A new preconditioner based on a block LDU factorization with algebraic multigrid subsolves for scalability is introduced for the large, structured systems appearing in implicit Runge-Kutta time integration of parabolic partial differential equations. This preconditioner is compared in condition number and eigenvalue distribution, and in numerical experiments with others in the literature: block Jacobi, block Gauss-Seidel, and the optimized block Gauss-Seidel method of 10.4173/mic.2006.2.3.[{\em  ] Experiments are run with implicit Runge-Kutta stages up to s=7, and it is found that the new preconditioner outperforms the others, with the improvement becoming more pronounced as spatial discretization is refined and as temporal order is increased.
A new preconditioner based on a block LDU factorization with algebraic multigrid subsolves for scalability is introduced for the large, structured systems appearing in implicit Runge-Kutta time integration of parabolic partial differential equations. This preconditioner is compared in condition number and eigenvalue distribution, and in numerical experiments with others in the literature: block Jacobi, block Gauss-Seidel, and the optimized block Gauss-Seidel method of Staff, Mardal, and Nilssen[{\em Modeling, Identification and Control , 27 (2006), pp. 109-123]. Experiments are run on two test problems, a 2D heat equation and a model advection-diffusion problem, using implicit Runge-Kutta methods with two to seven stages. We find that the new preconditioner outperforms the others, with the improvement becoming more pronounced as spatial discretization is refined and as temporal order is increased.
R
10.4173/mic.2006.2.3.
Staff, Mardal, and Nilssen
A
Modeling, Identification and Control
A
, 27 (2006), pp. 109-123
A
.
R
with
on two test problems, a 2D heat equation and a model advection-diffusion problem, using
R
stages up to s=7, and it is found
methods with two to seven stages. We find