A non-overlapping domain decomposition method for Maxwell’s equations in three dimensions

In this paper we propose a substructuring preconditioner for solving three-dimensional elliptic equations with strongly discontinuous coefficients. The new preconditioner can be viewed as a variant of the classical substructuring preconditioner introduced in Bramble, Pasiack and Schatz (1989), with simpler coarse solvers. We will show that, although the preconditioned system may not have a good condition-number bound, the convergence rate of PCG method with this substructuring preconditioner is nearly optimal and also robust with possible large jumps of the coefficient in the elliptic equation. Key words: domain decomposition, coarse subspace, substructuring preconditioner, inexact solver, condition number Mathematics Subject Classification(1991): 65F10, 65N30