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Preconditioners for inhomogeneous anisotropic problems in spherical geometry
Author(s) -
Brown D. E.,
Nichols N. K.,
Bell M. J.
Publication year - 2005
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.889
Subject(s) - conjugate gradient method , multigrid method , mathematics , discretization , geometry , preconditioner , mathematical analysis , convergence (economics) , relaxation (psychology) , diagonal , linear system , algorithm , partial differential equation , psychology , social psychology , economics , economic growth
Elliptic equations arising in free‐surface ocean models are typically solved using iterative methods. Anisotropy associated with standard spherical co‐ordinate systems causes the convergence of the iterative methods to be slow, particularly in polar regions. This behaviour is demonstrated here using a diagonally preconditioned conjugate gradient method (PCG) method to solve a Helmholtz elliptic model problem with a standard five‐point discretization scheme on a 2D spherical domain. The cause of the poor polar convergence is shown to be the increased importance, with increased mesh anisotropy, of eigenmodes with strong polar signals. Block diagonal and alternating direction implicit (ADI) preconditioners are found to give improved convergence. Crown copyright 2005. Reproduced with the permission of Her Majesty's Stationery Office. Published by John Wiley & Sons, Ltd.