A node-centered local refinement algorithm for poisson's equation in complex geometries

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This paper presents a method for solving Poisson's equation with Dirichlet boundary conditions on an irregular bounded three-dimensional region. The method uses a nodal-point discretization and adaptive mesh refinement (AMR) on Cartesian grids, and the AMR multigrid solver of Almgren. The discrete Laplacian operator at internal boundaries comes from either linear or quadratic (Shortley-Weller) extrapolation, and the two methods are compared. It is shown that either way, solution error is second order in the mesh spacing. Error in the gradient of the solution is first order with linear extrapolation, but second order with Shortley-Weller. Examples are given with comparison with ... continued below

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37 pages

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McCorquodale, Peter; Colella, Phillip; Grote, David P. & Vay, Jean-Luc May 4, 2004.

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Description

This paper presents a method for solving Poisson's equation with Dirichlet boundary conditions on an irregular bounded three-dimensional region. The method uses a nodal-point discretization and adaptive mesh refinement (AMR) on Cartesian grids, and the AMR multigrid solver of Almgren. The discrete Laplacian operator at internal boundaries comes from either linear or quadratic (Shortley-Weller) extrapolation, and the two methods are compared. It is shown that either way, solution error is second order in the mesh spacing. Error in the gradient of the solution is first order with linear extrapolation, but second order with Shortley-Weller. Examples are given with comparison with the exact solution. The method is also applied to a heavy-ion fusion accelerator problem, showing the advantage of adaptivity.

Physical Description

37 pages

Notes

INIS; OSTI as DE00837738

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  • Journal Name: Journal of Computational Physics; Journal Volume: 201; Journal Issue: 1; Other Information: Submitted to Journal of Computational Physics: Volume 201, No.1; Journal Publication Date: 11/20/2004

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  • Report No.: LBNL--54138
  • Report No.: HIFAN 1313
  • Grant Number: AC03-76SF00098
  • DOI: 10.1016/j.jcp.2004.04.022 | External Link
  • Office of Scientific & Technical Information Report Number: 837738
  • Archival Resource Key: ark:/67531/metadc780851

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

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  • May 4, 2004

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  • Dec. 3, 2015, 9:30 a.m.

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  • April 4, 2016, 1:45 p.m.

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McCorquodale, Peter; Colella, Phillip; Grote, David P. & Vay, Jean-Luc. A node-centered local refinement algorithm for poisson's equation in complex geometries, article, May 4, 2004; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc780851/: accessed July 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.