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An efficient MILU preconditioning for solving the 2D Poisson equation with Neumann boundary condition
- An efficient MILU preconditioning for solving the 2D Poisson equation with Neumann boundary condition
- Park, Yesom; Kim, Jeongho; Jung, Jinwook; Lee, Euntaek; Min, Chohong
- Ewha Authors
- SCOPUS Author ID
- Issue Date
- Journal Title
- JOURNAL OF COMPUTATIONAL PHYSICS
- JOURNAL OF COMPUTATIONAL PHYSICS vol. 356, pp. 115 - 126
- Poisson equation; Neumann boundary condition; MILU preconditioning; Purvis-Burkhalter method; Finite volume method
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- SCI; SCIE; SCOPUS
- Document Type
- MILU preconditioning is known to be the optimal one among all the ILU-type preconditionings in solving the Poisson equation with Dirichlet boundary condition. It is optimal in the sense that it reduces the condition number from O (h(-2)), which can be obtained from other ILU-type preconditioners, to O (h(-1)). However, with Neumann boundary condition, the conventional MILU cannot be used since it is not invertible, and some MILU preconditionings achieved the order O (h(-1)) only in rectangular domains. In this article, we consider a standard finite volume method for solving the Poisson equation with Neumann boundary condition in general smooth domains, and introduce a new and efficient MILU preconditioning for the method in two dimensional general smooth domains. Our new MILU preconditioning achieved the order O (h(-1)) in all our empirical tests. In addition, in a circular domain with a fine grid, the CG method preconditioned with the proposed MILU runs about two times faster than the CG with ILU. (c) 2017 Elsevier Inc. All rights reserved.
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