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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.

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
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