Path-following interior point method: Theory and applications for the Stokes flow with a stick-slip boundary condition. (March 2019)

• Record Type: Journal Article
• Authors: Brzobohatý, Tomáš; Jarošová, Marta; Kučera, Radek; Šátek, Václav
• Is Part Of: Advances in engineering software. Volume 129(2019)
• Page Start: 35
• Page End: 43
• Publication Date: 2019-03
• Subjects: Path-following interior point method -- Projected conjugate gradient method -- Preconditioning -- Domain decomposition -- Stokes flow -- Stick-slip boundary condition; 90C51 -- 65F35 -- 76D07; Computer-aided engineering -- Periodicals; Engineering -- Computer programs -- Periodicals; Engineering -- Software -- Periodicals; Periodicals; 620.0028553
• DOI: 10.1016/j.advengsoft.2018.06.010
• Languages: English
• ISSNs: 0965-9978

Abstract

Highlights: The improved path-following interior point method is proposed for minimization of quadratic functions subject to box and equality constraints. Numerical experiments include large-scale problems arising from the TFETI domain decom- position method applied for solving the Stokes flow with the stick-slip boundary condition. The TFETI decomposition leads to the problems with the singular Hessian that is symmetric, positive definite only on the null space of the equality constraint matrix. The inner linear systems are solved by the projected conjugate gradient method preconditioned by oblique projectors. Abstract: A path-following interior point method is proposed for minimization of quadratic functions subject to box and equality constraints. The problems with the singular Hessian that is symmetric, positive definite on the null space of the equality constraint matrix are considered. The inner linear systems are solved by the projected conjugate gradient method preconditioned by oblique projectors. Numerical experiments include large-scale problems arising from the TFETI domain decomposition method applied for solving the Stokes flow with the stick-slip boundary condition.