## An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations

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- by Ana Alonso and Alberto Valli PDF
- Math. Comp.
**68**(1999), 607-631 Request permission

## Abstract:

The time-harmonic Maxwell equations are considered in the low-frequency case. A finite element domain decomposition approach is proposed for the numerical approximation of the exact solution. This leads to an iteration-by-subdomain procedure, which is proven to converge. The rate of convergence turns out to be independent of the mesh size, showing that the preconditioner implicitly defined by the iterative procedure is optimal. For obtaining this convergence result it has been necessary to prove a regularity theorem for Dirichlet and Neumann harmonic fields.## References

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## Additional Information

**Ana Alonso**- Affiliation: Dipartimento di Matematica, Università di Trento, 38050 Povo (Trento), Italy
- Email: alonso@science.unitn.it
**Alberto Valli**- Affiliation: Dipartimento di Matematica, Università di Trento, 38050 Povo (Trento), Italy
- Email: valli@science.unitn.it
- Received by editor(s): December 2, 1996
- Received by editor(s) in revised form: July 30, 1997
- Additional Notes: Partially supported by H.C.M. contract CHRX 0930407
- © Copyright 1999 American Mathematical Society
- Journal: Math. Comp.
**68**(1999), 607-631 - MSC (1991): Primary 65N55, 65N30; Secondary 35Q60
- DOI: https://doi.org/10.1090/S0025-5718-99-01013-3
- MathSciNet review: 1609607