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Zbl 1017.78008
Toselli, Andrea; Widlund, Olof B.; Wohlmuth, Barbara I.
An iterative substructuring method for Maxwell's equations in two dimensions. (English)
[J] Math. Comput. 70, No.235, 935-949 (2001). ISSN 0025-5718; ISSN 1088-6842/e

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 2000:: *78M10 Finite element methods (optics)
65N30 Finite numerical methods (BVP of PDE)
65F10 Iterative methods for linear systems
65N55 Multigrid methods; domain decomposition (BVP of PDE)

Keywords: Maxwell's equations; Nédélec finite elements; domain decomposition; iterative substructuring methods

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