Advances in Computational Mathematics

, Volume 45, Issue 3, pp 1129–1161 | Cite as

A substructuring preconditioner with vertex-related interface solvers for elliptic-type equations in three dimensions

  • Qiya HuEmail author
  • Shaoliang HuEmail author


In this paper, we propose a variant of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the proposed preconditioner, we use the simplest coarse solver associated with the finite element space induced by the coarse partition and construct inexact interface solvers based on overlapping domain decomposition with small overlaps. This new preconditioner has an important merit: its construction and efficiency do not depend on the concrete form of the considered elliptic-type equations. We apply the proposed preconditioner to solve the linear elasticity problems and Maxwell’s equations in three dimensions. Numerical results show that the convergence rate of PCG method with the preconditioner is nearly optimal, and also robust with respect to the (possibly large) jumps of the coefficients in the considered equations.


Domain decomposition Substructuring preconditioner Linear elasticity problems Maxwell’s equations PCG iteration Convergence rate 

Mathematics Subject Classification (2010)

65N30 65N55 


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Authors and Affiliations

  1. 1.LSEC, ICMSEC, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina

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