Two grid iteration with a conjugate gradient fine grid smoother applied to a groundwater flow model [electronic resource].
- Published
- Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 1994.
- Physical Description
- pages 2, Paper 28 : digital, PDF file
- Additional Creators
- National Science Foundation (U.S.) and United States. Department of Energy. Office of Scientific and Technical Information
Access Online
- Restrictions on Access
- Free-to-read Unrestricted online access
- Summary
- This talk is concerned with the efficient solution of Ax=b, where A is a large, sparse, symmetric positive definite matrix arising from a standard finite element discretisation of the groundwater flow problem {triangledown}{sm_bullet}(k{triangledown}p)=0. Here k is the coefficient of rock permeability in applications and is highly discontinuous. The discretisation is carried out using the Harwell NAMMU finite element package, using, for 2D, 9 node biquadratic rectangular elements, and 27 node biquadratics for 3D. The aim is to develop a robust technique for iterative solutions of 3D problems based on a regional groundwater flow model of a geological area with sharply varying hydrogeological properties. Numerical experiments with polynomial preconditioned conjugate gradient methods on a 2D groundwater flow model were found to yield very poor results, converging very slowly. In order to utilise the fact that A comes from the discretisation of a PDE the authors try the two grid method as is well analysed from studies of multigrid methods, see for example {open_quotes}Multi-Grid Methods and Applications{close_quotes} by W. Hackbusch. Specifically they consider two discretisations resulting in stiffness matrices A{sub N} and A{sub n}, of size N and n respectively, where N > n, for both a model problem and the geological model. They perform a number of conjugate gradient steps on the fine grid, ie using A{sub N}, followed by an exact coarse grid solve, using A{sub n}, and then update the fine grid solution, the exact coarse grid solve being done using a frontal method factorisation of A{sub n}. Note that in the context of the standard two grid method this is equivalent to using conjugate gradients as a fine grid smoothing step. Experimental results are presented to show the superiority of the two grid iteration method over the polynomial preconditioned conjugate gradient method.
- Report Numbers
- E 1.99:conf-9404305--vol.2
conf-9404305--vol.2 - Subject(s)
- Other Subject(s)
- Note
- Published through SciTech Connect.
12/31/1994.
"conf-9404305--vol.2"
"DE96005736"
Colorado conference on iterative methods, Breckenridge, CO (United States), 5-9 Apr 1994.
Cliffe, K.A.; Spence, A.; Hagger, M.J.
Front Range Scientific Computations, Inc., Boulder, CO (United States)
USDOE, Washington, DC (United States)
View MARC record | catkey: 14142203