G. Juncu, Preconditioning by approximations of the discrete Laplacian for 2-D non-linear free convection elliptic equations, INT J N M H, 9(5-6), 1999, pp. 586-600
Citations number
34
Categorie Soggetti
Mechanical Engineering
Journal title
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
The paper analyses the preconditioning of non-linear nonsymmetric equations
with approximations of the discrete Laplace operator. The test problems ar
e non-linear 2-D elliptic equations that describe natural convection, Darcy
flow, in a porous medium. The standard second order accurate finite differ
ence scheme is used to discretize the models' equations. The discrete appro
ximations are solved with a double iterative process using. the Newton meth
od as outer iteration and the preconditioned generalised conjugate gradient
(PGCG) methods as inner iteration. Three PGCG algorithms, CGN, CGS and GMR
ES, are tested The preconditioning with discrete Laplace operator approxima
tions consists of replacing the solving of the equation with the preconditi
oner by a fete iterations of an appropriate iterative scheme. Two iterative
algorithms ave tested: incomplete Cholesky (IC) and multigrid (MG). The nu
merical results show that MG preconditioning leads to mesh independence. CG
S is the most robust algorithm but its efficiency is lower than that of GMR
ES.