A FAST POISSON SOLVER FOR COMPLEX GEOMETRIES

Citation
A. Mckenney et al., A FAST POISSON SOLVER FOR COMPLEX GEOMETRIES, Journal of computational physics, 118(2), 1995, pp. 348-355
Citations number
11
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematical Method, Physical Science","Computer Science Interdisciplinary Applications","Physycs, Mathematical
ISSN journal
0021-9991
Volume
118
Issue
2
Year of publication
1995
Pages
348 - 355
Database
ISI
SICI code
0021-9991(1995)118:2<348:AFPSFC>2.0.ZU;2-C
Abstract
Robust fast solvers for the Poisson equation have generally been limit ed to regular geometries, where direct methods, based on Fourier analy sis or cyclic reduction, and multigrid methods can be used. While mult igrid methods can be applied in irregular domains (and to a broader cl ass of partial differential equations), they are difficult to implemen t in a robust fashion, since they require an appropriate hierarchy of coarse grids, which are not provided in many practical situations, In this paper, we present a new fast Poisson solver based on potential th eory rather than on direct discretization of the partial differential equation. Our method combines fast algorithms for computing volume int egrals and evaluating layer potentials on a grid with a fast multipole accelerated integral equation solver. The amount of work required is O(m log m + N), where m is the number of interior grid points and N is the number of points on the boundary. Asymptotically,the cost of our method is just twice that of a standard Poisson solver on a rectangula r domain in which the problem domain can be embedded, independent of t he complexity of the geometry. (c) 1995 Academic Press, Inc.