Robust convergence of multilevel algorithms for convection-diffusion equations

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autorinnen und Autoren: Pflaum C
Zeitschrift: SIAM Journal on Numerical Analysis
Verlag: Society for Industrial and Applied Mathematics
Jahr der Veröffentlichung: 2000
Band: 37
Heftnummer: Issue 2
Seitenbereich: 443-469
ISSN: 0036-1429


Abstract


A new approach is developed to analyze convergence of multilevel algorithms for convection-diffusion equations. This approach uses a multilevel recursion formula, which can be applied to a variety of nonsymmetric problems. Here, the recursion formula is applied to a robust multilevel algorithm for convection-diffusion equations with convection in the x- or y-direction. The multilevel algorithm uses semicoarsening, line relaxation, and prewavelets. The convergence rate is proved to be less than 0.18 independent of the size of the convection term and the number of unknowns. The assumptions allow the convection term to have a turning point, so that an interior layer can appear in the solution of the convection-diffusion equation. The computational cost of the multilevel cycle is about O (N log N) independent of the size of the convection term, where N is the number of unknowns. It is proved that O (log N) multilevel cycles starting from the initial guess O lead to an O (N-2) algebraic error with respect to the L norm, independent of the size of the convection term.



FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Pflaum, Christoph Prof. Dr.
Professur für Informatik (Numerische Simulation mit Höchstleistungsrechnern)


Zitierweisen

APA:
Pflaum, C. (2000). Robust convergence of multilevel algorithms for convection-diffusion equations. SIAM Journal on Numerical Analysis, 37(Issue 2), 443-469. https://dx.doi.org/10.1137/S0036142998346870

MLA:
Pflaum, Christoph. "Robust convergence of multilevel algorithms for convection-diffusion equations." SIAM Journal on Numerical Analysis 37.Issue 2 (2000): 443-469.

BibTeX: 

Zuletzt aktualisiert 2018-28-11 um 06:03