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An iterative substructuring method for Maxwell’s equations in two dimensions. (English) Zbl 1017.78008
Summary: Iterative substructuring methods, also known as Schur complement methods, form an important family of domain decomposition algorithms. They are preconditioned conjugate gradient methods where solvers on local subregions and a solver on a coarse mesh are used to construct the preconditioner. For conforming finite element approximations of $H^1$, it is known that the number of conjugate gradient steps required to reduce the residual norm by a fixed factor is independent of the number of substructures, and that it grows only as the logarithm of the dimension of the local problem associated with an individual substructure. In this paper, the same result is established for similar iterative methods for low-order Nédélec finite elements, which approximate $H(\text{curl};\Omega)$ in two dimensions. Results of numerical experiments are also provided.

##### MSC:
 78M10 Finite element methods (optics) 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE) 65F10 Iterative methods for linear systems 65N55 Multigrid methods; domain decomposition (BVP of PDE)
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