An iterative boundary potential method for the infinite domain Poisson problem with interior Dirichlet boundaries

An iterative method is developed for the solution of Poisson’s problem on an infinite domain in the presence of interior boundaries held at fixed potential, in three dimensions. The method combines pre-existing fast multigrid-based Poisson solvers for data represented on Cartesian grids with the fas...

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Bibliographic Details
Published inJournal of computational physics Vol. 227; no. 16; pp. 7917 - 7928
Main Author Miller, G.H.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 10.08.2008
Elsevier
Subjects
Computational techniques
Embedded boundary method
Exact sciences and technology
Fast multipole method
Mathematical methods in physics
Multigrid
Physics
Poisson problem
Fast multipole method
Poisson problem
Embedded boundary method
Multigrid
Second order
Multipoles
Calculation
Iterative methods
Calculation methods
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Summary:An iterative method is developed for the solution of Poisson’s problem on an infinite domain in the presence of interior boundaries held at fixed potential, in three dimensions. The method combines pre-existing fast multigrid-based Poisson solvers for data represented on Cartesian grids with the fast multipole method. Interior boundaries are represented with the embedded boundary formalism. The implementation is in parallel and uses adaptive mesh refinement. Examples are presented for a smooth interior boundary for which an analytical result is known, and for an irregular interior boundary problem. Second-order accuracy in L 1 with respect to the grid resolution is demonstrated for both problems.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2008.05.005