TY - JOUR
T1 - A new block preconditioner for implicit Runge-Kutta methods for parabolic PDE problems
AU - Rana, Md Masud
AU - Howle, Victoria E.
AU - Long, Katharine
AU - Meek, Ashley
AU - Milestone, William
N1 - Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics.
PY - 2020
Y1 - 2020
N2 - A new preconditioner based on a block factorization into lower triangular, diagonal, and upper triangular factors (an LDU factoriaztion) 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 [Model. Identif. Control, 27 (2006), pp. 109-123]. Experiments are run on two test problems, a two-dimensional 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.
AB - A new preconditioner based on a block factorization into lower triangular, diagonal, and upper triangular factors (an LDU factoriaztion) 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 [Model. Identif. Control, 27 (2006), pp. 109-123]. Experiments are run on two test problems, a two-dimensional 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.
KW - Implicit Runge-Kutta
KW - Parabolic PDE
KW - Preconditioning
UR - http://www.scopus.com/inward/record.url?scp=85113335707&partnerID=8YFLogxK
U2 - 10.1137/20M1349680
DO - 10.1137/20M1349680
M3 - Article
AN - SCOPUS:85113335707
SN - 1064-8275
SP - S475-S495
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
ER -