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

Yesom Park, Jeongho Kim, Jinwook Jung, Euntaek Lee, Chohong Min

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2 Scopus citations


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.

Original languageEnglish
Pages (from-to)115-126
Number of pages12
JournalJournal of Computational Physics
StatePublished - 1 Mar 2018

Bibliographical note

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.


  • Finite volume method
  • MILU preconditioning
  • Neumann boundary condition
  • Poisson equation
  • Purvis–Burkhalter method


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