Rossi, Tuomo Fictitious domain methods with separable preconditioners. (English) Zbl 0835.65056 Bericht. Universität Jyväskylä. Mathematisches Institut. 69. Jyväskylä: Univ., Dept. of Math. (ISBN 951-34-0631-8). ii, 137 p. (1995). Summary: Efficient direct and iterative solution methods for solving linear systems which appear from the finite difference or the piecewise linear finite element discretization of a class of elliptic partial differential equations are considered.A fast direct method for solving linear systems with separable block band matrices is introduced, the standard and the approximate partial solution algorithms are discussed, and a new fictitious domain method which can be used in solving diffusion-type equations with mixed boundary conditions is described. Complexity estimates are given for all the methods proposed, and the results of the numerical experiments, which demonstrate their efficiency, are presented. Cited in 5 Documents MSC: 65F10 Iterative numerical methods for linear systems 65F05 Direct numerical methods for linear systems and matrix inversion 65Y20 Complexity and performance of numerical algorithms 65F35 Numerical computation of matrix norms, conditioning, scaling 65N06 Finite difference methods for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations Keywords:iterative method; elliptic equations; complexity estimates; finite difference; finite element; fast direct method; linear systems; fictitious domain method; diffusion-type equations; numerical experiments PDFBibTeX XMLCite \textit{T. Rossi}, Fictitious domain methods with separable preconditioners. Jyväskylä: Univ., Dept. of Math. (1995; Zbl 0835.65056)