TY - JOUR
T1 - An efficient MILU preconditioning for solving the 2D Poisson equation with Neumann boundary condition
AU - Park, Yesom
AU - Kim, Jeongho
AU - Jung, Jinwook
AU - Lee, Euntaek
AU - Min, Chohong
N1 - Funding Information:
The research of C. Min and Y. Park was supported by Basic Science Research Program through the National Re-search Foundation of Korea (NRF) funded by the Ministry of Education ( 2017-006688 ) and the research of J. Kim, J. Jung and E. Lee was supported by the Samsung Science and Technology Foundation under Project (Number SSTF-BA1301-03 ).
Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2018/3/1
Y1 - 2018/3/1
N2 - 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.
AB - 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.
KW - Finite volume method
KW - MILU preconditioning
KW - Neumann boundary condition
KW - Poisson equation
KW - Purvis–Burkhalter method
UR - http://www.scopus.com/inward/record.url?scp=85037619524&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2017.11.028
DO - 10.1016/j.jcp.2017.11.028
M3 - Article
AN - SCOPUS:85037619524
SN - 0021-9991
VL - 356
SP - 115
EP - 126
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -