An optimal Robin-type domain decomposition method for the Well-posed Maxwell's equations in two dimensions

ABSTRACT

In this paper, I present a Robin-type nonoverlapping domain decomposition (DD) preconditioner for the well-posed Maxwell's equations in two dimensions, which is deduced from the renew equation of the Robin-Robin iteration algorithm. The unknown variables to be solved in this preconditioned algebraic system are the Robin transmission data on the interface. Through choosing a suitable parameter on each subdomain boundary and using the tool of energy estimate, I prove that the condition number of the preconditioned system is optimal. Numerical results which confirm my theory are given in the last.

KEYWORDS:

• Finite element method
• Robin-type domain decomposition method
• condition number estimate
• Maxwell's equations
• optimal convergence rate

2010 Mathematics Subject Classifications:

• 65-Numerical anlaysis
• 65Nxx-Partial differential equations, boundary value problems
• 65N55-Multigrid methods, domain decomposition

Acknowledgments

We thank the editor and the anonymous referees who made many helpful comments and suggestions which led to an improved presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Zhixin Huo http://orcid.org/0000-0001-9656-1934