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Complexity of an algorithm for solving saddle-point systems with singular blocks arising in wavelet-Galerkin discretizations. (English) Zbl 1099.65150
Summary: The paper deals with fast solving of large saddle-point systems arising in wavelet-Galerkin discretizations of separable elliptic PDEs. The periodized orthonormal compactly supported wavelets of the tensor product type together with the fictitious domain method are used. A special structure of matrices makes it possible to utilize the fast Fourier transform that determines the complexity of the algorithm. Numerical experiments confirm theoretical results.

MSC:
65T60 Numerical methods for wavelets
65F10 Iterative numerical methods for linear systems
65T50 Numerical methods for discrete and fast Fourier transforms
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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