Efficient ILU preconditioning and inexact-Newton-GMRES to solve the 2D steady shallow water equations
Mourad Héniche, Yves Secretan, Michel Leclerc · Communications in Numerical Methods in Engineering · 2001
This paper presents a practical use of incomplete lower–upper factorization (ILU) preconditioning inexact-Newton-GMRES(m) for solving the steady shallow water equations. An efficient algorithm to store in a compact row format the ILU preconditioning matrix is proposed. Numerical experiments shows a linear variation of both CPU time and storage versus the matrix dimension until more than a million. Two examples are performed where the first one shows that an increment of solution norm based convergence is inaccurate. The second one reveal the importance of mesh numbering and unknowns ordering on convergence rate. An empirical criterion for choosing a good mesh numbering is also proposed. It is found that the Sloan numbering method enhances efficiency of the solver. Copyright © 2001 John Wiley & Sons, Ltd.