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On the solution of the Dirichlet problem for linear elliptic operators by a distributed Lagrande multiplier method. (English. Abridged French version) Zbl 1005.65127
Summary: In this note we discuss the construction of efficient preconditioners for the solution of finite-dimensional saddle-point problems. A particular attention is given to those linear systems associated to the solution of elliptic problems by methods combining fictitious domain and distributed Lagrange multiplier techniques to force boundary conditions. It is shown that with the approach discussed in this note we can construct preconditioners spectrally equivalent to the original saddle-point matrix and leading to algorithms of optimal arithmetic complexity.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F35 Numerical computation of matrix norms, conditioning, scaling
65F10 Iterative numerical methods for linear systems
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65Y20 Complexity and performance of numerical algorithms
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