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Iterative methods of decomposition into substructures. The general elliptic case. (Russian) Zbl 0674.65077

The author discusses domain decomposition methods for the problem \(a(u,v)=f(v)\) \(\forall v\in H^ 1_ 0(\Omega)\) where a is a symmetric bilinear form and f linear. The connection between the substructures is realized by the preconditioned method of conjugate gradients. Because of the lack of global information, this iterative method can decrease the efficiency of the domain decomposition. Making use of some numerical extension theorems and of some ideas from the multigrid method, the author shows how this drawback can be removed.
Reviewer: E.Schechter

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35J25 Boundary value problems for second-order elliptic equations
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