Geodesic
On incomplete factorization for the fast Fourier transform for the discrete Poisson equation in a~curvilinear boundary domain
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 3, pp. 197-216

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For the discrete Laplasian on the rectangular grid the spectral equivalent preconditioner of the type of the incomplete block-factorization is constructed. The inversion of this preconditioner with accuracy $\varepsilon=O(N^{-1})$ is realized with the help of the fast Fourier transform with $O(N\ln N\ln(1/\varepsilon))$ arithmetical operations. 
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     author = {I. A. Blatov},
     title = {On incomplete factorization for the fast {Fourier} transform for the discrete {Poisson} equation in a~curvilinear boundary domain},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {197--216},
     publisher = {mathdoc},
     volume = {1},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1998_1_3_a0/}
}
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I. A. Blatov. On incomplete factorization for the fast Fourier transform for the discrete Poisson equation in a~curvilinear boundary domain. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 3, pp. 197-216. http://geodesic.mathdoc.fr/item/SJVM_1998_1_3_a0/