Constructive Sobolev gradient preconditioning for semilinear elliptic systems
Date
2004-05-21
Authors
Karatson, Janos
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We present a Sobolev gradient type preconditioning for iterative methods used in solving second order semilinear elliptic systems; the n-tuple of independent Laplacians acts as a preconditioning operator in Sobolev spaces. The theoretical iteration is done at the continuous level, providing a linearization approach that reduces the original problem to a system of linear Poisson equations. The method obtained preserves linear convergence when a polynomial growth of the lower order reaction type terms is involved. For the proof of linear convergence for systems with mixed boundary conditions, we use suitable energy spaces. We use Sobolev embedding estimates in the construction of the exact algorithm. The numerical implementation has focus on a direct and elementary realization, for which a detailed discussion and some examples are given.
Description
Keywords
Sobolev gradient, Semilinear elliptic systems, Numerical solution, Preconditioning
Citation
Karatson, J. (2004). Constructive Sobolev gradient preconditioning for semilinear elliptic systems. <i>Electronic Journal of Differential Equations, 2004</i>(75), pp. 1-26.
Rights
Attribution 4.0 International