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Efficient algebraic multigrid solvers with elementary restriction and prolongation
Author(s) -
Webster R.
Publication year - 1998
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/(sici)1097-0363(19980815)28:2<317::aid-fld720>3.0.co;2-k
Subject(s) - multigrid method , krylov subspace , mathematics , residual , algebraic equation , prolongation , linear system , algorithm , mathematical optimization , mathematical analysis , partial differential equation , physics , nonlinear system , quantum mechanics , acoustics
An algebraic multigrid (AMG) scheme is presented for the efficient solution of large systems of coupled algebraic equations involving second‐order discrete differentials. It is based on elementary (zero‐order) intergrid transfer operators but exhibits convergence rates that are independent of the system bandwidth. Inconsistencies in the coarse‐grid approximation are minimised using a global scaling approximation which requires no explicit geometrical information. Residual components of the error spectrum that remain poorly represented in the coarse‐grid approximations are reduced by exploiting Krylof subspace methods. The scheme represents a robust, simple and cost‐effective approach to the problem of slowly converging eigenmodes when low‐order prolongation and restriction operators are used in multigrid algorithms. The algorithm investigated here uses a generalised conjugate residual (GCR) accelerator; it might also be described as an AMG preconditioned GCR method. It is applied to two test problems, one based on a solution of a discrete Poisson‐type equation for nodal pressures in a pipe network, the other based on coupled solutions to the discrete Navier–Stokes equations for flows and pressures in a driven cavity. © 1998 John Wiley & Sons, Ltd.