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An efficient MILU preconditioning for solving the 2D Poisson equation with Neumann boundary condition

Title
An efficient MILU preconditioning for solving the 2D Poisson equation with Neumann boundary condition
Authors
Park, YesomKim, JeonghoJung, JinwookLee, EuntaekMin, Chohong
Ewha Authors
민조홍
SCOPUS Author ID
민조홍scopus
Issue Date
2018
Journal Title
JOURNAL OF COMPUTATIONAL PHYSICS
ISSN
0021-9991JCR Link

1090-2716JCR Link
Citation
JOURNAL OF COMPUTATIONAL PHYSICS vol. 356, pp. 115 - 126
Keywords
Poisson equationNeumann boundary conditionMILU preconditioningPurvis-Burkhalter methodFinite volume method
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Indexed
SCI; SCIE; SCOPUS WOS
Document Type
Article
Abstract
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.
DOI
10.1016/j.jcp.2017.11.028
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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