Mathematics – Numerical Analysis
Scientific paper
2009-07-15
Mathematics
Numerical Analysis
29 pages, 10 figures. This version contains the linear algebra results of v1, with corrections and extensions. The application
Scientific paper
The novel contribution of this paper relies in the proposal of a fully implicit numerical method designed for nonlinear degenerate parabolic equations, in its convergence/stability analysis, and in the study of the related computational cost. In fact, due to the nonlinear nature of the underlying mathematical model, the use of a fixed point scheme is required and every step implies the solution of large, locally structured, linear systems. A special effort is devoted to the spectral analysis of the relevant matrices and to the design of appropriate iterative or multi-iterative solvers, with special attention to preconditioned Krylov methods and to multigrid procedures: in particular we investigate the mutual benefit of combining in various ways suitable preconditioners with V-cycle algorithms. Numerical experiments in one and two spatial dimensions for the validation of our multi-facet analysis complement this contribution.
Donatelli Marco
Semplice Matteo
Serra-Capizzano Stefano
No associations
LandOfFree
Multigrid and preconditioning strategies for implicit PDE solvers for degenerate parabolic equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Multigrid and preconditioning strategies for implicit PDE solvers for degenerate parabolic equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multigrid and preconditioning strategies for implicit PDE solvers for degenerate parabolic equations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-364677