:39 a.m.

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  • Sept. 22, 2017, 3:03 p.m.

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McCorquodale, Peter; Colella, Phillip; Balls, Gregory T. & Baden,Scott B. A Local Corrections Algorithm for Solving Poisson's Equation inThree Dimensions, article, October 30, 2006; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc898637/: accessed January 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.