Vol. 2, No. 1, 2007

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
A local corrections algorithm for solving Poisson's equation in three dimensions

Peter McCorquodale, Phillip Colella, Gregory T. Balls and Scott B. Baden

Vol. 2 (2007), No. 1, 57–81
Abstract

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.

Keywords
Poisson's equation, local corrections, domain decomposition, adaptive mesh refinement
Milestones
Received: 30 October 2006
Accepted: 31 March 2007
Published: 2 August 2007
Authors
Peter McCorquodale
Lawrence Berkeley National Laboratory
1 Cyclotron Road, MS 50A-1148
Berkeley, CA 94720
United States
Phillip Colella
Lawrence Berkeley National Laboratory
1 Cyclotron Road, MS 50A-1148
Berkeley, CA 94720
United States
Gregory T. Balls
Center for Scientific Computation in Imaging
University of California, San Diego
9500 Gilman Drive # 0854
La Jolla, CA 92093-0854
United States
Scott B. Baden
Department of Computer Science and Engineering
University of California, San Diego
9500 Gilman Drive
La Jolla, CA 92093-0114
United States