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Balancing domain decomposition. (English) Zbl 0796.65126
The author constructs a domain decomposition preconditioner for the iterative solution of finite element discretizations. The aim is to improve existing methods by e.g. Y.-H. De Roeck and P. LeTallec [Fourth international symposium on domain decomposition methods for partial differential equations, Proc. Symp., Moscow/Russ. 1990, 112- 128 (1991; Zbl 0770.65082)] in particular for problems with discontinuous coefficients. The problem of appearance of singularities is dealt with by using a pseudoinverse of Moore-Penrose type. A model problem for the Laplacian with partly Dirichlet and partly Neumann boundary conditions is studied.
It would have been interesting to see this numerical problem connected to e.g. the analytic theory for problems with mixed boundary values as given by G. I. Ehskin [Boundary value problems for elliptic pseudodifferential equations (1981; Zbl 0458.35002)].

MSC:
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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References:
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