A New Block Preconditioner for Implicit Runge-Kutta Methods for Parabolic PDE Problems
| Autor: | William Milestone, Katharine Long, Md. Masud Rana, Ashley Meek, Victoria E. Howle |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Preconditioner
Applied Mathematics Diagonal 65F08 Triangular matrix Numerical Analysis (math.NA) Parabolic partial differential equation Computer Science::Numerical Analysis Mathematics::Numerical Analysis Computational Mathematics Runge–Kutta methods Multigrid method Factorization FOS: Mathematics Computer Science::Mathematical Software Applied mathematics Mathematics - Numerical Analysis Mathematics Block (data storage) |
| Popis: | 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. 20 pages |
| Databáze: | OpenAIRE |
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