AuthorsK. Mardal, T. K. Nilssen and G. A. Staff
TitleOrder Optimal Preconditioners for Implicit Runge-Kutta Schemes Applied to Parabolic PDE's
AfilliationScientific Computing, Center for Biomedical Computing (SFF), Scientific Computing
Project(s)Center for Biomedical Computing (SFF)
StatusPublished
Publication TypeJournal Article
Year of Publication2007
JournalSIAM Journal on Scientific Computing
Volume29
Number1
Pagination361-375
Abstract

In this paper we show that standard preconditioners for parabolic PDEs discretized by implicit Euler or Crank-Nicolson schemes can be reused for higher-order fully implicit Runge-Kutta time discretization schemes. We prove that the suggested block diagonal preconditioners are order-optimal for A-stable and irreducible Runge-Kutta schemes with invertible coefficient matrices. The theoretical investigations are confirmed by numerical experiments.

Notes

Accepted for publication at SIAM Journal of Scientific Computing

Citation KeyMardal.2006.5