Efficient algebraic multigrid solvers with elementary restriction and prolongation
✍ Scribed by R. Webster
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 274 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0271-2091
No coin nor oath required. For personal study only.
✦ Synopsis
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.