Numerical and computational efficiency of solvers for two-phase problems

0388267 - ÚGN 2013 RIV GB eng J - Journal Article
Axelsson, Owe - Boyanova, P. - Kronbichler, M. - Neytcheva, M. - Wu, X.
Numerical and computational efficiency of solvers for two-phase problems.
Computers & Mathematics With Applications. Roč. 65, č. 3 (2013), s. 301-314. ISSN 0898-1221. E-ISSN 1873-7668
Institutional support: RVO:68145535
Keywords : Cahn–Hilliard equation * preconditioning * Inexact Newton method * Quasi-Newton method * parallel tests
Subject RIV: BA - General Mathematics
Impact factor: 1.996, year: 2013
http://ac.els-cdn.com/S0898122112004191/1-s2.0-S0898122112004191-main.pdf?_tid=e77dd742-63a2-11e2-9070-00000aab0f02&acdnat=1358756389_e11eaef264d0bac8123c4a00be3f6efa

We consider two-phase flow problems, modelled by the Cahn–Hilliard equation. In this work, the nonlinear fourth-order equation is decomposed into a system of two coupled second-order equations for the concentration and the chemical potential. We analyse solution methods based on an approximate two-by-two block factorization of the Jacobian of the nonlinear discrete problem. We propose a preconditioning technique that reduces the problem of solving the non-symmetric discrete Cahn–Hilliard system to a problem of solving systems with symmetric positive definite matrices where off-the-shelf multilevel and multigrid algorithms are directly applicable. The resulting solution methods exhibit optimal convergence and computational complexity properties and are suitable for parallel implementation. Weillustrate the efficiency of the proposed methods by various numerical experiments, including parallel results for large scale three dimensional problems.
Permanent Link: http://hdl.handle.net/11104/0217100