Iterative substructuring preconditioners for mortar element methods in two dimensions. (English) Zbl 0931.65110
The paper is devoted to the construction of effective model grid operators (preconditioners) for classes of linear grid systems with positive operators. The suggested constructions lead to estimates of the spectral condition number like \(O(\log^2N)\); the model operators are almost spectrally equivalent to the original ones.
The grid systems under consideration correspond to special nonconforming methods for the Dirichlet problem for Poisson’s equation in the two-dimensional case. The methods are effective means to combine different approximations in the subdomains, but they lead to good approximations only in energy spaces for the subdomains but not in the whole original domain.
The grid systems under consideration correspond to special nonconforming methods for the Dirichlet problem for Poisson’s equation in the two-dimensional case. The methods are effective means to combine different approximations in the subdomains, but they lead to good approximations only in energy spaces for the subdomains but not in the whole original domain.
Reviewer: E.D’yakonov (Moskva)
MSC:
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
65F30 | Other matrix algorithms (MSC2010) |
65F10 | Iterative numerical methods for linear systems |
65F35 | Numerical computation of matrix norms, conditioning, scaling |
65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |