KIAM Main page Web Library  •  Publication Searh  Русский 

KIAM Preprint № 69, Moscow, 2013
Authors: Belov A.A., Kalitkin N. N.
Evolutional factorization and superfast relaxation count
In finite-difference solution of multi-dimensional elliptic equations the systems of linear algebraic equations with strongly rarefied matrices of enormous sizes appear. They are solved by iteratonal methods with slow convergence. For rectangular nets, variable coefficients and net steps much more fast method is proposed. In case of finite difference schemes for parabolic equations an efficient method, called evolutional factorization, is built. For elliptic equations relaxation count for evolutionally factorized schemes is proposed. This iterational method has logarithmic convergence. A set of steps, that practically optimizes the method's convergence, and Richardson-like procedure of steps regulation are proposed. The procedure delivers an a posteriori asymptotically precise estimation for the iterational process error. Such estimations were not known before.
evolutional factorization, logarithmic relaxation count
Publication language: russian,  pages: 36
Research direction:
Mathematical problems and theory of numerical methods
Russian source text:
List of publications citation:
Export link to publication in format:   RIS    BibTeX
View statistics (updated once a day)
over the last 30 days — 2 (+0), total hit from 01.09.2019 — 184
About authors:
  • Belov A.A.,  ,  Физический факультет МГУ им. М.В. Ломоносова
  • Kalitkin Nikolaj Nikolaevich, RAS