An efficient MILU preconditioning for solving the 2D Poisson equation with Neumann boundary condition
- 주제(키워드) Poisson equation , Neumann boundary condition , MILU preconditioning , Purvis-Burkhalter method , Finite volume method
- 주제(기타) Computer Science, Interdisciplinary Applications; Physics, Mathematical
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 ACADEMIC PRESS INC ELSEVIER SCIENCE
- 발행년도 2018
- URI http://www.dcollection.net/handler/ewha/000000160193
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.jcp.2017.11.028
초록/요약
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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