AuthorsK. Mardal, T. K. Nilssen and G. A. Staff
TitleOrder Optimal Preconditioners for Implicit Runge-Kutta Schemes Applied to Parabolic PDE's
AfilliationScientific Computing, , 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