Superlinear convergence of the conjugate gradient method for elliptic PDEs and systems with unbounded reaction coefficients

Témavezető:	Karátson János
	ELTE TTK, Alkalmazott Analízis és Számításmatematikai Tanszék
email:	karatson66@gmail.com

Projekt leírás

The conjugate gradient method is a widespread way of the iterative solution of discretized elliptic partial differential equations. Operator preconditioning can provide mesh-independent superlinear convergence under certain conditions. Convergence estimation can be given using tools of numerical functional analysis, based on eigenvalues in Sobolev spaces. The goal is to extend existing results to the case of unbounded reaction coefficients in some Lebesgue spaces, and to the case of systems of PDEs.

Előfeltételek

funkcionálanalízis, PDE-k, MATLAB programozás, angol nyelvtudás.

Hivatkozások

O. Axelsson, J. Karátson, Equivalent operator preconditioning for elliptic problems, Numer. Algor. (2009) 50:297–380. J. Vybíral, Widths of embeddings in function spaces, Journal of Complexity, Volume 24, Issue 4, 2008, Pages 545-570.