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IMA Journal of Numerical Analysis 2004 24(4):643-669; doi:10.1093/imanum/24.4.643
© 2004 by Institute of Mathematics and its Applications
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Preconditioning Poincaré–Steklov operators arising from domain decompositions with mortar multipliers

Qiya Hu1

1 Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, People's Republic of China

In this paper, we are concerned with the non-overlapping domain decomposition method with non-matching grids for three-dimensional elliptic equations. For this method, the interface variable is chosen as the mortar multiplier. We first develop a class of inexact solvers for the interface Poincaré–Steklov operator associated with such a domain decomposition. Then we use the inexact solver to construct a new preconditioner for the interface problem arising from the Finite Element Tearing and Interconnecting method. It will be shown that the condition number of the preconditioned system grows only as the logarithm of the dimension of the local problem associated with an individual substructure, and is independent of possible jumps of the coefficient in the elliptic equation.

Key Words: domain decomposition; non-matching grids; mortar multiplier; Poincaré–Steklov operator; inexact solver; preconditioner; condition number

Received 21 January 2003. Revised 1 November 2003.


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